The dignity and object of this science

All men naturally desire to know.

A sign of this is the delight we take in the senses; for apart from their usefulness they are loved for themselves, and most of all the sense that operates through the eyes. For not only that we may act, but even when we intend to do nothing, we prefer sight (as we may say) to all the other senses. The reason is that of all the senses this most enables us to know and reveals many differences between things.

Animals by nature, then, are born with sensory power.

Now in some animals memory arises from the senses, but in others it does not; for this reason the former are prudent and more capable of being taught than those that are unable to remember. Those that cannot hear sounds are prudent but unable to learn, as the bee and any other similar type of animal there may be. But any that have this sense together with memory are able to learn.

Thus other animals live by imagination and memory and share little in experience, whereas the human race lives by art and reasoning.

Now in men experience comes from memory, for many memories of the same thing produce the capacity of a single experience. And experience seems to be somewhat like science and art.

But in men science and art come from experience, for experience causes art and inexperience causes luck, as Polus rightly states. Art comes into being when from many conceptions acquired by experience a single universal judgment is formed about similar things.

For to judge that this [medicine] has been beneficial to Callias and Socrates and many other individuals who suffer from this disease is a matter of experience; but to judge that it has been beneficial to all individuals of a particular kind (such as the phlegmatic, the bilious, or the feverish) who suffer from this disease is a matter of art.

In practical matters, then, experience seems to differ in no way from art. But we see that men of experience are more proficient than those who have theory without experience. The reason is that experience is a knowledge of singulars, whereas art is a knowledge of universals. But all actions and processes of generation are concerned with singulars. For the physician heals man only incidentally, but he heals Socrates, or Callias, or some individual that can be named, to whom the nature of man happens to belong. Therefore, if anyone has theory without experience, and knows the universal but not the singulars contained in this, he will very often make mistakes. For it is only the individual man who can be cured.

Yet we think that to know and to refute objections belong to art rather than to experience, and we are of the opinion that those who are proficient in art are wiser than men of experience, as it is more to know if one’s wisdom pursues all things.

Now this is because the former know the cause whereas the latter do not. For those who have experience know that something is so but do not know why, whereas the others know the why and the cause.

For this reason, too, we think that the architects in each art are more honorable, and that they know more and are wiser than the manual laborers, because they understand the causes of the things done.

Indeed, we think that the latter resemble certain inanimate things, which act but do not know what they do, like a fire which burns. Therefore, inanimate things perform each of their actions as a result of a certain natural disposition, whereas manual laborers perform theirs through habit, implying that some men are wiser not insofar as they are practical, but insofar as they themselves have the theories and know the causes.

In general, a sign of scientific knowledge is the ability to teach, and for this reason we think that art rather than experience is science. For those who have an art are able to teach, whereas the others are not.

Furthermore, we do not hold that any one of the senses is wisdom, since the cognition of singular things belongs especially to the senses. However, these do not tell us why a thing is so; for example, they do not tell us why fire is hot but only that it is so.

It is only fitting, then, that the one who discovered any art whatsoever that went beyond the common perceptions of men should be admired by men, not only because of some usefulness of his discoveries, but as one who is wise and as distinguishing from others. And as more of the arts were discovered, some to supply the necessities of life, and others to introduce us [to the sciences], those who discovered the latter were always considered to be wiser than those who discovered the former, because their sciences were not for the sake of utility.

Hence, after all such arts had already been developed, those sciences were discovered which are pursued for the sake of neither pleasure nor necessity. This happened first in those places where men had leisure. Hence the mathematical arts originated in Egypt, for there the priestly class was permitted leisure.

(The difference between art and science and similar mental states has been stated in the Nicomachean Ethics.)

Now the reason for undertaking this investigation is that all men think that the science that is called wisdom deals with the primary causes and principles of things. Hence, as we have said before (981a24–981a28), the man of experience is considered to be wiser than one who has any of the senses; the artist wiser than the man of experience; the architect wiser than the manual laborer; and speculative knowledge wiser than practical knowledge. It is quite evident, then, that wisdom is a science of certain causes and principles.

Three reasons people naturally desire to know

1. Aristotle first sets down an introduction to this science, in which he treats of two things.

First [2], he points out with what this science is concerned.

Second [53], he explains what kind of science it is, at that this is not a practical science (982b11).

In regard to the first he does two things.

First, he shows that the office of this science, which is called wisdom, is to consider the causes of things.

Second [36], he explains with what causes or kinds of causes it is concerned, at but since we are in search (982a4).

In regard to the first, he prefaces certain preliminary considerations from which he argues in support of his thesis.

Second [35], he draws a conclusion from these considerations, at now the reason for undertaking (981b27).

In regard to the first he does two things.

First, he makes clear the dignity of scientific knowledge in general.

Second [9], he explains the hierarchy in knowing, at animals by nature (980a27).

Now he establishes the dignity of scientific knowledge from the fact that it is naturally desired as an end by all men. Hence, in regard to this he does two things.

First, he states his intention.

Second [2], he proves it, at a sign of this (980a21).

Accordingly, he first says that the desire to know belongs by nature to all men.

2. Three reasons can be given for this. The first is that each thing naturally desires its own perfection. Hence matter is also said to desire form as any imperfect thing desires its perfection. Therefore, since the intellect, by which man is what he is, considered in itself is all things potentially, and becomes them actually only through knowledge, because the intellect is none of the things that exist before it understands them, as is stated in On the Soul 3, so each man naturally desires knowledge just as matter desires form.

3. The second reason is that each thing has a natural inclination to perform its proper operation, as something hot is naturally inclined to heat, and something heavy to be moved downwards. Now the proper operation of man as man is to understand, for by reason of this he differs from all other things. Hence the desire of man is naturally inclined to understand and therefore to possess scientific knowledge.

4. The third reason is that it is desirable for each thing to be united to its source, since it is in this that the perfection of each thing consists. This is also the reason why circular motion is the most perfect motion, as is proved in Physics 8, because its terminus is united to its starting point. Now it is only by means of his intellect that man is united to the separate substances, which are the source of the human intellect and to which the human intellect is related as something imperfect to something perfect. It is for this reason, too, that the ultimate happiness of man consists in this union. Therefore, man naturally desires to know.

The fact that some men do not devote any study to this science does not disprove this thesis. For those who desire some end are often prevented from pursuing it for some reason or other, either because of the difficulty of attaining it or because of other occupations. And in this way, too, even though all men desire knowledge, still not all devote themselves to the pursuit of it because they are held back by other things such as pleasures or the needs of the present life—or they may even avoid the effort that learning demands because they are lazy.

Now Aristotle makes this statement in order to show that it is not pointless to search for a science that is not useful for anything else (such as this science), since a natural desire cannot exist in vain.

5. Then he establishes his thesis by means of an example. Since our senses serve us in two respects—in knowing things and in meeting the needs of life—we love them for themselves inasmuch as they enable us to know and also assist us to live. This is evident from the fact that all men take the greatest delight in the sense that is most knowing, the sense of sight. We value it not merely so we can do things, but even when we are not required to act at all. This is because this sense of sight is the most knowing of all our senses and makes us aware of many differences between things.

6. In this part, it is clear that he gives two reasons why sight is superior to the other senses in knowing.

The first is that it knows in a more perfect way, and this belongs to it because it is the most spiritual of all the senses. For the more immaterial a power is, the more perfectly it knows. And evidently sight is a more immaterial sense if we consider the modification produced in it by its object. All other sensible objects change both the organ and medium of a sense by a material modification: for example, the object of touch by heating and cooling, the object of taste by affecting the organ of taste with some flavor through the medium of saliva, the object of hearing by means of motion in the body, and the object of smell by means of the evaporation of vaporous elements. But the object of sight changes the organ and medium of sight only by a spiritual modification. Neither the pupil of the eye nor the air becomes colored, but they only receive the form of color in a spiritual mode of being. Therefore, because actual sensation consists in the actual modification of a sense by its object, it is evident that that sense which is changed in a more immaterial and spiritual way is more spiritual in its operation. Hence sight judges about sensible objects in a more certain and perfect way than the other senses do.

7. The other reason which he gives for the superiority of sight is that it gives us more information about things. This is attributable to the nature of its object, for touch and taste, and likewise smell and hearing, perceive those accidents by which lower bodies are distinguished from higher ones. But sight perceives those accidents that lower bodies have in common with higher ones. For a thing is actually visible by means of light, which is common both to lower and higher bodies, as is said in On the Soul 2. Hence the celestial bodies are perceptible only by means of sight.

8. There is also another reason. Sight informs us of many differences between things, for we seem to know sensible things best by means of sight and touch, but especially by means of sight. The reason for this can be drawn from the fact that the other three senses perceive those accidents that in a way flow from a sensible body and do not remain in it. Thus sound comes from a sensible body inasmuch as it flows away from it and does not remain in it. The same thing is true of the evaporation of volatile elements, with which and by which odor is diffused. But sight and touch perceive those accidents that remain in sensible bodies, such as color, warmth, and coldness. Hence the judgment of sight and touch is extended to things themselves, whereas the judgment of hearing and smell is extended to those accidents that flow from things and not to things themselves. It is for this reason that figure and size and the like, by which a sensible being itself is disposed, are perceived more by sight and touch than by the other senses. And they are perceived more by sight than by touch, both because sight knows more efficaciously, as has been pointed out [6], and also because quantity and those [accidents] which naturally follow from it (which are seen to be the common sensibles) are more closely related to the object of sight than to that of touch. This is clear from the fact that the object of sight belongs in some degree to every body having some quantity, whereas the object of touch does not.

9. Animals by nature, then (980a27). Here he considers the hierarchy in knowledge.

He first does this [9] with respect to brute animals;

and then [14], with respect to men, at thus other animals (980b25).

With respect to brute animals he mentions first what all animals have in common;

second [10], that by which they differ and surpass one another, at now in some animals (980a28).

Now all animals are alike in the respect that they possess by nature the power of sensation. For an animal is an animal by reason of the fact that it has a sentient soul, which is the nature of an animal in the sense in which the distinctive form of each thing is its nature. But even though all animals are naturally endowed with sensory power, not all animals have all the senses, but only perfect animals. All have the sense of touch, for this sense in a way is the basis of all the other senses. However, not all have the sense of sight, because this sense knows in a more perfect way than all the other senses. But touch is more necessary, for it perceives the elements of which an animal is composed (the hot, cold, moist and dry). Hence, just as sight knows in a more perfect way than the other senses, in a similar way touch is more necessary inasmuch as it is the first to exist in the process of generation. For those things that are more perfect according to this process come later in the development of the individual, which is moved from a state of imperfection to one of perfection.

10. Now in some animals (980a28). Here he indicates the different kinds and three levels of knowing found among brute animals. For there are certain animals that have sensation, although they do not have memory, which comes from sensation. For memory accompanies imagination, which is a movement caused by the senses in their act of sensing, as we find in On the Soul 2. But in some animals imagination does not accompany sensation, and therefore memory cannot exist in them. This is found verified in imperfect animals, which are incapable of local motion, such as shellfish. Since sensory cognition enables animals to make provision for the necessities of life and to perform their characteristic operations, those animals that move toward something at a distance by means of local motion must have memory. If the anticipated goal by which they are induced to move did not remain in them through memory, they could not continue to move toward the intended goal which they pursue. But in the case of immobile animals, the reception of a present sensible quality is sufficient for them to perform their characteristic operations, since they do not move toward anything at a distance. Hence these animals have an indefinite movement as a result of vague imagination alone, as is said in On the Soul 3.

11. Again, from the fact that some animals have memory and some do not, it follows that some are prudent and some not. For, since prudence makes provision for the future from memory of the past (hence Cicero makes memory, understanding, and foresight parts of prudence in Rhetoric 2), prudence cannot be had by those animals that lack memory. Now those animals that have memory can have some prudence, although prudence has one meaning in the case of brute animals and another in the case of man. Men are prudent inasmuch as they deliberate rationally about what they ought to do. Hence Ethics 6 says that prudence is a rationally regulated plan of things to be done. But the judgment about things to be done that is not a result of any rational deliberation, but of some natural instinct, is called prudence in other animals. Hence in other animals prudence is a natural estimate about the pursuit of what is fitting and the avoidance of what is harmful, as a lamb follows its mother and runs away from a wolf.

12. But among those animals that have memory, some have hearing and some do not. And all those that cannot hear (as the bee or any other such animal) are still incapable of being taught even though they have prudence; that is, they cannot be habituated to the doing or avoiding of something through someone else’s instruction, because such instruction is received chiefly by means of hearing. Hence in On Sense and Sense Perception it is stated that hearing is the sense by which we receive instruction. Furthermore, the statement that bees do not have hearing is not opposed in any way to the observation that they are frightened by certain sounds. For just as a very loud sound kills an animal and splits wood, as is evident in the case of thunder, not because of the sound but because of the violent motion of the air in which the sound is present, in a similar fashion those animals that lack hearing can be frightened by the sounding air even though they have no perception of sound. However, those animals that have both memory and hearing can be both prudent and teachable.

13. It is evident, then, that there are three levels of knowing in animals.

The first level is that had by animals that have neither hearing nor memory, which are therefore neither capable of being taught nor of being prudent.

The second level is that of animals that have memory but are unable to hear, which are therefore prudent but incapable of being taught.

The third level is that of animals that have both of these faculties, and which are therefore prudent and capable of being taught.

Moreover, there cannot be a fourth level, so that there would be an animal that had hearing but lacked memory. For those senses that perceive their sensible objects by means of an external medium—and hearing is one of these—are found only in animals that have locomotion and which cannot do without memory, as has been pointed out [10].

14. Thus other animals (980b25). Here he explains the levels of human knowing. In regard to this he does two things.

First [14], he explains how human knowing surpasses the knowing of the abovementioned animals.

Second [17], he shows how human knowing is divided into different levels, at now in men (980b28).

Accordingly, in the first part (980b25), he says that the life of animals is ruled by imagination and memory: by imagination in the case of imperfect animals, and by memory in the case of perfect animals. For even though the latter also have imagination, still each thing is said to be ruled by that [power] which holds the highest place within it. Now in this discussion life does not mean the being of a living thing, as it is understood in On the Soul 2, when he says that for living things to live is to be; for the life of an animal in this sense is not a result of memory or imagination but is prior to both of these. But “life” is taken to mean “vital activity,” just as we are also accustomed to speak of association as the life of men. But by the fact that he establishes the truth about the cognition of animals with reference to the management of life, we are given to understand that knowing belongs to these animals not for the sake of knowing, but because of the need for action.

15. Now, as is stated below [18], in men the next thing above memory is experience, which some animals have only to a small degree. For an experience arises from the association of many singular [intentions] received in memory. And this kind of association is proper to man, and pertains to the cogitative power (also called particular reason), which associates particular intentions just as universal reason associates universal ones. Now since animals are accustomed to pursue or avoid certain things as a result of many sensations and memory, they seem to share something of experience, even though it be slight. But above experience, which belongs to particular reason, men have as their chief power a universal reason by means of which they live.

16. And just as experience is related to particular reason [in men], and customary activity to memory in animals, in a similar way art is related to universal reason. Therefore, just as the life of animals is ruled in a perfect way by memory together with activity that has become habitual through training, or in any other way whatsoever, in a similar way man is ruled perfectly by reason perfected by art. Some men, however, are ruled by reason without art; but this rule is imperfect.

17. Now in men (980b28). Here he explains the different levels of human knowing. And in regard to this he does two things.

First [17], he compares art with experience;

second [31], he compares speculative art with practical art, at it is only fitting (981b13).

He treats the first point in two ways.

First, he explains how art and experience originate.

Second [20], he explains how one is superior to the other, at in practical matters (981a12).

In regard to the first, he does two things.

First, he explains how each of the above originates.

Second [19], he makes this clear by means of an example, at for to judge (981a7).

In regard to the first, he does two things.

First, he describes how experience originates;

and second [18], how art originates, at but in men science (981a2).

He says first, then, that in men experience is caused by memory. This is the way in which it is caused: from several memories of a single thing a man acquires experience about some matter, and by means of this experience he is able to act easily and correctly. Therefore, because experience provides us with the ability to act easily and correctly, it seems to be almost the same as science and art. For they are alike inasmuch as in either case from many instances a single view of a thing is obtained. But they differ inasmuch as universals are grasped by art and singular things by experience, as is stated later [18].

18. But in men science and art (981a2). Here he describes the way in which art arises. He says that in men science and art come from experience, and he proves this on the authority of Polus, who says that experience causes art and inexperience causes luck. For when an inexperienced person acts correctly, this happens by chance. Furthermore, the way in which art arises from experience is the same as the way spoken of above in which experience arises from memory. Just as one experiential cognition comes from many memories of a thing, so does one universal judgment about all similar things come from the apprehension of many experiences. Hence art has this more than does experience, because experience is concerned only with singulars while art is concerned with universals.

19. Next, he makes this clear by means of examples, at for to judge (981a7). When a man has learned that this medicine has been beneficial to Socrates, and to Plato, and to many other individuals who were suffering from some particular disease (whatever it may be), this is a matter of experience. But when a man learns that this particular treatment is beneficial to men who have some particular kind of disease and some particular kind of physical constitution, as it has benefited the feverish, the phlegmatic, and the bilious, it is now a matter of art.

20. In practical matters (981a12). He compares art to experience from the viewpoint of preeminence; and in regard to this he does two things.

First, he compares them from the viewpoint of action;

second [23], from the viewpoint of knowledge, at yet we think (981a24).

He says, then, that in practical matters experience seems to differ in no way from art: when it comes to acting, the difference between experience and art (which is a difference between the universal and the singular) disappears, because art operates with reference to singulars just as experience does. Therefore, the aforesaid difference pertains only to the way in which they come to know. But even though art and experience do not differ in the way in which they act, because both act on singular things, nevertheless they differ in the effectiveness of their action. For men of experience act more effectively than those who have the universal knowledge of an art but lack experience.

21. This is because actions have to do with singular things, and all processes of generation belong to singular things. For universals are neither generated nor moved except accidentally, inasmuch as this belongs to singular things. For man is generated when this man is generated. Hence a physician heals man only accidentally, but properly he heals Plato or Socrates, or some man that can be individually named, to whom the nature of man belongs—or rather to whom it is accidental inasmuch as he is the one healed. For even though the nature of man belongs to Socrates per se, still it belongs only accidentally to the one healed or cured. The proposition “Socrates is a man” is an per se one, because, if Socrates were defined, man would be given in his definition, as will be said below in book 4. But the proposition “What is healed or cured is man” is an accidental one.

22. Hence, since art has to do with universals and experience with singulars, if anyone has the theoretical knowledge of an art but lacks experience, he will be perfect insofar as he knows the universal, but since he does not know the singular (since he lacks experience), he will very often make mistakes in healing. For healing belongs to the realm of the singular rather than to that of the universal, because it belongs to the former per se and to the latter accidentally.

23. Yet we think (981a24). Here he compares art with experience from the viewpoint of knowing. In regard to this he does two things.

First, he states how art is superior to experience;

and second [24], he proves this at now this is because (981a28).

He claims that art and science are superior to experience in three respects.

First, they are superior from the viewpoint of scientific knowledge, which we think is attained by art rather than by experience.

Second, they are superior from the viewpoint of meeting objections, which occurs in disputes. For in a dispute the one who has an art is able to meet the objections raised against that art, but one who has only experience cannot do this.

Third, they are superior from this point of view. Those who have an art come nearer to the goal of wisdom than men of experience, as it is, that is, it happens to be, more to know if one’s wisdom pursues all things, insofar as it pursues universals. For one who has an art is judged wiser than one who has experience, because he considers universals.

Or in another version: as it is more according to wisdom to know as one pursuing all things, that is, universals.

Another reading has: as more conformable to knowing, since wisdom pursues all things, as if to say: as more dependent upon knowing than upon doing, since wisdom pursues all things, that is, it seeks to reach each single thing, so that those are rather called wise who are more knowing, not those who are more men of action.

Hence another reading expresses this meaning more clearly, saying: as all pursue wisdom more with respect to knowing.

24. Now this is because (981a28). Then he proves the superiority of art and science mentioned above, and he does this by means of three arguments.

The first runs thus. Those who know the cause and reason why a thing is so are more knowing and wiser than those who merely know that it is so but do not know why. Now men of experience know that something is so but do not know the reason, whereas men who have an art not only know that something is so but also know its cause and reason. Hence those who have an art are wiser and more knowing than those who have experience.

25. For this reason, too (981a30). Here he proves the first aspect of superiority, and this runs as follows. Those who know the cause and reason why a thing is so are compared to those who merely know that it is as the architectonic arts are to the arts of manual laborers. But the architectonic arts are nobler. In a similar way, then, those who know the causes and reasons of things are more knowing than those who merely know that things are so.

26. The first part of this proof becomes clear from the fact that architects know the causes of the things that are done. In order to understand this we must note that architect means chief artist, from ἄρχος meaning chief, and τέχνη meaning art. Now that art is said to be a chief art which performs a more important operation. Indeed, the operations of artists are distinguished in this way, for some operations are directed to disposing the material of the artifact. Carpenters, for example, by cutting and planing the wood, dispose matter for the form of a ship. Another operation is directed to introducing this form into the matter—for example, when someone builds a ship out of wood that has been disposed and prepared. A third operation is directed to the use of the finished product, and this is the highest operation. But the first operation is the lowest because it is directed to the second and the second to the third. Hence the shipbuilder is a superior artist compared with the one who prepares the wood; the navigator, who uses the completed ship, is a superior artist compared with the shipbuilder.

27. Further, since matter exists for the sake of form, and ought to be such as to befit the form, the shipbuilder knows the reason why the wood should be shaped in some particular way; but those who prepare the wood do not know this. And in a similar way, since the completed ship exists in order to be used, the one who uses the ship knows why it should have some particular form; for the form should be one that befits its use. Thus it is evident that the reason for the operations that dispose the matter is taken from the design of the product in the artist’s mind, and the reason for the operations that produce the form of the artifact is taken from its use.

28. It is evident, then, that the architects know the causes of the things that are done. In fact, we judge and speak about the others—the manual laborers—as we do about certain inanimate things. This is not because they do not perform artful operations, but because they do things without knowing the cause; they know that something is to be done but not why it is, just as fire burns without knowing why. Hence there is a likeness between inanimate things and manual laborers from this point of view: just as inanimate things act without knowing the causes, inasmuch as they are directed to their proper end by a superior intellect, so also do manual laborers. But they differ in this respect: inanimate things perform each of their operations as a result of their nature, whereas manual laborers perform theirs through habit. And while habit is practically the same as nature inasmuch as it is inclined to one definite effect, still habit differs from nature inasmuch as it is open to opposites by reason of human knowledge. For we do not habituate natural bodies, as is stated in Ethics 2. Indeed, it is impossible to cause habits in things that lack knowledge. Now the statements that have been made—as is evident from the statements themselves—must be interpreted as meaning that some men are wiser not insofar as they are practical men of action, as befits men of experience. Rather, they are wiser insofar as they have a plan for things to be done and know their causes, which are the basis of such a plan, as befits architects.

29. In general, a sign of scientific knowledge (981b7). Here he gives the second argument, which is as follows: a sign of knowledge is the ability to teach, and this is so because each thing is perfect in its activity when it can produce another thing similar to itself, as is said in Meteorology 4. Therefore, just as the possession of heat is indicated by the fact that a thing can heat something else, the possession of knowledge is indicated by the fact that one can teach (that is, cause knowledge in another).

But men who have an art can teach, for since they know causes they can demonstrate from these; and demonstration is a syllogism that produces knowledge, as is said in Posterior Analytics 1. But men who have experience alone cannot teach; since they do not know the causes, they cannot cause knowledge in someone else. And if they do teach others the things that they know by experience, these things are not learned after the manner of scientific knowledge, but after that of opinion or belief. Hence, it is clear that men who have an art are wiser and more knowing than those who have experience.

30. Furthermore, we do not hold (981b10). Here he gives the third argument, which is as follows. Knowing singular things is proper to the senses rather than to any other type of knowing, since our entire knowledge of singular things originates with the senses. Yet we do not hold that any one (that is, any one of the senses) is wisdom, because even though each sense knows that a thing is so, it does not know why it is so. Touch judges that fire is hot but does not know why it is hot. Therefore, men of experience, who have a knowledge of singular things but do not know their causes, cannot be called wise men.

31. It is only fitting (981b13). Here he compares practical art with speculative art; and in regard to this he does two things.

First [31], he shows that a speculative art is wisdom to a greater degree than a practical art.

Second [34], he answers an objection, at the difference (981b25).

He proves his first statement by this argument. In any of the sciences or arts we find that men with scientific knowledge are more admired and are held in higher esteem than all other men, because their knowledge is held to be nobler and more worthy of the name of wisdom. Now the discoverer of any art at all is admired because he perceives, judges, and discerns a cause beyond the perceptions of other men, and not because of the usefulness of his discoveries. We admire him rather as one who is wise and as distinguishing from others. As being wise, indeed, in the subtle way in which he investigates the causes of his discoveries, and as distinguishing from others insofar as he investigates the ways in which one thing differs from another. Or, according to another interpretation, as distinguishing from others is to be read passively, as being distinguished in this respect from others. Hence another text has one who is different. Some sciences, then, are more admirable and worthy of the name of wisdom because their observations are more outstanding, not because they are useful.

32. Therefore, since many useful arts have been discovered (some to provide the necessities of life, as the mechanical arts, and others to introduce us to the sciences, as the logical disciplines), those artists must be said to be wiser whose sciences were discovered not for the sake of utility but merely for the sake of knowing. These are the speculative sciences.

33. That the speculative sciences were not discovered for the sake of utility is made clear by this fact: after all sciences had already been developed (that is, acquired or discovered) which can serve as introductions to the other sciences, or provide the necessities of life, or give pleasure (as those arts whose object is to delight man), the speculative sciences were discovered not for this kind of end, but for their own sake. The fact that they were not discovered for the sake of utility becomes evident from the place in which they were discovered. For they originated in those places where men first applied themselves to such things.

Another version reads, and first in those places where men had leisure, that is, they had time for study because they were released from other occupations as a result of the abundance of necessary things. Hence the mathematical arts, which are speculative in the highest degree, were first discovered in Egypt by the priests, who were given time for study, and whose expenses were defrayed by the community, as we also read in Genesis 47:22.

34. But because the names “wisdom,” “science,” and “art” have been used indifferently, lest someone should think that these terms are synonymous, he excludes this opinion and refers to Ethics 6, where he has explained the difference between art, wisdom, science, prudence, and understanding. To give the distinction briefly, wisdom, science, and understanding pertain to the speculative part of the soul, which he speaks of in that work as the scientific part of the soul. But they differ in that understanding is the habit of the first principles of demonstration, whereas science has to do with conclusions drawn from subordinate causes, and wisdom with first causes. This is the reason it is spoken of there as the chief science. But prudence and art belong to the practical part of the soul, which reasons about our contingent courses of action. And these also differ, for prudence directs us in actions that do not pass over into some external matter but are perfections of the one acting—this is why prudence is defined in that work as the right reason of things to be done. But art directs us in those productive actions, such as building and cutting, which pass over into external matter—this is why art is defined as the right reason of things to be made.

Wisdom deals with causes

35. Now the reason (981b27). From what has been said he proves his major thesis: wisdom deals with the causes of things. He says that the reason for undertaking this investigation, that is, the above piece of reasoning, is that the science which is called wisdom seems to be about first causes and principles. This is evident from the foregoing, for the more a man attains to a knowledge of the cause, the wiser he is. This is also evident from the foregoing because the man of experience is wiser than one who has sensation alone without experience; because the artist is wiser than any man of experience; and because among artists the architect is wiser than the manual laborer. And similarly among the arts and sciences the speculative are more scientific than the practical. All these things are clear from the foregoing remarks. It follows, then, that that science which is wisdom in an absolute sense is concerned with the causes of things. The method of arguing would be similar if we were to say that that which is hotter is more afire, and therefore that that which is afire in an absolute sense is hot in an absolute sense.

What wisdom considers

But since we are in search of this science, it will therefore be necessary to consider with what kind of causes and principles wisdom or science deals. This will perhaps become evident if we take the opinions that we have about the wise man. First of all, then, we think that the wise man is one who knows all things in the highest degree, as becomes him, without having a knowledge of them individually.

Next, we say that that man is wise who is capable of knowing things that are difficult and not easy for man to understand. For sensory perception is common to all, and is therefore easy and not a matter of wisdom.

Again, [we consider him wise who is] more certain.

And in every branch of science we say that he is wiser who is more capable of teaching us about the causes of things.

Again, among the sciences we think that that science which exists for itself and is desirable for the sake of knowledge is wisdom to a greater degree than one that is desirable for the sake of contingent effects.

And we think that a superior science which is rather the more venerable comes nearer to wisdom than a subordinate science. For a wise man must not be directed but must direct, and he must not obey another but must be obeyed by one who is less wise. Such then and so many are the opinions that we have about the wise and about wisdom.

Now of these attributes, that of knowing all things necessarily belongs to him who has universal knowledge in the highest degree, because he knows which are subordinate.

But the things that are just about the most difficult for man to understand are also those that are most universal; for they are farthest removed from the senses.

Again, the most certain of the sciences are those that are most concerned with primary things. For sciences based on fewer principles are more certain than those that have additional principles, as arithmetic is more certain than geometry.

Moreover, that science which speculates about the causes of things is more instructive. For those who teach us are those who assign the causes of every single thing.

Again, to understand and to know for their own sake are found most in the science of what is most knowable. For one who desires scientific knowledge for itself will desire in the highest degree science in the highest degree, and such a science is of what is most knowable.

Now first principles and causes are most knowable, for it is by reason of these and from these that other things are known, but these are not known through things subordinate to them.

But that science is highest and superior to subordinate sciences which knows the reason why each single thing must be done. This is the good of every single thing, and viewed universally it is the greatest good in the whole of nature.

In view of everything that has been said, then, the term that we are investigating evidently falls to the same science. For this science must speculate about first principles and causes, because the good, or that for the sake of which something is done, is also one of the causes.

Six opinions about who is wise

36. Having shown that wisdom is a knowledge of causes, the Philosopher’s aim here is to establish with what kinds of causes and what kinds of principles it is concerned. He shows that it is concerned with the most universal and primary causes, and he argues this from the definition of wisdom. In regard to this he does three things.

First, he formulates a definition of wisdom from the different opinions that men have about the wise man and about wisdom.

Second [44], he shows that all of these are proper to that universal science which considers first and universal causes, at now of these (982a21).

Third [51], he draws the conclusion at which he aims, at in view of everything (982b7).

In regard to the first he gives six common opinions which men have entertained about wisdom.

He states the first where he says, but since we are in search (982a4). This opinion is that in general we all consider those especially to be wise who know all things, as befits them, without having a knowledge of every singular thing. For this is impossible since singular things are infinite in number, and an infinite number of things cannot be comprehended by the intellect.

37. Next, we say that (982a10). Here he gives the second opinion, which is this: we hold that man to be wise who is capable, by reason of his intellect, of knowing difficult things and those that are not easy for ordinary men to understand. For sensory perception, that is, the knowing of sensible things, is common to all, and is therefore easy and not a matter of wisdom. That is to say, it is neither a mark nor the office of a wise man. Thus it is clear that whatever pertains properly to wisdom is not easily known by all.

38. Again, [we consider] (982a12). Here he gives the third opinion: we say that he is wise who, regarding what he knows, is more certain than other men generally are.

39. And in every branch (982a13). Here he gives the fourth opinion. That man is said to be wiser in every science who can give the causes of anything that is brought into question, and can teach by means of this.

40. Again, among the sciences (982a14). Here he gives the fifth opinion. Among the many sciences, that science which is more desirable and willed for its own sake (that is, chosen for the sake of knowledge and for knowledge itself alone), is more of the nature of wisdom than one that is for the sake of any of the other contingent effects that can be caused by knowledge (such as the necessities of life, pleasure, and so forth).

41. And we think (982a16). Here he gives the sixth opinion, namely, that this wisdom, of which mention has been made, must be or is said to be rather the more venerable, that is, nobler, than a subordinate science. This can be understood from the foregoing. For in the field of the mechanical arts, subordinate artists are those who execute by manual operations the commands of superior artists, whom he referred to above as architects and wise men.

42. He proves by two arguments that the notion of wisdom belongs to sciences that give orders rather than to those that take them.

The first is that subordinate sciences are directed to superior sciences. For subordinate arts are directed to the end of a superior art, as the art of horsemanship to the end of the military art. But in the opinion of all it is not fitting that a wise man should be directed by someone else, but that he should direct others.

The second is that inferior artists are induced to act by superior artists inasmuch as they rely upon superior artists for the things that they must do or make. Thus the shipbuilder relies upon the instructions of the navigator for the kind of form that a ship ought to have. However, it does not befit a wise man that he should be persuaded to act by someone else, but that he should use his knowledge to persuade others to act.

43. These, then, are the kind of opinions that men have of wisdom and the wise. From all of these a description of wisdom can be formulated, so that the wise man is described as one who knows everything (even difficult matters) with certitude and through their cause, seeking this knowledge for its own sake, and directing and persuading others to act. And in this way the major premise of the syllogism becomes evident. For every wise man must be such, and conversely whoever is such is wise.

These six attributes are found in the metaphysician

44. Now of these (982a21). Here he shows that all of the above attributes come together in the man who knows the first and universal causes of things, following the same order as he did above. Thus he held first that knowledge of all things in the highest degree belongs to him who has universal knowledge. This was the first opinion, and it is made clear in this way. Whoever knows universals knows in some respect the things that are subordinate to universals, because he knows the universal in them. But all things are subordinate to those that are most universal. Therefore, the one who knows the most universal things in a sense knows everything.

45. But the things (982a23). Here he proves that the second attribute belongs to the same person by the following argument. Those things that are farthest removed from the senses are difficult for men to know, for sensory perception is common to all men (since all human knowledge originates with this). But those things that are most universal are farthest removed from sensible things, because the senses have to do with singular things. Hence universals are the most difficult for men to know. Thus it is clear that that science is the most difficult which is most concerned with universals.

46. But the statement that appears in Physics 1 seems to contradict this. For it is said there that more universal things are known first by us, and those things that are known first are those which are easier. Yet it must be said that those things that are more universal according to simple apprehension are known first, for being is the first thing that comes into the intellect (as Avicenna says), and animal comes into the intellect before man does. Just as in the order of nature, which proceeds from potency to act, animal is prior to man, so too in the genesis of knowledge the intellect conceives animal before it conceives man. But with respect to the investigations of natural properties and causes, less universal things are known first, because we discover universal causes by means of the particular causes that belong to one genus or species.

Now those things that are universal in causing are known subsequently by us (notwithstanding the fact that they are things that are primarily knowable according to their nature), although things that are universal by predication are known to us in some way before the less universal (notwithstanding the fact that they are not known prior to singular things). In us, sensory knowledge, which is cognitive of singular things, precedes intellective knowledge, which is about universals. And some importance must also be attached to the fact that he does not say that the most universal things are the most difficult absolutely, but just about. For those things that are entirely separate from matter in being, as immaterial substances, are more difficult for us to know than universals. Therefore, even though this science which is called wisdom is the first in dignity, it is still the last to be learned.

47. Again, the most certain (982a25). Here he shows that the third attribute belongs to the same science. This is his argument: the more any sciences are prior by nature, the more certain they are. This is clear from the fact that those sciences which are said to originate as a result of adding something to the other sciences are less certain than those which take fewer things into consideration; for example, arithmetic is more certain than geometry because the objects considered in geometry are a result of adding to those considered in arithmetic. This becomes evident if we consider what these two sciences take as their first principle, namely, the point and the unit. For the point adds to the unit the notion of position, because undivided being constitutes the intelligible structure of the unit; insofar as this has the function of a measure it becomes the principle of number. And the point adds to this the notion of position.

However, particular sciences are subsequent in nature to universal sciences, because their subjects add something to the subjects of universal sciences. For example, it is evident that mobile being (with which the philosophy of nature deals) adds to simple being (with which metaphysics is concerned), and to quantified being (with which mathematics is concerned). Hence that science which treats of being and the most universal things is the most certain. Moreover, the statement here that this science deals with fewer principles is not opposed to the one made above, that it knows all things. For the universal takes in fewer inferiors actually, but many potentially. And the more certain a science is, the fewer actual things it has to consider in investigating its subject matter. Hence the practical sciences are the least certain, because they must consider the many circumstances attending individual effects.

48. Moreover, that science (982a28). Here he proves that the fourth attribute belongs to the same science by this argument. That science is more instructive (or better able to teach) which is concerned to a greater degree with causes. For only those teach who assign the causes of every single thing, because scientific knowledge comes about through some cause, and to teach is to cause knowledge in another. But that science which considers universals considers the first of all the causes. Hence it is evidently the best fitted to teach.

49. Again, to understand (982a30). Here he proves that the fifth attribute belongs to the same science by this argument. It is most properly the office of the sciences about the most knowable things to know and understand for their own sake—that is, for the sake of those sciences themselves and not for something else. But it is the sciences that deal with first causes which consider the most knowable things. Therefore, those sciences are desired most for their own sake.

He proves the first premise thus. One who most desires knowledge for the sake of knowledge most desires scientific knowledge. But the highest kind of knowledge is concerned with things that are most knowable. Therefore, those sciences are desired most for their own sake which have to do with things that are most knowable.

He proves the second premise thus. Those things from which and by reason of which other things are known are more knowable than the things that are known by means of them. But these other things are known through causes and principles, and not vice versa, and so on.

50. But that science (982b4). Here he proves that the sixth attribute belongs to the same science by the following argument. That science which considers the final cause (or that for the sake of which particular things are done) is related to the other sciences as a chief or master science is to a subordinate or ancillary one, as is evident from the foregoing remarks. For the navigator, to whom the use, or end, of the ship belongs, is a kind of architect in relation to the shipbuilder who serves him. But the aforesaid science is concerned most with the final cause of all things. This is clear when we consider how that for the sake of which all particular things are done is the good of every single thing, that is, a particular good. But the end in any genus of things is a good, and that which is the end of all things (that is, of the universe itself) is the greatest good in the whole of nature. Now this belongs to the consideration of the science in question, and therefore it is the chief or architectonic science with reference to all the others.

51. In view of everything (982b7). Here he draws from the foregoing arguments his intended conclusion, saying that it is clear from everything that has been said that the name “wisdom” which we are investigating belongs to the same science that considers or speculates about first principles and causes. This is evident from the six primary conditions which clearly pertain to the science that considers universal causes. But because the sixth condition touched on the consideration of the end, which was not clearly held to be a cause among the ancient philosophers, as will be said below [1177], he therefore shows in a special way that this condition belongs to the same science, namely, the one which considers first causes. For the end, which is a good and that for the sake of which other things are done, is one of the many causes. Hence the science that considers first and universal causes must also be the one that considers the universal end of all things, which is the greatest good in the whole of nature.

Metaphysics’ nature and goal

That this is not a practical science is evident from those who first philosophized. For it is because of wonder that men both now and formerly began to philosophize, about less important matters, and then progressing little by little, they raised questions about more important ones, such as the phases of the moon and the courses of the sun and the stars and the generation of the universe. But one who raises questions and wonders seems to be ignorant. Hence the philosopher is also to some extent a lover of myth, for myths are composed of wonders. If they philosophized, then, in order to escape from ignorance, they pursued their studies for the sake of knowledge and not for any utility.

And what has happened bears witness to this. For when nearly all the things necessary for life, pastimes, and learning were acquired, this kind of prudence began to be sought. It is evident, then, that we do not seek this knowledge for the sake of any other necessity.

But just as we say that a man is free who exists for himself and not for another, in a similar fashion this is the only free science, because it alone exists for itself.

For this reason, too, it might rightly be thought that this science is not a human possession, since in many respects human nature is servile.

Hence, according to Simonides, only God has this honor, and it is unfitting that man should not seek knowledge that befits him. Some poets accordingly say that the deity is naturally envious. It is most likely that it should happen in this case, and that all those who are imperfect are unfortunate. But it is not fitting that the deity should be envious, for as the proverb says: the poets tell many lies.

Nor must we think that any other science is more honorable than this. For what is most divine is most honorable. But then it alone will be such, and in two ways. For of all knowledge that which God most properly has is divine; if there is any such knowledge, it is concerned with divine matters.

But this science alone has both of these characteristics, for God seems to be a cause and in some sense a principle according to all men, and such [knowledge as this] God either alone has, or has in the highest degree. Therefore, all the other sciences are more necessary, but none is more excellent.

But it is necessary in a sense to bring to a halt the progression of this science at the contrary of our original questions. Indeed, as we have said, all men begin by wondering whether things are like strange chance occurrences to those who do not yet know the cause, or by wondering about reversals in the course of the sun, or about the incommensurability of the diagonal [of a square].

For it would seem wonderful to all if something having the nature of number were immeasurable. But it is necessary to advance to the contrary state and, as the proverb says, the worthier one, as also happens in a sense in these matters when men have learned them. For nothing would surprise a geometrician more than if the diagonal [of a square] were commensurable [with its side].

It has been stated, then, what the nature is of the science that we are seeking and what its goal is for which our search and whole method must be undertaken.

Why this science is called speculative

52. Having indicated the things with which this science deals, Aristotle now shows what kind of science it is. In regard to this he does two things.

First (982b11; [53]), he reveals the dignity of this science;

second (983a11; [66]), the goal which it attempts to reach, at but it is necessary.

In regard to the first he does four things.

First, he shows that this is not a practical science but a speculative one;

second (982b25; [58]), that it is free in the highest degree, at but just as we say;

third (982b28; [60]), that it is not human, at for this reason;

fourth (983a4; [64]), that it is the most honorable science, at nor must we think that.

He proves the first in two ways.

First, by an argument;

second (982b22; [57]), by an example, at and what has happened.

53. First, he gives this argument. No science in which knowledge itself is sought for its own sake is a practical science, but a speculative one. But that science which is wisdom, or philosophy as it is called, exists for the sake of knowledge itself. Hence it is speculative and not practical. He proves the minor premise in this way. Whoever seeks as an end to escape from ignorance tends toward knowledge for itself. But those who philosophize seek as an end to escape from ignorance. Therefore, they tend toward knowledge for itself.

54. That they seek to escape from ignorance is made clear from the fact that those who first philosophized and who now philosophize did so from wonder about some cause, although they did this at first differently from now. For at first they wondered about less important problems, which were more obvious, in order that they might know their cause; but later on, progressing little by little from the knowledge of more evident matters to the investigation of obscure ones, they began to raise questions about more important and hidden matters, such as the phases of the moon, such as its eclipse, and its change of shape, which seems to vary inasmuch as it stands in different relations to the sun. And similarly they raised questions about the phenomena of the sun (such as its eclipse, its movement, and its size), and about the phenomena of the stars (such as their size, arrangement, and so forth), and about the origin of the whole universe, which some said was produced by chance, others by an intelligence, and others by love.

55. Further, he points out that perplexity and wonder arise from ignorance. For when we see certain obvious effects whose cause we do not know, we wonder about their cause. And since wonder was the motive which led men to philosophy, it is evident that the philosopher is, in a sense, a lover of myth, that is, a lover of myth, as is characteristic of the poets. Hence the first men to deal with the principles of things in a mythical way, such as Perseus and certain others who were the seven sages, were called the theologizing poets. Now the reason why the philosopher is compared to the poet is that both are concerned with wonders. For the myths with which the poets deal are composed of wonders, and the philosophers themselves were moved to philosophize as a result of wonder. And since wonder stems from ignorance, they were obviously moved to philosophize in order to escape from ignorance. It is accordingly evident from this that they pursued knowledge, or diligently sought it, only for itself and not for any utility or usefulness.

56. Now we must note that, while this science was first designated by the name “wisdom,” this was later changed to the name “philosophy,” since they mean the same thing. For while the ancients who pursued the study of wisdom were called sophists (that is, wise men), Pythagoras, when asked what he professed himself to be, refused to call himself a wise man as his predecessors had done because he thought this was presumptuous, but called himself a philosopher (that is, a lover of wisdom). And from that time the name “wise man” was changed to “philosopher,” and “wisdom” to “philosophy.” This name also contributes something to the point under discussion, for that man seems to be a lover of wisdom who seeks wisdom, not for some other reason, but for itself alone. For he who seeks one thing on account of something else has greater love for that on whose account he seeks than for that which he seeks.

57. And what has happened (982b22). Here he proves the same point by means of an example. He says that the statement that wisdom or philosophy is not sought for any utility but for knowledge itself is proved by what has happened, that is, by what has occurred in the case of those who have pursued philosophy. For when nearly everything was discovered which is necessary for life, pastimes (that is, for the pleasure which consists in a life of ease), and learning, such as the logical sciences which are not sought for themselves but as introductions to the other arts, then man began for the first time to seek this kind of prudence, namely, wisdom. And from this it is clear that wisdom is not sought because of any necessity other than itself but for itself alone, for no one seeks something which he already possesses. Hence, because wisdom was sought after all other knowledge had been discovered, it is evident that it was not sought for some reason other than itself, but for itself.

Why this science is liberal

58. But just as (982b25). Here he proves the second attribute—namely, that wisdom is free—and he uses the following argument. That man is properly said to be free who does not exist for someone else but for himself. For slaves exist for their masters, work for them, and acquire for them whatever they acquire. But free men exist for themselves inasmuch as they acquire things for themselves and work for themselves. But only this science exists for itself. Therefore, among all the sciences only this science is free.

59. Now we must note that this can be understood in two ways. In one way, the expression this is the only may indicate every speculative science as a genus. And then it is true that only this genus of science is sought for itself. Hence, only those arts which are directed to knowing are called liberal arts, whereas those which are directed to some useful end attained by action are called mechanical or servile arts.

Understood in another way, the expression may specifically indicate this philosophy or wisdom which deals with the highest causes, for the final cause is also one of the highest causes, as was stated above [51]. Therefore, this science must consider the highest and universal end of all things. And in this way all the other sciences are subordinated to it as an end. Hence only this science exists in the highest degree for itself.

Why this science is superhuman

60. For this reason (982b28). Here he proves the third attribute, namely, that this science is not human. In regard to this he does two things.

First, he proves his thesis.

Second [61], he criticizes an erroneous view held by certain men, at hence, according to Simonides (982b30).

He proves his thesis by the following argument. A science which is free in the highest degree cannot be a possession of that nature which is servile and subordinate in many respects. But human nature is servile in many respects, that is, in many ways. Therefore, this science is not a human possession. Now human nature is said to be servile insofar as it stands in need of many things. And on this account it happens that man sometimes neglects what should be sought for its own sake because of the things necessary for life. Thus it is said in Topics 3 that it is better to philosophize than to become wealthy, although sometimes becoming wealthy is more desirable—that is, to one lacking life’s necessities. From this it is clear that the wisdom which is sought for itself alone does not belong to man as his proper possession. For man has as his possession what he can have at his command and use freely. But man cannot use freely that science which is sought for itself alone, since he is often kept from it because of the necessities of life. Nor again is it subject to man’s command, because man cannot acquire it perfectly. Yet that very small part of it which he does have outweighs all the things known through the other sciences.

61. Hence, according to Simonides (982b30). Here he rejects the error of a certain poet, Simonides, who said that it is proper to God alone to have the honor of desiring that knowledge which ought to be sought for its own sake and not for the sake of something else. But it is unfitting that man should not seek knowledge that befits him, namely, that which is directed to the necessities of life required by man.

62. Now Simonides’ error came from that of certain poets who said that the deity is envious, and that since he is envious he does not desire that the things that pertain to his honor should be shared by all. And if God is envious of men in other things, he is rightly more so in this case—that is, in the case of the science which is sought for its own sake, which is the most honorable of all the sciences. And according to the opinion of these men it follows that all who are imperfect are unfortunate, for they said that men are fortunate as a result of the providence of the gods, who communicate their goods to men. Hence as a result of the envy of the gods, who are unwilling to communicate their goods, it follows that men, who remain outside the perfection of this science, are unfortunate.

63. But the basis of this opinion is most false, because it is not fitting that any divinity should be envious. This is evident from the fact that envy is sadness at someone else’s prosperity. But this can occur only because the one who is envious thinks that someone else’s good diminishes his own. Now it is impossible that God should be sad, because he is not subject to evil of any kind. Nor can his goodness be diminished by someone else’s goodness, since every good flows from his goodness as from an unfailing spring. Hence Plato also said that there is no envy of any kind in God. But the poets have lied not only in this matter but in many others, as is stated in the common proverb.

Why this science is most honorable

64. Nor must we think (983a4). Here he proves the fourth attribute—namely, that this is the most honorable science—by the following argument. That science which is most divine is most honorable, just as God himself is also the most honorable of all things. But this science is the most divine, and is therefore the most honorable.

The minor premise is proved in this way: a science is said to be divine in two ways, and only this science is said to be divine in both ways. First, the science which God has is said to be divine; second, the science which is about divine matters is said to be divine. But it is evident that only this science meets both of these requirements, because, since this science is about first causes and principles, it must be about God, for God is understood in this way by all inasmuch as he is one of the causes and a principle of things. Again, either God alone has such a science which is about God and first causes, or, if not he alone, at least he has it in the highest degree. Indeed, he alone has it in a perfectly comprehensive way. And he has it in the highest degree inasmuch as it is also had by men in their own way, although it is not had by them as a human possession, but as something borrowed from him.

65. From these considerations he draws the further conclusion that all other sciences are more necessary than this science for use in practical life, for these sciences are sought least of all for themselves. But none of the other sciences can be more excellent than this one.

The relation between wonder and wisdom

66. But it is necessary (983a11). He now gives the goal toward which this science moves. He says that its progression comes to rest, or is terminated, in the contrary of what was previously found in those who first sought this science, as also happens in the case of natural generations and motions. For each motion is terminated in the contrary of that from which the motion begins. Hence, since investigation is a kind of movement towards knowledge, it must be terminated in the contrary of that from which it begins.

But, as was stated above [53], the investigation of this science began with man’s wonder about all things, because the first philosophers wondered about less important matters and subsequent philosophers about more hidden ones. And the object of their wonder was whether the case was like that of strange chance occurrences, that is, things that seem to happen mysteriously by chance.

For things that happen as if by themselves are called chance occurrences. Hence men wonder most of all when things happen by chance in this way, supposing that they were foreseen or determined by some cause. For chance occurrences are not determined by a cause, and wonder results from ignorance of a cause. Therefore, when men were not yet able to recognize the causes of things, they wondered about all things as if they were chance occurrences, just as they wondered about reversals in the course of the sun, which are two in number (namely, the solstices of winter and of summer).

For at the summer solstice the sun begins to decline toward the south, after previously declining toward the north. But at the winter solstice the opposite occurs. And they wondered also that the diagonal of a square is not commensurable with a side. For, since to be immeasurable seems to belong to the indivisible alone (just as unity alone is what is not measured by number but itself measures all numbers), it seems to be a matter of wonder that something which is not indivisible is immeasurable, and consequently that what is not a smallest part is immeasurable. Now it is evident that the diagonal of a square and its side are neither indivisible nor smallest parts. Hence it seems a matter of wonder if they are not commensurable.

67. Therefore, since philosophical investigation began with wonder, it must end in or arrive at the contrary of this, and this is to advance to the worthier view, as the common proverb agrees which states that one must always advance to the better. For it is evident in the above wonders what that opposite and worthier view is, because when men have already learned the causes of these things they do not wonder. Thus the geometrician does not wonder if the diagonal is incommensurable with a side. For he knows the reason for this—namely, that the proportion of the square of the diagonal to the square of a side is not as the proportion of the square of a number to the square of a number, but as the proportion of two to one. Hence it follows that the proportion of a side to the diagonal is not as the proportion of number to number. And from this it is evident that they cannot be made commensurable. For only those lines are commensurable which are proportioned to each other as number to number. Hence the goal of this science to which we should advance will be that, in knowing the causes of things, we do not wonder about their effects.

68. From what has been said, then, it is evident what the nature of this science is. It is speculative and free, and it is not a human possession but a divine one. It is also evident what its aim is, for which the whole inquiry, method, and art must be conducted. For its goal is the first and universal causes of things, about which it also makes investigations and establishes the truth. And by reason of the knowledge of these it reaches this goal, namely, that there should be no wonder because the causes of things are known.

Opinions about the material cause

It is evident, then, that one must acquire scientific knowledge of those causes which stand at the beginning, for we say that we have scientific knowledge of each thing when we think we comprehend its first cause. Now causes are spoken of in four ways. Of these we say that one is the substance or quiddity¹ of a thing, for the first “why” of a thing is reduced to its ultimate intelligible structure, and the first why of a thing is a cause or principle. Another is the matter or subject. A third is the source of motion. A fourth is the cause which is opposite to this, namely, that for the sake of which, or the good; for this is the goal of every generation and motion. There has been sufficient consideration of these in our works on nature.

However, let us examine those who have undertaken an investigation of existing things and have philosophized about the truth before us. For evidently they too speak of certain principles and causes. Therefore, to us who come later [their views] will serve as an introduction to the study which we are now making, for we shall either discover some other genus of cause, or be more convinced of those which have just been expounded.

Most of those who first philosophized thought that only the things that belong to the species of matter are the principles of all things. For that of which all things are composed, from which they first come to be, and into which they are finally dissolved while their substance remains (although it is changed in its attributes)—this they call the element and principle of existing things.

And for this reason they thought that nothing is either generated or corrupted, as if such a reality always remained in existence. And just as we do not say that Socrates comes to be in an unqualified sense when he becomes good or musical, or is corrupted when he loses these states, because the subject Socrates himself remains, in the same way they say that nothing else is generated or corrupted. For there must be some matter, either one or more than one, from which other things come to be, and which itself remains in existence. However, they do not all speak in the same way about the number and nature of such a principle.

Thales, the originator of this kind of philosophy, says that this principle is water; this is why he also claimed that the earth rests upon water.

For presumably he took this position because he saw that the nutriment of all things is moist, that heat itself is generated from this, and that animal life comes from this. But that from which each thing comes to be is a principle of all things. He bases his opinion on this, then,

and on the fact that the seeds of all things have a moist nature, and water is by nature the principle of moist things.

But there are some who think that the ancients who lived long before the present generation and were the first to speculate about the gods held this view about the nature of things. For they made Oceanus and Tethys the parents of generation, and held the oath of the gods to be by a body of water, to which the poets gave the name Styx. For what is oldest is most honorable, and what is most honorable is that by which one swears. Whether this view of nature is in fact the ancient and primary one is perhaps uncertain. Thales is said to have expressed himself in this way about the first cause, but no one could say that Hippo is to be included in this group, because of the weakness of his understanding.

Anaximenes and Diogenes hold that air is prior to water and is the most fundamental of the simple bodies.

Hippasus of Metopontium and Heraclitus of Ephesus hold that fire [is the primary principle].

Empedocles holds that there are four [simple bodies], since he adds a fourth—earth—to those already mentioned. For he says that these always remain and only become many or few in number by being combined into a unity and separated out of a unity.

Anaxagoras of Clazomenae, who was prior to Empedocles in years but later in his speculations, says that the principles of things are infinite in number. For he says that nearly all bodies which are made up of parts like themselves, such as fire or water, are generated or corrupted merely by combining and separating; but that otherwise they are neither generated nor corrupted but always remain in existence. From these views, then, one might think that the only cause is the one which is said to belong to the species of matter.

69. Having set forth a preface in which he indicates the aim of this science, its dignity and goal, Aristotle begins to deal with this science; and this is divided into two parts.

In the first [70], he explains what the first philosophers had to say about the causes of things.

In the second [274], he begins to pursue the truth of this science. He does this in book 2, at theoretical or speculative knowledge (993a30).

The first part is divided into two members.

First, he gives the opinions of the philosophers about the causes of things.

Second [181], he criticizes them insofar as their statements are unsatisfactory, at therefore, all those (988b22).

In regard to the first he does two things.

First, he takes up again the enumeration of causes which was treated in greater detail in Physics 2.

Second [72], he presents the opinions of the philosophers, at however, let us examine (983b1).

The four causes and three characteristics of final cause

70. Accordingly, he first says that, since it is evident that wisdom speculates about causes, we ought to begin by acquiring knowledge from the causes of things. This also seems to be in keeping with the intelligible structure of science, because we say that we know each thing scientifically when we think we are not ignorant of its cause.

Now causes are spoken of in four ways. One of these is the formal cause, which is the very substance of a thing by which we know what each thing is. For it is well known, as is stated in Physics 2, that we do not say that anything has a nature before it has received a form. Now it is clear that a form is a cause, because to answer the question “Why is something so?” we go back to its formal cause as its ultimate explanation, beginning with proximate forms and proceeding to the ultimate form. But evidently the “why” asks about a cause and principle. Hence it is evident that a form is a cause. A second cause is the material cause. A third is the efficient cause, which is the source of motion. A fourth is the final cause, which is opposite to the efficient cause as a goal is to a starting-point, for motion begins with the efficient cause and terminates with the final cause. This cause is also that for the sake of which a thing comes to be, and the good of each nature.

71. He makes the final cause known by three considerations. It is the goal of motion, and thus is opposite to the source of motion, which is the efficient cause. It is first in intention, and for this reason is said to be that for the sake of which. And it is desirable of itself, and for this reason is called a good, for the good is what all desire.

Hence, in explaining how the final cause is opposite to the efficient cause, he says that it is the end of every process of generation and motion, whose starting point is the efficient cause. By these two types of change he seems to imply that there is a twofold goal. For the goal of a process of generation is the form itself, which is a part of a thing. But the goal of motion is something sought for outside the thing moved. He says that he has treated these causes at sufficient length in the Physics, lest he should be asked to make a more extensive treatment of them.

72. However, let us examine (983b1). Here he states what the philosophers had to say about the causes; and in regard to this he does two things.

First, he gives the reasons why this must be done;

and, second (983b6; [73]), he begins to carry out his plan, at most of those.

Accordingly, he says that even though there is a treatise on the causes in the Physics it is still necessary to consider the opinions of the philosophers who first undertook an investigation of the natures of existing things, and have philosophized about the truth before him; because they too set down causes and principles. Therefore, for us who have come later, a consideration of their opinions will be first, or a preamble, in the study, that is, to the art which we are now seeking.

Hence the text of Boethius also says: therefore, as we enter upon the task of this science, their opinions will constitute a preamble to the road that is now to be traveled. Another text has: therefore, as we enter upon our present course it will be a certain work of life in the investigation that now confronts us, and it must be read in this way: therefore, as we enter upon our present course, that is, upon the present study and art, it will be necessary to consider the opinion of these men as a work of life, that is to say, as necessary, like works which are done for the preservation of life, so that this reading is interpreted as a metaphorical way of speaking, meaning by work of life anything necessary.

Now this is useful, because from the opinions of these men we will either discover another genus of causes over and above those already enumerated, or be more convinced of the things that have just been stated about the causes, namely, that there are four of them.

73. Most of those (983b6). Here he begins to deal with the opinions of the ancient philosophers; and in regard to this he does two things.

First (983b6), he states their opinions;

second (988b22; [181]), he finds fault with them, at therefore, all those.

In regard to the first he does two things.

First, he states the opinions which each one of the philosophers held about the causes.

Second (988a18; [171]), he summarizes the discussion, at we have examined.

The first part is divided into two parts.

In the first (983b6; [74]), he gives the opinions of those who omitted the formal cause.

In the second (987a29; [151]), he gives the opinion of Plato, who was the first to posit a formal cause, at after the philosophies.

In regard to the first he does two things.

First, he gives the opinion of those who claimed that certain evident things are principles.

Second (985b4; [112]), he gives the opinions of those who devised extrinsic principles, at Leucippus and his colleague.

In regard to the first he does two things.

First, he touches on the opinions which the ancient philosophers held about the material cause;

second (984a18; [93]), on their opinions about the efficient cause, at but as men.

In regard to the first he does two things.

First, he states in a general way the views of those who posited a material cause.

Second (983b20; [77]), he examines their views in detail, at Thales, the originator.

In regard to the first he does two things.

First, he states their opinions about the material cause.

Second (983b11; [75]), he states their opinions about the generation of things, which follow from the first, at and for this reason.

Opinions of those who gave only material cause; four characteristics of matter

74. Accordingly, he says first (983b6) that most of those who first philosophized about the natural world held that the principles of all things are merely those which are referred to the species of material cause. In regard to this, it must be said that they took the four conditions of matter which seem to belong to the notion of a principle.

For that of which a thing is composed seems to be a principle of that thing. But matter is such a thing, for we say that a thing that has matter is “of” its matter, as a knife is of iron.

That from which a thing comes to be (which is also a principle of the process of generation of that thing) seems to be one of its causes, because a thing comes into being by way of generation. But a thing first comes to be from matter, because the matter of things precedes their production. And a thing does not come from matter in an accidental way, for a thing is generated in an accidental way from its contrary or privation, as when we say that white comes from black.

Third, that into which all things are ultimately dissolved by corruption seems to be a principle of things. For just as principles are first in the process of generation, in a similar way they are last in the process of dissolution. Obviously this too pertains to matter.

Fourth, since a principle must remain in existence, then that which remains throughout the process of generation and corruption seems to be a principle. Now the matter which they said is the substance of a thing remains throughout every transmutation, although its attributes, such as its form and everything that accrues to it over and above its material substance, are changed. From all these considerations they concluded that matter is the element and principle of all beings.

No generation or corruption without a material cause

75. And for this reason (983b11). Then he gives, as a secondary point, what they held as following from the above—namely, that in the world nothing is generated or corrupted in an absolute sense.

For when some change occurs with regard to a thing’s attributes, and its substance remains unchanged, we do not say that it is generated or corrupted in an absolute sense, but only in a qualified one. For example, when Socrates becomes good or musical, we do not say that he simply comes to be, but comes to be this. And similarly when he loses a state of this kind, we do not say that he is corrupted in an absolute sense, but only in a qualified one. But matter (which is the substance of things according to them) always remains, and every change affects some of a thing’s accidents, such as its attributes.

From this they concluded that nothing is generated or corrupted in an absolute sense, but only in a qualified one.

76. Yet even though they all agreed in positing a material cause, nevertheless they differed in their position in two respects: first, with respect to the number of material causes, because some held that there is one, and others many; second, with respect to its nature, because some held that it is fire, others water, and so on. Similarly, among those who posited many material causes, some assigned certain ones as the material principles of things, and some the others.

77. Thales, the originator (983b20). Here he begins to give the opinions of each of the philosophers about the material cause.

First, he gives the opinions of those who posited one material cause;

second [88], the opinions of those who posited many, at Empedocles (984a8).

In regard to the first he does three things.

First, he gives the opinions of those who claimed that water is the principle of all things;

second [86], he gives the opinion of those who made air the principle of things, at Anaximenes (984a5);

and third [87], the opinion of those who claimed that fire is the principle of things, at Hippasus (984a7).

In regard to the first he does two things.

First, he gives the opinion of Thales, who said that water is the principle of things;

second [79], the reason for this opinion (for presumably).

He says then that Thales, the originator of this kind of philosophy, speculative philosophy, said that water is the first principle of all things. Thales is said to have been the originator of speculative philosophy because he was the only one of the seven wise men who came after the theological poets to make an investigation into the causes of things, the other sages being concerned with moral matters.

The names of the seven wise men are as follows. The first was Thales of Miletus, who lived during the time of Romulus and when Achaz, King of Israel, was reigning over the Hebrews. The second was Pittacus of Mitylene, who lived when Sedecias was reigning over the Hebrews and when Tarquinius Priscus was reigning over the Romans. The other five sages were Solon of Athens, Chilo of Lacedaemon, Periander of Corinth, Cleobulus of Lydia, and Bias of Prienne, all of whom lived during the period of the Babylonian captivity.

Hence, since Thales alone among these men investigated the natures of things and distinguished himself by committing his arguments to writing, he is described here as the originator of this science.

78. Nor should it be thought unfitting if he touches here on the opinions of those who have treated only the philosophy of nature, because, according to the ancients, who knew no other substance except the bodily and mobile, it was necessary that first philosophy be the philosophy of nature, as is stated in book 4. And from this position Thales next adopted this one, that the earth rests upon water, as anything having a principle is based on its principle.

79. For presumably he took (983b22). Here he gives the reasons by which Thales could be led to the above position.

First, he shows how he was led to this position by his own reasoning;

and second [82], by the authority of his predecessors, at but there are some (983b27).

Now he was led by two lines of reasoning.

One is taken from the cause itself of a thing.

The other is taken from a consideration of the generation of things, at and on the fact (983b22).

Therefore, these premises are related. For the second follows from the first, because that which is a principle of being of other things is also the first principle from which things are generated. The third follows from the second, because by corruption each thing is dissolved into that from which it was generated. The fourth follows from the second and the third; for that which precedes the generation of things and remains after they have been corrupted must always remain in being.

80. In the first line of reasoning he uses three indications to show that water is the principle of being of things.

The first of these is that the nutriment of living things must be moist. But living things derive nourishment and being from the same principle; thus moisture appears to be the principle of being of things.

The second indication is that the being of any physical thing, and especially of a living one, is conserved by its proper and natural heat. But heat seems to be generated from moisture, since moisture itself is in a sense the matter of heat. Hence from this it appears that moisture is a principle of being of things.

The third indication is that animal life depends on moisture. Hence an animal dies as a result of its natural moisture being dried up, and is kept in existence as a result of its moisture being preserved. But in living things, to live is to be. Hence it is also evident from this that moisture is a principle of being of things.

These three indications also have a natural connection with one another. For an animal is nourished by moisture, because its natural heat is sustained by moisture. And from these two it follows that animal life is always due to moisture. But that from which a thing comes to be (that is, from which a thing gets its being) is a principle of everything that derives being from it. And for this reason he adopted this opinion that moisture is the principle of all things.

81. In a similar way, he also draws an indication of this from the generation of things, because the processes of generation of living things, which are the noblest of beings, come from seed. But the seed or spermata of all living things has a moist nature. Hence from this it also appears that moisture is a principle of generation of things. Again, if we add to all of the above points the fact that water is the principle of moisture, it follows that water is the first principle of things.

82. But there are some (983b27). Here he shows how Thales was led to the above position by the authority of the ancients. He says that prior to Thales and many years before the men of Aristotle’s time there were some men, the first to speculate about the gods, who seem to have held this opinion about nature, namely, that water is the principle of all things.

83. With a view to making this clear, we must bear in mind that among the Greeks the first who were famous for their learning were certain theological poets, so called because of the songs that they wrote about the gods. These poets, who were three in number—Orpheus, Museus, and Linus (of whom Orpheus was the more famous)—lived during the time when the judges ruled over the Jewish people. Hence it is clear that they lived long before Thales and much longer before Aristotle, who lived during the time of Alexander. These poets dealt to some extent with the nature of things by means of certain figurative representations in myths. For they said that Oceanus, where the greatest aggregation of waters is found, and Tethys, which is the name they gave to the goddess of the waters, are the parents of generation, implying under the form of a myth that water is the principle of generation.

84. They cloaked this view in another fabulous story, saying that the oath or vow of the gods was by a certain body of water, which the poets call Styx and describe as an underground swamp. And when they said that the gods swore by water, they implied that water was nobler than the gods themselves, because an oath or vow is taken on what is most honorable. Now that which is prior is more honorable, for the perfect is prior absolutely to the imperfect, both in nature and in time, although in a particular being imperfection is prior temporally to perfection. Hence, from this it is evident that they thought that water is prior to the gods themselves, whom they thought to be celestial bodies. And since these earliest thinkers said that water is the principle of things, if there was any opinion about natural bodies prior to theirs, we do not know what it was. Thus, what Thales is said to have thought about the first cause of things is now clear.

85. A certain philosopher named Hippo was not credited with adding anything to those mentioned because of the imperfection of his knowledge or understanding. Hence, in On the Soul, Hippo is placed among the ruder thinkers; for in that work it is stated that Hippo, basing his argument on the seeds of things (as was said here of Thales), held water to be the soul and principle of things. Hence it is clear that he adds nothing to Thales’ view. Or the statement can mean that, since he spoke imperfectly, he did not make himself worthy to have his doctrine included here with the others.

86. Anaximenes and Diogenes (984a5). Here he gives the opinions of those who held that air is the principle of things. These were Diogenes and Anaximenes, who held that air is naturally prior to water and is the principle of all simple bodies, that is, of the four elements, and thus of all other things. Anaximenes is the third philosopher after Thales and the disciple of Anaximander, who was the disciple of Thales; Diogenes is said to have been the disciple of Anaximenes. Yet there is this difference between the opinion of Diogenes and that of Anaximenes: Anaximenes held that air is the principle of things in an absolute sense, whereas Diogenes said that air could be the principle of things only if it possessed a divine nature. From this comes the opinion which is touched on in On the Soul 1. Now the reason why he held that air is the principle of things could be taken from the process of respiration, by which the life of animals is conserved, and because the processes whereby things are generated and corrupted seem to be modified as a result of changes in the air.

87. Hippasus of Metopontium (984a7). Here he states that two philosophers, Hippasus and Heraclitus, held that fire is the material principle of things. And they could have been influenced by its subtleness, as is said below.

88. Empedocles (984a8). Here he gives the opinions of those who posited many material principles.

First, he gives the opinion of Empedocles, who held that there are a limited number of such principles;

second [90], that of Anaxagoras, who held that there are an infinite number, at Anaxagoras (984a11).

First (984a8), he gives Empedocles’ opinion regarding the three elements mentioned above (water, air, and fire), which he says are the principles of things, adding to them a fourth, earth.

89. Second, he gives Empedocles’ opinion about the permanence of these elements; like those who hold that there is one material cause, he holds that these elements always remain and are neither generated nor corrupted. However, he said that other things are generated from and divided into these elements according as a greater or smaller number of them are combined or separated out (that is, inasmuch as these four are united by the process of combination and lose their unity by the process of separation).

90. Anaxagoras (984a11). Here he gives the opinion of Anaxagoras, who was the other disciple of Anaximenes and the classmate of Diogenes. A native of Clazomenae, he was prior to Empedocles in years but later in his activity or work, either because he began to philosophize later, or because his explanation of the number of principles is less satisfactory than that of Empedocles. For he said that there are an infinite number of material principles, whereas it is better to take a limited and smaller number, as Empedocles did, as is stated in Physics 1.

For Anaxagoras not only said that fire, water, and the other elements are the principles of things, as Empedocles did, but also claimed that all things having like parts, such as flesh, bones, marrow and so forth, whose smallest parts are infinite in number, are the principles of things. For he claimed that in each being there are an infinite number of parts of each type of thing, because he found that in the case of inferior things one of these can be generated from another. He said, in fact, that things could be generated only by being separated out from a mixture, as Aristotle has explained more fully in Physics 1.

91. Second, Anaxagoras also agrees with Empedocles on this point: things are generated and corrupted only insofar as the parts of these infinite principles are combined or separated out, and that if this were not the case nothing would be generated or corrupted. But he said that the infinite number of principles of this kind, from which the substances of things are produced, always remain in being.

92. From the opinions of these philosophers, then, Aristotle concludes that the only cause which these men recognized was the one which belongs to the species of material cause.

Opinions about the efficient cause

But as men proceeded in this way, reality itself again opened up a path and forced them to make investigations. For if every process of generation and corruption is from some one thing or more than one, why does this occur, and what is the cause? For certainly the subject itself does not cause itself to change. I mean, for example, that neither wood nor bronze is the cause of the change undergone by either one of them; for wood does not produce a bed, or bronze a statue, but something else is the cause of the change. But to seek this is to seek another principle, as if one were to say that from which the beginning of motion comes.

Now in general those who have taken such a course from the very beginning, and who said that the subject is one, created no difficulty for themselves when they said that everything is one. Some, being baffled, so to speak, by this question, say that this [one subject] and the whole of nature is immobile not only with respect to generation and corruption (for this is an ancient opinion and one which all men confess to be true), but also with respect to every other change. This opinion is peculiar to them.

Hence, of those who said that the [universe] itself is one, it occurred to none of them to conceive of such a cause, except perhaps Parmenides, and to him only insofar as he claims that there is not one cause but also in a sense two causes. But for those who make the elements of things many, such as the hot and cold, or fire and earth, a better explanation is possible, because they use fire as if it were a material principle which is active in nature, but water and earth and the like they use in the opposite way.

After these men and such principles, as if they were insufficient to generate the natures of existing things, men were again compelled, as we said (984a18), by the truth itself to seek for the next principle. For perhaps it is unlikely that either fire or earth or anything else of this kind should be the cause of the good dispositions of things that are or come to be; nor was it consistent that they should think this to be the case. Nor again would it be right to attribute so important a matter to chance occurrence and fortune.

And when someone said that there is one intellect present in nature as in animals, and that this is the cause of the world and the arrangement of the whole, he seemed to atone for the untenable statements made by his predecessors. We know that Anaxagoras expressed these views, although Hermotimus of Clazomenae was the first to speak of such a cause. Those, therefore, who held these opinions likewise posited a principle in existing things, which is the cause of their goodness, and that sort of cause that is the source of motion in the world.

Now someone might have suspected that Hesiod was the first to have investigated this sort of cause, or anyone else who held that love or desire is a principle in existing things, as Parmenides did. For in the place where he attempts to explain the generation of the universe, he says that Love, the first of all the gods, was made. And Hesiod says that the first of all things to be made was chaos, then broad earth, and Love, who is pre-eminent among the immortals—as though there must be in the world some cause which moves things and brings them together. Which of these thinkers is prior will be decided later on.

93. Having given the philosophers’ opinions about the material cause, Aristotle now gives their opinions about the efficient cause, which is the source of motion. This is divided into two parts.

First, he gives the opinion of those who assigned without qualification a cause of motion and generation.

Second [97], he examines the opinion of those who posited an efficient cause, which is also the principle of good and evil in the world, at after these men (984b8).

In regard to the first he does two things.

First, he gives the reasoning which compelled them to posit an efficient cause.

Second [94], he shows the different positions which different men have held regarding this, at now in general (984a25).

He says (984a18), then, that some philosophers have proceeded in this way in positing a material cause, but that the very nature of reality clearly provided them with a course for understanding or discovering the truth, and compelled them to investigate a problem which led them to the efficient cause. This problem is as follows.

No thing or subject changes itself—for example, wood does not change itself so that a bed comes from it, nor does bronze cause itself to be changed in such a way that a statue comes from it—but there must be some other principle which causes the change they undergo, and this is the artist. But those who posited a material cause, whether one or more than one, said that the generation and corruption of things come from this cause as a subject. Therefore, there must be some other cause of change, and to seek this is to seek another genus of principle and cause, which is called the source of motion.

94. Now in general (984a25). He shows here that the philosophers have adopted three positions with respect to the foregoing issue. For those who adopted this course from the very beginning, and said that there is one material cause, were not greatly concerned with the solution of this problem. For they were content with their view of matter and neglected the cause of motion altogether.

95. But others, who said that all things are one, being defeated (as it were) by this issue since they were unable to go so far as to assign a cause of motion, denied motion altogether. Hence they said that the whole universe is one immobile being.

In this respect, they differed from the first philosophers of nature, who said that one cause is the substance of all things although it is moved by rarefaction and condensation, so that in this way many things come to be in some measure from one principle. However, they did not say that this principle is subject to generation and corruption in an absolute sense. For the view that nothing was generated or corrupted without qualification is an ancient one admitted by all of them, as is clear from what was said above [75].

But it was peculiar to these later thinkers to say that the whole of reality is one immobile being, devoid of every kind of motion. These men were Parmenides and Melissus, as will be explained below [138].

Hence it is evident that it was impossible for those who said that the whole is one immobile being to conceive of such a cause, that is, a cause of motion. By the very fact that they did away with motion, they sought in vain for a cause of motion. An exception was Parmenides, for even though he held that there is only one thing according to reason, he held that there are many things according to the senses, as will be stated below [101].

Hence, inasmuch as Parmenides held that there are many things, it was in keeping with his position to hold that there are many causes, one of which would be a mover and the others something moved. For just as he held that there are many things according to the senses, in a similar way it was necessary for him to hold that there is motion according to the senses, because a plurality of things can be understood to be produced from one subject only by some kind of motion.

96. Third, there were those who, in making the substances of things many, assented to the aforesaid reasoning by positing a cause of motion. For they maintained that the hot or the cold (that is, fire or earth) are causes; and of these they used fire as having a mobile (that is, an active) nature, but water, earth, and air they used in the opposite way, as having a passive nature. Thus fire was a sort of efficient cause, but the others a sort of material cause.

97. After these men (984b8). Here he gives the opinion of those who posited an efficient cause, not only as a principle of motion, but also as a principle of good and evil in things. In regard to this he does two things.

First, he expounds their views.

Second [107], he shows in what respect they failed in assigning the causes of things, at these thinkers (985a10).

In regard to the first he does two things.

First, he gives the reasons for their position by which they were induced to posit another cause besides the foregoing one.

Second [100], he shows how they posited this kind of cause in different ways, at and when someone (984b15).

He says first, then, that after the foregoing philosophers who held that there is only one material cause, or many bodies, one of which was active and the others passive, and after the other first principles given by them, men were again compelled by the truth itself, as we said, as was stated above [93], to seek the next principle (the one which naturally follows the foregoing one), namely, the cause of good. This is really the final cause, although it was held by them only accidentally, as will be seen below [177]. For they held that there is a cause of goodness in things only after the manner of an efficient cause. They were compelled to do this because the foregoing principles were not sufficient to account for the generation of the natural world, in which some things are found to be well disposed. The fact that bodies are conserved in their proper places and are corrupted outside of them proves this. So do the benefits resulting from the parts of animals, which are found to be disposed in this manner according as this is in keeping with an animal’s good state of being.

98. But neither fire nor earth nor any such bodies were held to be adequate causes of this kind of good disposition or state of being, which some things already have but others acquire by some kind of production. For these bodies act in one definite way according to the necessity of their proper forms, as fire heats things and tends upward, and water cools things and tends downward. But the aforesaid benefits and good states of the being of things must have a cause which is not limited to one effect only, since the parts of different animals are found to be disposed in different ways, and in each one insofar as it is in keeping with its nature.

99. Hence, it is not reasonable that fire or earth or the like should be the cause of the aforesaid good state of being which things have, nor was it reasonable that these men should have thought this to be the case. Nor again would it be reasonable to say that these things are chance occurrences—that is, that they are accidental or come about by chance, and that their causality is changed only fortuitously—although some of these thinkers had said this, as Empedocles and all those who posited a material cause, as is evident in Physics 2.

However, this is also seen to be false because good dispositions of this kind are found either always or for the most part, whereas things that come about by chance or fortune do not occur always or for the most part, but seldom. For this reason, then, it was necessary to discover besides the four elements some other principle which would account for the good dispositions of things. Another text has nor again would it be right to attribute so important a matter to chance occurrence and fortune, but this means the same as the above.

Opinions on efficient cause: intellect or love

100. And when someone said (984b15). Here he gives in detail the opinions about the aforesaid principle.

First, he gives the opinions of those who held that there is one efficient cause;

second [104], the opinions of those who held that there are two such causes, at but since there would seem (984b32).

In regard to the first he does two things.

First, he gives the views of those who held that the first efficient cause is an intellect;

second [101], the opinions of those who held that it is love, at now someone might (984b23).

He says, then, that after the foregoing doctrine someone appeared who said that there is an intellect present in nature at large, just as there is in animals, and that this is the cause of the world and the order of the whole (that is, of the universe), in which order the good of the entire universe and that of every single part consists. And this man atoned for the first philosophers by reducing to pure truth those who said unreasonable things and did not mention this kind of cause. Now Anaxagoras clearly stated this doctrine, although another philosopher—Hermotimus of Clazomenae—first gave him the idea of proposing this opinion. Hence it is evident that those who held this opinion claimed at the same time that the principle by which things are well disposed and the one which is the source of motion in things are one and the same.

101. Now someone might (984b23). Here he gives the opinion of those who claimed that love is the first principle, although they did not hold this very explicitly or clearly. Accordingly, he says that some suspected that Hesiod had sought for such a principle to account for the good disposition of things, or anyone else who posited love or desire in nature. For when Parmenides attempted to explain the generation of the universe, he said that in the establishing of the universe, love, the first of all the gods, was made.

Nor is this opposed to his doctrine that there is one immobile being, of which Aristotle speaks here, because this man held that there are many things according to the senses, although there is only one thing according to reason, as was stated above and will be stated below. Moreover, he called the celestial bodies (or perhaps certain separate substances) gods.

102. But Hesiod said that first of all there was chaos, and then broad earth was made to be the receptacle of everything else; for it is evident that the receptacle and place are principles, as is stated in Physics 4. And he also held that love, which instructs all the immortals, is a principle of things. He did this because the communication of goodness seems to spring from love, for a good deed is a sign and effect of love. Hence, since corruptible things derive their being and every good disposition from immortal beings of this kind, this must be attributed to the love of the immortals. Furthermore, he held that the immortals are either the celestial bodies themselves or material principles themselves. Thus he posited chaos and love as though there had to be in existing things not only a material cause of their motions, but also an efficient cause which moves and unites them, which seems to be the office of love. For love moves us to action because it is the source of all the emotions, since fear, sadness and hope proceed only from love. That love unites things is clear from this: love itself is a certain union between the lover and the thing loved, seeing that the lover regards the beloved as himself. This man Hesiod is to be numbered among the poets who lived before the time of the philosophers.

103. Now, as to which one of these thinkers is prior, that is, more competent in knowledge, whether the one who said that love is the first principle, or the one who said that intellect is, can be decided later on, that is, where God is discussed. He calls this decision an arrangement, because the degree of excellence belonging to each man is allotted to him in this way. Another translation states this more clearly: therefore, in what order it is fitting to go over these thinkers, and who in this order is prior, can be decided later on.

Love and hate as causes

But since there would seem to be in nature things that are contrary to those that are good, and not only order and good but also disorder and what is base, and evil things more numerous than good ones, and base things more numerous than noble ones, for this reason another thinker introduced love and strife as causes, each of its own type of effects.

For if anyone grasps what Empedocles said, taking it according to its meaning rather than according to its faltering expression, he will find that love is the cause of things that come to be by aggregation, and strife the cause of evil things.

Hence, if anyone were to say that Empedocles, in a sense, both said and was the first to say that good and evil are principles, he would perhaps speak correctly, that is, if the cause of all good things is good and that of all evil things is evil.

These thinkers, then, as we have said, to this extent have touched on two of the causes which we established in the Physics—matter and the source of motion—though only obscurely and with no clarity, much as untrained men conduct themselves in battle. For the latter, though encircled, often deal telling blows, but without science. In the same way these thinkers do not seem to be aware of what they are saying. For it seems that they almost never make use of the causes except to a small degree.

Anaxagoras uses “intellect” in an artificial way in generating the world. For when he is in difficulty as to what is necessarily the cause of something, he drags in this intellect; but in other cases he makes everything but intellect the cause of what comes to be.

Empedocles, it is true, makes greater use of causes than Anaxagoras, though not sufficiently; nor does one find in his use of them what he professed. In many places he argues that love separates things, and that strife brings them together. For when being itself is separated into its elements by strife, then fire and each of the other elements are brought together into a unity. But when they are united by love, the particles must again be separated out from each element.

In contrast to the first philosophers, then, Empedocles was the first to introduce this cause, dividing it in such a way as to make the source of motion not a single principle, but different and contrary ones.

Moreover, he was the first to claim that the elements, which are said to belong to the species of matter, are four in number, although he does not use them as four but as two, taking fire by itself alone, and its opposites—earth, air, and water—as a single nature (984a25). But anyone may see this by studying his basic sayings.

This philosopher, then, as we have said, has spoken in this way about the principles of things and their number.

104. Here Aristotle gives the opinion of those who posited contrariety in beings of this kind, and the reason which moved them, which is as follows.

There would seem to be in nature things that are contrary to those that are good, because in nature one finds not only things that are ordered and good, but sometimes things that are disordered and base. Now it cannot be said that evil things have no cause but happen by chance, because evil things are more numerous than good ones, and base things more numerous than those which are unqualifiedly noble. But those things that come to be by chance without a definite cause do not occur for the most part, but in the smaller number of cases.

Hence, since contrary effects have contrary causes, it was necessary to hold as a cause of things not only love, from which the order and good in things originate, but also hate, which is the source of disorder and baseness or evil in things, so that in this way particular instances of evil and good have their own type of causes.

105. That this was the reason which moved Empedocles is evident if anyone grasps what he says, taking his statement according to its meaning rather than according to the words which he used imperfectly and as though he were stammering.

For he said that it is the office of love to bring the elements together, and of hate to separate them. But since the generation of things is a result of the coming together of the elements (by reason of which there is being and good in things), and their corruption a result of the separation of the elements (which is the way to non-being and evil), it is now evident that he wanted love to be the cause of things that come to be by aggregation, that is, of good things, and hate the cause of evil things.

Thus if one were to say that Empedocles was the first to maintain that good and evil are principles, he would perhaps speak correctly.

106. That is to say, this would follow if Empedocles did hold that good is the cause of all good things, and evil the cause of all evil things. For it is evident that he posited evil as the cause of some evil things, namely, of corruption, and good as the cause of some good things, namely, of generation. But because it would not follow that all good things would be caused by friendship or all evil things by hate, since the parts of the world would be differentiated by hate and fused together by friendship, therefore he did not always hold that good is the cause of good things, and evil the cause of evil things.

107. These thinkers (985a10). Here he shows that in giving these causes the philosophers treated them inadequately.

First, he mentions them in a general way.

Second [108], he treats each one individually, at Anaxagoras (985a18).

He says first, then, that these philosophers—Anaxagoras and Empedocles—arrived at a doctrine of two of the causes which have been established in the Physics, namely matter and the cause of motion, although they treated these obscurely and with no clarity because they did not explain that those principles which they held to be the causes of things could be reduced to these genera of causes. But insofar as they posited two of these causes, they may be likened to untrained warriors who, though encircled by the enemy, sometimes strike good blows, not by art but by chance. This is evident because even though they happen to do this sometimes, this does not occur always or for the most part. In like manner, too, these philosophers were not accustomed to express themselves accurately, nor was it their custom to speak knowingly, that is, as men who know.

Hence another translation has: but these men neither have science, nor are they to be compared with men who realize what they are saying. This is shown by the fact that, although they had proposed these causes, they hardly ever used them, because they employed them in few instances. Hence it seems that they introduced them not as a result of art, but by accident, because they were moved to do so by necessity.

108. Anaxagoras (985a18). Here he shows in what particular respect the view of each is unsatisfactory.

First, he speaks of Anaxagoras;

second [109], of Empedocles, at Empedocles (985a21).

He says first, then, that Anaxagoras uses “intellect” to generate the world, and in so doing he seems to speak of it in an artificial way. For when he inquires about the causes of the world’s generation, he drags it in of necessity—that is, he invents this intelligence only because he is unable to attribute the generation of the world to any other cause which would differentiate things except to one which is essentially distinct and unmixed, and intellect is a thing of this kind. But in all other cases he draws his causes from any other source rather than intellect, as in the case of the particular natures of things.

109. Empedocles (985a21). Here he shows in what respect Empedocles’ doctrine is inadequate, and in regard to this he does two things.

First, he shows in what respect Empedocles’ doctrine is inadequate.

Second [111], he explains what Empedocles himself held in contrast to the other philosophers, at in contrast (985a29).

He says, first (985a21), that Empedocles, in dealing with the particular natures of things, makes greater use of causes posited by him (the four elements, and love and hate) than Anaxagoras did, because he reduced the generation and corruption of particular things to these causes, and not to intelligence as Anaxagoras did. But Empedocles failed in two ways.

First, he failed because he does not treat causes of this kind adequately enough; for he uses things that are not self-evident as though they were self-evident axioms, as is stated in Physics 1, insofar as he assumed that they are self-evident, because at one definite time strife has dominion over the elements and at another does love.

110. Second, he failed because in the matters which he investigates, one does not find what he has professed (that is, what he held as a principle)—namely, that love combines things and that strife separates them, because in many places love must on the contrary separate or divide things, and strife bring them together or unite them. For when the universe itself is separated out, or divided into its parts, by hate, as occurs when the world is generated, all particles of fire are then combined into one whole, and so also are the individual particles of the other elements brought together, or joined to each other. Hence, strife not only separates the particles of fire from those of air, but also brings together the particles of fire. But, on the other hand, when the elements come together through love, which occurs when the universe is destroyed, the particles of fire must then be separated from each other, and so also must the particles of the other elements. For fire can be mixed with air only if the particles of fire are separated from each other. And the same is true of the particles of air only if these elements penetrate one another, so that love not only unites unlike things but also separates like things, according to what follows from his position.

111. In contrast (985a29). Here he shows in what respect Empedocles’ own doctrine differs from that of the other philosophers. He says that Empedocles maintained two things in contrast to the others.

First, he divided the cause which is the source of motion into two contrary parts.

Second, he held the material cause to be constituted of four elements—not that he uses the four elements as four, but rather as two, because he contrasts fire with the other three, saying that fire is active in nature and the others passive in nature.

Anyone can gather this from the elements of things treated by him, or from his basic sayings in the sense of the rudiments of the doctrine which he propounded.

Another version reads from his verses, because he is said to have written his philosophy in meters. And still another version, which says from his statements, agrees with this. As has been stated, then, this philosopher was the first to stipulate in this way that the principles of things are four in number, and to speak of those which have been mentioned.

Atomists’ and Pythagoreans’ opinions

Leucippus and his colleague Democritus say that the elements of things are the full and the void, calling the one being and the other non-being. For this reason they say that the full or solid is being, and the void is non-being. For this reason too they say that being no more is than non-being, because the void no more is than body; and they hold that these are the material causes of things.

And just as those who make the underlying substance one generate other things from this by means of its attributes, holding that rarity and density are the principles of these attributes, in the same way these men say that the differences of the atoms are the causes of different things. These differences, they say, are three: shape, arrangement, and position. For they claim that what exists differs only by rhythm, inter-contact, and turning; of these, rhythm means shape, inter-contact arrangement, and turning position. For A differs from N in shape, and Z from N in position.

But with regard to motion, from whence it comes or how it is present in things, these men carelessly dismissed this question as the other thinkers did. As we have said before, then, these two types of causes seem to have been investigated to this extent by the first thinkers.

But during the time of these and prior to them lived those called the Pythagoreans who dealt with mathematics and were the first to develop it; having been reared in mathematics, they thought that their principles were the principles of all things.

But since among these principles numbers are naturally first, they thought they saw in numbers, more than in fire and earth, many resemblances to things that are and come to be, because this attribute of numbers is justice, another is soul and mind, and still another is time, and similarly, so to speak, with each thing.

Moreover, since they considered the attributes and ratios of harmonies in terms of numbers, and since other things in their whole nature seemed to be likened to numbers, and since numbers are the first things in the whole of nature, they thought that the elements of numbers are the elements of all things, and that the whole heaven is a harmony and number. And whatever they had revealed in the case of numbers and harmonies which they could show to be in agreement with the motions and parts of the heavens, and its whole arrangement, they collected and adapted to these. And if anything was lacking anywhere, they called it in order that their undertaking might be complete. I mean that since the number ten seems to be the perfect number and to comprise the whole nature of numbers, they said that the bodies which move in the heavens are ten in number; but as only nine are observable they therefore invented a tenth, the counter-earth. These things have been dealt with more exactly in another work.¹

112. Here he begins to give the positions of those who held strange and obscure views about the principles of things.

First, he gives the position of those who held that there are many principles of things;

and second [134] the position of those who held that there is only one being, at but there are some (983b27).

In regard to the first he does two things.

First, he gives the opinion of Leucippus and Democritus, who held that the principles of things are bodily.

Second [119], he gives the opinion of the Pythagoreans, who held that the principles of things are incorporeal entities, at but during the time (985b23).

In regard to the first he does two things.

First, he gives the opinion of Democritus and Leucippus about the material cause of things;

and second [115], their opinion about the cause of diversity, that is, how matter is differentiated into many things. In this discussion, the cause of the generation and corruption of things also becomes evident; this is a point on which these men agreed with the ancient philosophers, at and just as those who (985b10).

He says, then, that two philosophers, Democritus and Leucippus, who are called friends because they followed each other in all things, held that the principles of things are the full and the void or “empty,” of which the full is being, and the void or empty is non-being.

113. Now in order to clarify this opinion we must recall what the Philosopher says in On Generation and Corruption 1, where he treats it more fully. For certain philosophers had held that everything is one continuous immobile being, because it seems that there cannot be motion without a void, or any distinction between things, as they said. And though they could not comprehend the privation of continuity (by reason of which bodies must be understood to be differentiated) except by means of a void, they claimed that the void existed in no way. Democritus, who came after them, and who agreed with their reasoning but was unable to exclude diversity and motion from things, held that the void existed, and that all bodies are composed of certain indivisible bodies. He did this because it seemed to him that no reason could be given why the whole of being should be divided in one part rather than another.

And lest he should hold that the whole of being is continuous, he therefore chose to maintain that this whole is divided everywhere and in its entirety; this could not be the case if anything divisible remained undivided. And according to him indivisible bodies of this kind can neither exist nor be joined together except by means of the void. For if the void did not come between any two of them, one continuous whole would result from the two, which he did not hold for the above reason. Hence he said that the continuous quantity of each body is constituted both of those indivisible bodies filling indivisible spaces and of certain empty spaces, which he called pores, coming between these indivisible bodies.

114. And since the void is non-being and the full is being, it is evident from this that he did not hold that a thing was constituted by being rather than non-being, because the bodies did not constitute things more than the void or the void more than bodies, but he said that a body is composed at once of these two things, as is clear in the text. Hence he held that these two things are the causes of things as their matter.

115. And just as those (985b10). Here he shows in what respect these philosophers agreed with the ancients who claimed that there is only one matter. He indicates agreement in two respects.

First, just as the ancient philosophers held that there is one matter, and from that one matter generated something else according to the different attributes of matter (namely, the rare and dense, which they accepted as the principles of all other attributes), in a similar way Democritus and Leucippus said that there were different causes of different things (namely, of the bodies composed of these indivisible bodies)—that is, that different beings were produced as a result of certain differences of these indivisible bodies and their pores.

116. Now they said that these differences are first differences in shape, because things are angular, circular, and square;

second, differences in arrangement, that is, insofar as the indivisible bodies are prior or subsequent;

third, differences in position, insofar as these bodies are in front or behind, right or left, or above and below. Hence they said that one being differs from another either by rhythm, which is shape, or by inter-contact, which is arrangement, or by turning, which is position.

117. He illustrates this by using the letters of the Greek alphabet, which differ from each other in shape just as in our alphabet one letter also differs from another; for A differs from N in shape. Again, AN differs from NA in arrangement, because one letter is placed before the other. And one letter also differs from another in position, as Z from N, just as in our language we also see that semivowels cannot stand after liquids preceded by mutes in the same syllable.

Therefore, just as “license” and “silence” come from the same letters as a result of the letters being disposed in different ways because of this threefold difference, in a similar fashion different species of things are produced from the same indivisible bodies as a result of the latter being disposed in different ways.

118. The second respect in which these philosophers agreed with the ancients is this. Just as the ancient philosophers neglected to posit a cause which accounts for motion in things, so also did these men, although they would say that these indivisible bodies are capable of self-motion. Thus it is evident that these philosophers mentioned only two of the causes: all of them spoke of the material cause, and some of the efficient cause.

119. But during the time of these (985b23). Here he gives the opinions of the Pythagoreans, who held that numbers are the substances of things. In regard to this he does two things.

First, he gives their opinions about the substance of things;

and second [124], their opinions about the principles of things, at but the reason (986a13).

In regard to the first he gives two reasons by which they were led to assert that numbers are the substances of things.

He gives the second reason [121] where he says, moreover, since they considered (985b31).

He says that the Pythagoreans were philosophers who lived during the time of these, that is, they were contemporaries of some of the foregoing philosophers; and prior to them, because they preceded some of them.

Now it must be understood that there were two groups of philosophers. One group was called the Ionians, who inhabited the land which is now called Greece. This group originated with Thales, as was pointed out above [77]. The other group of philosophers were the Italians, who lived in that part of Italy which was once called Greater Greece and is now called Apulia and Calabria. The leader of these philosophers was Pythagoras, a native of Samos, so called from a certain city of Calabria. These two groups of philosophers lived at the same time, and this is why he says that they lived during the time of these and prior to them.

120. These Italian philosophers, also called Pythagoreans, were the first to develop certain mathematical entities, so that they said that these are the substances and principles of sensible things. He says that they were the first because the Platonists were their successors. They were moved to bring in mathematics because they were brought up in the study of these sciences, and therefore they thought that the principles of mathematics are the principles of all existing things. For men are wont to judge about things in terms of what they already know. And since among mathematical entities numbers are first, these men therefore tried to see resemblances of natural things, both as regards their being and generation, in numbers rather than in the sensible elements (earth, water, and the like).

For just as the foregoing philosophers adapted the attributes of sensible things to those of natural things because of a certain resemblance which they bear to the properties of fire, water, and bodies of this kind, in a similar fashion these mathematicians adapted the properties of natural things to the attributes of numbers when they said that some one attribute of number is the cause of justice, another the cause of soul and intellect, and still another the cause of opportunity, and so on for other things. And in this way the attributes of numbers are understood to be the intelligible structures and principles of all things appearing in the sensible world, both in the realm of voluntary matters (signified by justice), and in that of the substantial forms of natural things (signified by soul and intellect), and in that of accidents (signified by opportunity).

Strange and obscure views about the principles of things; hidden principles: numbers

121. Moreover, since they (985b31). Here he gives the second reason which motivated them. For they thought of the attributes of harmonies—musical consonants and their ratios or proportions—in terms of the nature of numbers. Hence, since harmonious sounds are certain sensible things, they attempted by the same reasoning to liken all other sensible things (both in their intelligible structure and in their whole nature) to numbers, so that numbers are the first things in the whole of nature.

122. For this reason too they thought that the principles of numbers are the principles of all existing things, and they said that the whole heaven is merely a kind of nature and harmony of numbers, a kind of numerical proportion similar to the proportion found in harmonies. Hence, whatever they had revealed, or had shown, which they could adapt to numbers and harmonies, they also adapted both to the changes undergone by the heavens (as its motion, eclipses, and the like), and to its parts (as the different orbs), and to the whole arrangement of the heavens (as the different stars and different figures in the constellations).

123. And if anything was lacking in the observable order of things that did not seem to be adapted to numbers, they called it in, that is, they invented something new in order that their whole undertaking, which was to adapt sensible things to numbers, might be made complete, until they had adapted all sensible things to numbers, as is evident in one example. For the number ten seems to be the perfect number, because it constitutes the first limit and contains within itself the nature of all numbers; for all other numbers are merely a kind of repetition of the number ten. This is why Plato counted up to ten, as Aristotle says in Physics 4.

Hence Pythagoras also said that the spheres which move in the heavens are ten in number, although only nine of these are observable; we observe seven in the motions of the planets, an eighth in the motion of the fixed stars, and a ninth in the daily motion, which is the first motion.

But Pythagoras adds a tenth sphere, which was that of the counter-earth, that is, which is moved in the opposite direction to the motion in the lower spheres and therefore produces a contrary sound. For he said that a kind of harmony results from the motion of the celestial bodies, so that just as a harmony is produced from a proportion of contrary sounds of low and high notes, in a similar way he claimed that in the heavens there was a single motion in the opposite direction to that of the other motions in order that a harmony might result. According to this position, the daily motion belonged to the tenth sphere, which moves from east to west, the other spheres being revolved in the opposite direction from west to east. In fact, according to him, it could have been the ninth sphere which first revolved all the lower spheres in the opposite direction to the first motion. The things that pertain to this opinion of Pythagoras are considered more extensively and more definitely in the last books of this science.

The Pythagoreans’ doctrine of contraries

But the reason we have come [to examine these philosophers] is that we may also learn from them what they hold the principles of things to be, and how these principles fall under the causes already described. Now these men also seem to think that number is the principle of existing things both as their matter and as their attributes and states.

According to them, the elements of number are the even and odd; of these the latter is limited and the former is unlimited. The unit is composed of both of these, since it is both even and odd, and number is derived from the unit. And number, as has been stated (985b31), constitutes the whole heaven.

But other members of the same school say that the principles of things are ten in number, which they give as co-elements: the limited and unlimited, even and odd, one and many, right and left, masculine and feminine, rest and motion, straight and curved, light and darkness, good and evil, the quadrangular and rectangular.

Alcmaeon of Croton seems to have formed his opinion in the same way, and either he derived the theory from them or they from him; for Alcmaeon (who had reached maturity when Pythagoras was an old man) expressed views similar to those of the Pythagoreans.

For he says that many things in human affairs are in twos, calling them contrarieties, not distinguished as these men had distinguished them, but such as are taken at random, for example, white and black, sweet and bitter, good and evil, small and great. It is true that this philosopher threw out vague remarks about the other contrarieties, but the Pythagoreans have declared both what the contrarieties are and how many there are.

From both of these, then, we can gather this much, that contraries are the principles of existing things; but how many they are and that they are these we must gather from other thinkers. The way in which many principles can be brought together under the causes described is not clearly expressed by them, although they seem to allot their elements to the species of matter; for they say that substance is composed and molded out of these as something inherent.

From these remarks, then, it is possible to get an adequate understanding of the ancient philosophers’ meaning who said that the elements of things are many.

124. Here he states what the Pythagoreans had to say about the principles of things. In regard to this he does two things.

First, he expounds their opinions about the principles of things;

second [132], he indicates to what genus of cause the principles laid down by them are reduced, at from both of these (986b2).

In regard to the first he gives three opinions.

The second [127] begins at the words, but other members (986a22);

and the third [131] at Alcmaeon of Croton (986a27).

He says first (986a13), then, that the reason he came to examine the opinions of the Pythagoreans is that he might show from their opinions what the principles of things are and how the principles laid down by them fall under the causes given above. For the Pythagoreans seem to hold that number is the principle of existing things as matter, and that the attributes of number are the attributes and states of existing things. By “attributes” we mean transient accidents, and by “states,” permanent accidents. They also held that evenness of number is justice, because of the equality of division. Such a number is evenly divided into two parts right down to the unit: for example, the number eight is divided into two fours, the number four into two twos, and the number two into two units. And in a similar way they likened the other accidents of things to the accidents of numbers.

125. In fact, they said that the even and odd, which are the first differences of numbers, are the principles of numbers. And they said that even number is the principle of unlimitedness and odd number the principle of limitation, as is shown in the Physics 3; but in reality the unlimited seems to result chiefly from the division of the continuous. An even number is capable of division, but an odd number includes within itself an even number plus a unit, and this makes it indivisible.

He also proves this as follows. When odd numbers are added to each other successively, they always retain the figure of a square, whereas even numbers change their figure. For when the number three is added to the unit, which is the principle of numbers, the number four results, which is the first square, because two times two equals four. Again, when the number five, which is an odd number, is added to the number four, the number nine results, which is also a square number. And so on with the others.

But if the number two, which is the first even number, is added to the number one, a triangular number results—the number three. And if the number four, which is the second even number, is added to the number three, there results a septangular number—the number seven. And when even numbers are added to each other successively in this way, they do not retain the same figure. This is why they attributed the unlimited to the even and the limited to the odd. And since limitedness pertains to form, to which active power belongs, they therefore said that even numbers are feminine, and odd numbers masculine.

126. From these two (namely, the even and odd, the limited and unlimited), they produced not only number but also the unit itself—unity. For unity is virtually both even and odd, because all differences of number are virtually contained in the unit, all being reduced to the unit. Hence, in the list of odd numbers the unit is found to be the first. And the same is true in the list of even numbers, square numbers, and perfect numbers. This is also the case with the other differences of number, because even though the unit is not actually a number, it is still virtually all numbers. And just as the unit is said to be composed of the even and odd, in a similar way number is composed of units. Indeed, the heavens and all sensible things are composed of numbers. This was the sequence of principles which they gave.

127. But other members (986a22). Here he gives another opinion which the Pythagoreans held about the principles of things. He says that among these same Pythagoreans there were some who claimed that there is not just one contrariety in principles, as the foregoing did, but ten principles, which they give as co-elements, that is, by taking each of these principles with its co-principle, or contrary.

The reason for this position was that they took not only the first principles but also the proximate principles attributed to each genus of things. Hence, they posited first the limited and the unlimited (as did those who have just been mentioned), and subsequently the even and the odd (to which the limited and unlimited are attributed). And because the even and odd are the first principles of things, and numbers are first produced from them, they posited third a difference of numbers—namely, the one and the many, both of which are produced from the even and the odd. Again, because continuous quantities are composed of numbers, inasmuch as they understood numbers to have position (for, according to them, the point was merely the unit having position, and the line the number two having position), they therefore claimed next that the principles of positions are the right and left, for the right is found to be perfect and the left imperfect. Therefore, the right is determined from the aspect of oddness, and the left from the aspect of evenness. But because natural bodies have both active and passive powers in addition to mathematical extensions, they therefore next maintained that masculine and feminine are principles. For masculine pertains to active power, and feminine to passive power; of these, masculine pertains to odd number and feminine to even number, as has been stated [125].

128. Now it is from active and passive power that motion and rest originate in the world. Of these, motion is placed in the class of the unlimited and even, because it partakes of irregularity and otherness, and rest in the class of the unlimited and odd. Furthermore, the first differences of motions are the circular and straight, so that as a consequence of this the straight pertains to even number. Hence they said that the straight line is the number two, but that the curved or circular line, by reason of its uniformity, pertains to odd number, which retains its undividedness because of the form of unity.

129. And they posited principles not only to account for the natural operations and motions of things, but also to account for the operations of living things. In fact, they held that light and darkness are principles of knowing, but that good and evil are principles of appetite. For light is a principle of knowing, whereas darkness is ascribed to ignorance; good is that to which appetite tends, whereas evil is that from which it turns away.

130. Again, they said that the difference of perfection and imperfection is found not only in natural things and in voluntary powers and motions, but also in continuous quantities and figures. These figures are understood to be something over and above the substances of continuous quantities, just as the powers responsible for motions and operations are something over and above the substances of natural bodies. Therefore, with reference to this they held that what is quadrangular (that is, the square and the rectangle) is a principle. Now a square is said to be a figure of four equal sides whose four angles are right angles, and such a figure is produced by multiplying a line by itself. Therefore, since it is produced from the unit itself, it belongs to the odd numbers. But a rectangle is defined as a figure whose angles are all right angles and whose opposite sides alone, not all sides, are equal to each other. Hence it is clear that, just as a square is produced by multiplying one line by itself, in a similar way a rectangle is produced by multiplying one line by another. Hence it pertains to the even numbers, of which the first is the number two.

131. Alcmaeon of Croton (986a27). Here he gives the third opinion of the Pythagoreans, saying that Alcmaeon of Croton, so named from the city in which he was raised, seems to maintain somewhat the same view as that expressed by these Pythagoreans, namely, that many contraries are the principles of things. For either he derives the theory from the Pythagoreans, or they from him. That either of these might be true is clear from the fact that he was a contemporary of the Pythagoreans, granted that he began to philosophize when Pythagoras was an old man.

But whichever happens to be true, he expressed views similar to those of the Pythagoreans. For he said that many of the things in the realm of human affairs (that is, many of the attributes of sensible things) are arranged in pairs, understanding by pairs opposites which are contrary. Yet in this matter he differs from the foregoing philosophers, because the Pythagoreans said that determinate contraries are the principles of things. But he throws them in, as it were, without any order, holding that any of the contraries which he happened to think of are the principles of things, such as white and black, sweet and bitter, and so on.

132. From both of these (986b2). Here he gathers together from the above remarks what the Pythagoreans thought about the principles of things, and how the principles which they posited are reduced to some genus of cause. He says, then, that from both of those mentioned above (namely, Alcmaeon and the Pythagoreans), it is possible to draw one common opinion not expressed by earlier thinkers: the principles of existing things are contraries. This must be understood with reference to the material cause.

For Empedocles posited contrariety in the case of the efficient cause, and the ancient philosophers of nature posited contrary principles, such as rarity and density, although they attributed contrariety to form. But even though Empedocles held that the four elements are material principles, he still did not claim that they are the first material principles by reason of contrariety, but because of their natures and substance. These men, however, attributed contrariety to matter.

133. The nature of the contraries posited by these men is evident from the foregoing discussion. But how the aforesaid contrary principles posited by them can be brought together under (or reduced to) the types of causes described is not clearly expressed (or distinctly stated) by them. Yet it seems that such principles are allotted to the species of material cause, for they say that the substance of things is composed and molded out of these principles as something inherent, and this is the notion of a material cause. For matter is that from which a thing comes to be as something inherent. This is added to distinguish it from privation, from which something also comes to be but which is not inherent, as the musical is said to come from the non-musical.

Eleatics and Pythagoreans’ opinions

But there are some who spoke of the whole as if it were a single nature, although the statements which they made are not all alike with regard to either their acceptableness or their conformity with nature.

Therefore, a consideration of these men pertains in no way to the present investigation of causes. For they do not, like certain of the philosophers who supposed being to be one, still generate it from the one as matter; but they speak of this in another way. For the others assume motion when they generate this whole, whereas these thinkers say it is immobile.

Yet their opinion is relevant to the present investigation to some extent; for Parmenides seems to touch on unity according to concept and Melissus on unity according to matter. This is why the former says that it is limited, and the latter that it is unlimited. Xenophanes, the first of those to speak of the one (for Parmenides is said to have been his disciple), made nothing clear, nor does he seem to come up to these men. But with regard to the whole heaven he says that the one is God.

As we have stated, then, these men must be dismissed for the purposes of the present inquiry. In fact, two of them—Xenophanes and Melissus—are to be disregarded altogether as being a little too rustic.

Parmenides, however, seems to speak with more insight, for he thought that besides being there is only non-being, and this is thought to be nothing. This is why he thinks that being is necessarily one and nothing else. We have discussed this point more clearly in the Physics.

But being compelled to follow the observed facts, and having assumed that what is one from the viewpoint of reason is many from the viewpoint of the senses, he postulates in turn two principles (that is, two causes), the hot and cold, calling the one fire and the other earth. Of these he ranks the hot with being and the cold with non-being.

From what has been said, then, and from the wise men who have already agreed with this reasoning, we have acquired these things. From the first philosophers we have learned that the principle of all things is bodily, because water and fire and the like are bodies; and from some we have learned that there is one bodily principle, and from others, many (although both suppose that these belong to the species of matter).

And from others we have learned that in addition to this cause there is the source from which motion begins, which some claim to be one and others two. Down to the Italian philosophers, then, and independent of them, others have spoken of these things in a more trivial way, except that, as we have said, they have used two kinds of causes, and one of these—the source of motion—some thinkers consider as one and others as two.

Now the Pythagoreans have spoken of these two principles in the same way, but added this much (which is peculiar to them)—they did not think that the limited, unlimited, and one are different natures, like fire or earth or anything else of this kind, but that the unlimited itself and the one itself are the substance of the things of which they are predicated. And this is why they considered number as the substance of all things.

These thinkers, then, have expressed themselves thus with regard to these things, and they began to discuss and define the “what” itself of things, although they treated it far too simply. For they defined things superficially and thought that the substance of a thing is that to which a given definition first applies—just as if one supposed that double and two are the same because that to which the double first belongs is the number two.

But perhaps “to be double” is not the same as “to be two”; and if it is not, then the one itself will be many. This, indeed, is the conclusion which they reached. From the first philosophers and others, then, this much can be learned.

Unitarians

134. Here he gives the opinions of those philosophers who spoke of the whole universe as one being; and in regard to this he does two things.

First, he gives the opinion which they held in common;

and second [135], he shows how a consideration of this opinion is relevant to the present treatise, and how it is not, at therefore, a consideration (986b12).

He says, then, that there were certain philosophers, other than those just mentioned, who spoke of the whole, that is, of the universe, as if it were of one nature—as if the whole universe were a single being or a single nature. However, not all maintained this position in the same way, as he will make clear below [138–49]. Yet in the way in which they differ their statements are neither acceptable nor in conformity with nature. None of their statements are in conformity with nature, because they did away with motion in things. And none of them are acceptable, because they held an impossible position and used sophistical arguments, as is clear in Physics 1.

135. Therefore, a consideration (986b12). Here he shows how a consideration of this position pertains to the present investigation and how it does not.

He shows, first, that it has no bearing on this investigation if we consider their position itself;

second [137], that it does have a bearing on this investigation if the reasoning or method behind their position is considered, at yet their opinion (986b17).

He says, then, that since these philosophers held that there is only one being, and a single thing cannot be its own cause, it is clear that they could not discover the causes. For the position that there is a plurality of things demands a diversity of causes in the world. Hence, a consideration of their statements is of no value for the purposes of the present study, which deals with causes.

But the situation is different in the case of the ancient philosophers of nature, who held that there is only one being, and whose statements must be considered here. For they generated many things from that one principle as matter, and thus posited both cause and effect. But these men with whom we are now dealing speak of this in a different way. For they do not say that all things are one materially, so that all things are generated from one matter, but that all things are one in an absolute sense.

136. The reason for this difference is that the ancient philosophers of nature added motion to the view of those who posited one being and one principle, and said that this one being is mobile; therefore, different things could be generated from that one principle by a certain kind of motion (that is, by rarefaction and condensation). And they said that the whole universe with respect to the diversity found in its parts is generated in this way. Yet, since they held that the only change affecting substance is accidental, as was stated above [75], the conclusion then followed that the whole universe is one thing substantially but many things accidentally. But these thinkers said that the one being which they posited is immobile in an absolute sense; therefore, a diversity of things could not be produced from that one being. Since this being is immobile, they could not posit any plurality in the world, either substantial or accidental.

137. Yet their opinion (986b17). Here he shows how their opinion is relevant to the present inquiry.

First, he deals with all of these thinkers in general;

second [142], with Parmenides in particular, at as we have stated (986b25).

He says first that, although they did away with diversity in the world (and consequently with causality), nevertheless their opinion is relevant to the present study so far as regards the method by which they establish their position and the reason for their position.

138. Parmenides, who was a member of this group, seems to touch on unity according to concept, or according to form, for he argued as follows. Besides being there is only non-being, and non-being is nothing. Therefore, besides being there is nothing. But being is one. Therefore, besides the one there is nothing. In this argument he clearly considered the concept itself of being, which seems to be one, because nothing can be understood to be added to the concept of being by which it might be diversified. For whatever is added to being must be other than being. But anything such as this is nothing.

Hence it does not seem that this can diversify being, just as we also see that differences added to a genus diversify it, even though these differences are outside the substance of that genus. For differences do not participate in a genus, as is stated in the Topics 4—otherwise a genus would have the substance of a difference. And definitions would be nonsense if when a genus is given the difference were added, granted that the genus were the substance of the difference, just as it would be nonsense if the species were added. Moreover, a difference would not differ in any way from a species. But those things that are outside the substance of being must be non-being, and thus cannot diversify being.

139. But they were mistaken in this matter, because they used being as if it were one in intelligible structure and in nature, like the nature of any genus. But this is impossible. For being is not a genus but is predicated of different things in many ways. Therefore, in Physics 1, it is said that the statement being is one is false. For being does not have one nature like one genus or one species.

140. But Melissus considered being in terms of matter. For he argued that being is one by reason of the fact that being is not generated from something prior, and this characteristic pertains properly to matter, which is ungenerated.

For he argued in this way. Whatever is generated has a starting-point. But being is not generated and therefore does not have a starting-point. But whatever lacks a starting-point lacks an end and therefore is unlimited. And if it is unlimited, it is immobile, because what is unlimited has nothing outside itself by which it is moved. That being is not generated he proves thus. If being were generated, it would be generated either from being or from non-being. But it is not generated from non-being, because non-being is nothing and from nothing nothing comes. Nor is it generated from being, because then a thing would be before it came to be. Therefore, it is not generated in any way.

In this argument he obviously treats being as matter, because it is of the very nature of matter not to be generated from something prior. And since limitation pertains to form, and unlimitedness to matter, Melissus, who considered being under the aspect of matter, said that there is one unlimited being. But Parmenides, who considered being under the aspect of form, said that being is limited. Hence, insofar as being is considered under the aspect of form and matter, a study of these men is relevant to the present investigation, because matter and form are included among the causes.

141. But Xenophanes, who was the first of those to say that everything is one (and therefore Parmenides was his disciple), did not explain by what reasoning he maintained that all things are one by arguing either from the viewpoint of matter or from that of form. Hence, with respect to neither nature—that is, neither matter nor form—does he seem to come up to these men, that is, to reach and equal them in their irrational manner of arguing. But concerning the whole heaven he says that the one is God. For the ancients said that the world itself is God. Hence, seeing that all parts of the universe are alike insofar as they are bodies, he came to think of them as if they were all one. And just as the foregoing philosophers held that beings are one by considering those things that pertain either to matter or to form, in a similar way these philosophers maintained this position regarding the composite itself.

142. As we have stated (986b25). His aim here is to explain in a special way how the opinion of Parmenides pertains to the present investigation. He concludes from the foregoing that, since these men did away with diversity in the world (and therefore with causality), all of them must be disregarded so far as the present study is concerned. Two of them—Xenophanes and Melissus—must be disregarded altogether, because they are a little too rustic, that is, they proceeded with less accuracy. But Parmenides seems to have expressed his views with more insight, that is, with greater understanding. For he employs the following argument. Besides being there is only non-being, and whatever is non-being is thought to be nothing—that is, he considers it worthy to be nothing. Hence he thought that it necessarily followed that being is one, and that whatever is other than being is nothing. This argument has been treated more clearly in Physics 1.

143. But even though Parmenides was compelled by this argument to hold that all things are one, yet, because there appeared to the senses to be many things in reality, and because he was compelled to accept what appeared to the senses, it was his aim to make his position conform to both of these—that is, to what is apprehended both by the senses and by reason.

Hence he said that all things are one according to reason but many according to the senses. And inasmuch as he held that there is a plurality of things according to the senses, he was able to hold that there is in the world both cause and effect. Hence he posited two causes, the hot and the cold, one of which he ascribed to fire, and the other to earth. And one of these (the hot or fire) seemed to pertain to the efficient cause, and the other (cold or earth) to the material cause. And lest his position should seem to contradict the conclusion of his own argument that whatever is besides being is nothing, he said that one of these causes (the hot) is being, and that the other cause (the one besides being, or the cold) is non-being, according to both reason and the truth of the thing itself, and is a being only according to sensory perception.

144. Now in this matter he comes very close to the truth; for the material principle, which he held to be earth, is not an actual being. And in a similar way, too, one of two contraries is a privation, as is said in Physics 1. But privation does not belong to the intelligible constitution of being. Hence in a sense cold is the privation of heat, and thus is non-being.

145. From what has been said (987a2). Here he summarizes the remarks which have been made about the doctrines of the ancient philosophers, and in regard to this he does two things.

First, he summarizes the remarks made about the doctrines of the ancient philosophers of nature;

second [147], those made about the doctrines of the Pythagoreans, who introduced mathematics, at now the Pythagoreans (987a13).

Therefore, from the above remarks he concludes first that we learn the causes which have been mentioned from the foregoing philosophers, who adopted the same opinion that the material cause is the substance of things, and who were already beginning by the use of reason to know the causes of things by investigating them. For from the first philosophers we have learned that the principle of all things is bodily. This is evident from the fact that water and the like, which are given as the principles of things, are bodies.

However, they differed in this respect: some (such as Thales, Diogenes, and similar thinkers) claimed that there is only one bodily principle, whereas others (such as Anaxagoras, Democritus, and Leucippus) held that there are several bodily principles. Yet both groups (that is, both those who posited one principle and those who posited many) placed such bodily principles in the species of material cause. And some of them not only posited a material cause but added to this the cause from which motion begins. Some held it to be one (as Anaxagoras did in positing intellect, and Parmenides did in positing love), and others to be two (as Empedocles did in positing love and hate).

146. Hence, it is clear that these philosophers who lived down to the time of the Italians, or Pythagoreans, and [were] independent of them—that is, who had their own opinions about reality and were unaware of those of the Pythagoreans—spoke obscurely about the principles of things, for they did not designate to what genus of cause such principles might be reduced. Yet they made use of two causes, the source from which motion begins and matter. Some said that the former (the source from which motion begins) is one, and others two, as has been pointed out [145].

147. Now the Pythagoreans (987a13). Here he summarizes the opinions expressed by the Pythagoreans, both what they held in common with the foregoing philosophers and what was peculiar to themselves. Now the opinion common to some of the foregoing philosophers and to the Pythagoreans was this: that they posited, in a sense, two principles in the same way as the foregoing philosophers did. For Empedocles held that there are two contrary principles, one being the principle of good things, and the other the principle of evil things, and the Pythagoreans did the same thing, as is clear from the coordination of contrary principles which they posited.

148. However, they did not do this in the same way, because Empedocles placed these contrary principles in the species of material cause, as was stated above [111], but the Pythagoreans added their own opinion to that of the other thinkers. The first thing that they added is this: they said that what I call the “one,” the “limited,” and the “unlimited” are not accidents of any other natures, such as fire or earth or the like, but claimed that what I call the “one,” the “limited,” and the “unlimited” constitute the substance of the same things of which they are predicated. From this they concluded that number, which is constituted of units, is the substance of all things. But while the other philosophers of nature posited the one, the limited, and the unlimited, they nevertheless attributed these to another nature, as accidents are attributed to a subject—for example, to fire or water or something of this kind.

149. The second addition which they made to the views of the other philosophers is this: they began to discuss and to define the “what” itself, that is, the substance and quiddity of things, although they treated this far too simply by defining things superficially. For in giving definitions they paid attention only to one thing, because they said that if any given definition were to apply primarily to some thing, this would be the substance of that thing—just as if one were to suppose that the ratio “double” is the substance of the number two, because such a ratio is found first in the number two. And since being was found first in the one rather than in the many (for the many is composed of ones), they therefore said that being is the substance itself of the one.

But this conclusion of theirs is not acceptable, for although the number two is double, the essence of two-ness is not the same as that of the double in such a way that they are the same conceptually, as the definition and the thing defined.

But even if their statements were true, it would follow that the many would be one. For some plurality can belong primarily to something one: for example, evenness and the ratio double belong first to the number two. Hence it would follow that the even and the double are the same. And it would likewise follow that that to which the double belongs is the same as the number two, so long as the double is the substance of the number two. This, indeed, is also the conclusion which the Pythagoreans drew, for they attributed plurality and diversity to things as if they were one, just as they said that the properties of numbers are the same as the properties of natural beings.

150. Hence, Aristotle concludes that it is possible to learn this much from the early philosophers, who posited only one material principle, and from the later philosophers, who posited many principles.

The Platonic theory of ideas

After the philosophies described came the system of Plato, which followed them in many respects, but also had other theses of its own in addition to the philosophy of the Italians. For Plato, agreeing at the very beginning with the opinions of Cratylus (1010a7) and Heraclitus that all sensible things are always in a state of flux, and that there is no scientific knowledge of them, also accepted this doctrine in later years. However, when Socrates, concerning himself with moral matters and neglecting nature as a whole, sought for the universal in these matters and fixed his thought on definition, Plato accepted him because of this kind of investigation, and assumed that this consideration refers to other entities and not to sensible ones.

For, according to him, it is impossible that there should be a common definition of any one of these sensible things that are always changing. Such entities, then, he called ideas or forms, and he said that all sensible things exist because of them and in conformity with them, for there are many individuals of the same name because of participation in these forms. With regard to participation, he changed the name, for while the Pythagoreans say that things exist by imitation of numbers, Plato says that they exist by participation, changing the name. Yet what this participation or imitation of forms is they commonly neglected to investigate.

Further, he says that besides sensible things and ideas there are the objects of mathematics, which are an intermediate genus. These differ from sensible things in being eternal and immobile; from the ideas in that there are many alike, whereas each idea is itself only one.

And since the forms are the causes of other things, he thought that the elements of these are the elements of all existing things. Hence, according to him, the great and small are principles as matter, and the one as substance. For it is from these by participation in the one that the ideas are numbers.

Yet Plato said that the one is substance and that no other being is to be called one, just as the Pythagoreans did. Also like them, he said that numbers are the causes of real substance.

But to posit a dyad in place of the indeterminate one, and to produce the unlimited out of the great and small, is peculiar to him. Moreover, he says that numbers exist apart from sensible things, whereas they say that things themselves are numbers. Further, they do not maintain that the objects of mathematics are an intermediate class.

Therefore, his making the one and numbers to exist apart from things and not in things (as Pythagoreans did), and his introducing the separate forms, was due to his investigation into the ideas of things. For the earlier philosophers were ignorant of dialectic.

But his making the dyad to be a different nature was due to the fact that all numbers, with the exception of prime numbers, are naturally generated from the number two as a matrix.

Yet what happens is the contrary of this. For this view is not a reasonable one, because the Platonists produce many things from matter but their form generates only once.

And from one matter one measure seems to be produced, whereas he who induces the form, even though he is one, produces many measures. The male is also related to the female in a similar way, for the latter is impregnated by one act, but the male impregnates many females. And such are the changes in these principles. Concerning the causes under investigation, then, Plato defines them thus.

From the foregoing account it is evident that Plato used only two causes: one being the whatness of a thing, and the other, matter. For the forms are the cause of the whatness in other things, and the one is the cause of the whatness in the forms.

It is also evident what the underlying matter is of which the forms are predicated in the case of sensible things, and the one in the case of the forms—it is this duality, the great and small.

Moreover, he assigned the cause of good and evil to these two elements, one to each of them, which is rather a problem, as we say (984b15) that some of the first philosophers (such as Empedocles and Anaxagoras) have attempted to investigate.

Plato and form

151. Having given the opinion of the ancient philosophers about the material and efficient cause, he gives a third opinion, that of Plato, who was the first to clearly introduce the formal cause. This is divided into two parts.

First, he gives Plato’s opinion.

Second [171], from all of the foregoing remarks he makes a summary of the opinions which the other philosophers expressed about the four genera of causes, at we have examined (988a18).

In regard to the first he does two things.

First, he gives Plato’s opinion about the substances of things;

second [159], his opinion about the principles of things, at and since the forms (987b18).

In regard to the first he does two things.

First, he gives Plato’s opinion insofar as he posited ideas;

and second [157], insofar as he posited intermediate substances, the separate mathematical entities, at further, he says (987b14).

He first says that after all the foregoing philosophers came the system of Plato, who immediately preceded Aristotle; for Aristotle is considered to have been his disciple. And even if Plato followed in many respects the natural philosophers who preceded him, such as Empedocles, Anaxagoras, and the like, he nevertheless had certain other doctrines of his own in addition to those of the preceding philosophers, because of the philosophy of the Italians, or Pythagoreans. For insofar as he was devoted to the study of truth he sought out the philosophers of all lands in order to learn their teachings. Hence he came to Tarentum in Italy, and was instructed in the teachings of the Pythagoreans by Archytas of Tarentum, a disciple of Pythagoras.

152. Now Plato would seem to follow the natural philosophers who lived in Greece; of this group some of the later members held that all sensible things are always in a state of flux, and that there can be no scientific knowledge of them (which was the position of Heraclitus and Cratylus). And since Plato became accustomed to positions of this kind from the very beginning, and agreed with these men in this position, which he acknowledged to be true in later years, he therefore said that scientific knowledge of particular sensible things must be abandoned.

And Socrates (who was Plato’s master and the disciple of Archelaus, a pupil of Anaxagoras), because of this position which arose in his time—that there can be no science of sensible things—was unwilling to make any investigation into the nature of physical things, but busied himself only with moral matters. And in this field he first began to investigate what the universal is, and to insist upon the need for definition.

153. Hence, Plato, being Socrates’ pupil, accepted Socrates, that is, followed him, and adopted this method for the purpose of investigating natural beings. He did so believing that in their case the universal in them could successfully be grasped and a definition be assigned to it, with no definition being given for any sensible thing. For, since sensible things are always changing, or being changed, no common intelligible structure can be assigned to any of them.

Every definition must conform to each thing defined and must always do so, and thus each requires some kind of immutability. Hence universal entities of this kind, which are separate from sensible things and that to which definitions are assigned, he called the ideas or forms of sensible things. He called them ideas, or exemplars, inasmuch as sensible things are made in likeness to them; and he called them forms inasmuch as sensible things have substantial being by participating in them. Or he called them ideas inasmuch as they are principles of being, and forms inasmuch as they are principles of knowledge.

Hence all sensible things have being because of them and in conformity with them. They have being because of the ideas insofar as the ideas are the causes of the being of sensible things, and in conformity with them insofar as they are the exemplars of sensible things.

154. The truth of this is clear from the fact that many individuals of the same name are attributed to one form alone—that is, there are many individuals which have the same form predicated of them, and predicated by participation. For the form or idea of man is the specific nature itself by which there exists man essentially.

But an individual is man by participation inasmuch as the specific nature is participated in by this designated matter. For that which is something in its entirety does not participate in it but is essentially identical with it, whereas that which is not something in its entirety but has this other thing joined to it is said properly to participate in that thing.

Thus, if heat were a self-subsistent heat, it would not be said to participate in heat, because it would contain nothing but heat. But since fire is something other than heat, it is said to participate in heat.

155. In a similar way, since the separate idea of man contains nothing but the specific nature itself, it is man per se; and for this reason it was called by him man-in-itself. But since Socrates and Plato have in addition to their specific nature an individuating principle, which is designated matter, they are therefore said to participate in a form, according to Plato.

156. Now Plato took this term “participation” from Pythagoras, although he made a change in the term. For the Pythagoreans said that numbers are the causes of things, just as the Platonists said that the ideas are, and claimed that sensible things of this kind exist as certain imitations of numbers. For inasmuch as numbers, which have no position of themselves, received positions, they caused bodies. But because Plato held that the ideas are unchangeable in order that there might be scientific knowledge of them, he did not agree that the term “imitation” could be used of the ideas, but in place of it he used the term “participation.” However, it must be noted that even though the Pythagoreans posited participation or imitation, they still did not investigate the way in which a common form is participated in by individual sensible things or imitated by them. But the Platonists have treated of this.

157. Further, he says (987b14). Here he gives Plato’s opinion about the mathematical substances. He says that Plato posited other substances—the objects of mathematics—in addition to the forms and sensible things. Moreover, he said that beings of this kind were an intermediate genus among the three kinds of substances, or that they were above sensible substances and below the forms, and differed from both.

The mathematical substances differed from sensible substances because sensible substances are corruptible and changeable, whereas the mathematical substances are eternal and immobile. The Platonists got this idea from the way in which mathematical science conceives its objects, for mathematical science abstracts from motion.

The mathematical substances also differed from the forms, because the objects of mathematics are found to be numerically different and specifically the same—otherwise the demonstrations of mathematics would prove nothing. For unless two triangles belonged to the same species, geometry would attempt in vain to demonstrate that some triangles are similar; and the same thing is true of other figures.

But this does not happen in the case of the forms. For, since a form is just the specific nature itself of a thing, each form can only be unique. Even though the form of man is one thing, and the form of ass another thing, nevertheless the form of man is unique, and so is the form of ass; the same thing is true of other things.

158. Now to one who carefully examines Plato’s arguments it is evident that Plato’s opinion was false, because he believed that the mode of being which the thing known has in reality is the same as the one which it has in the act of being known.

Therefore, since he found that our intellect understands abstractions in two ways—in one way as we understand universals abstracted from singulars, and in another way as we understand the objects of mathematics abstracted from sensible things—he claimed that for each abstraction of the intellect there is a corresponding abstraction in the essences of things. Hence he held that both the objects of mathematics and the forms are separate.

But this is not necessary. For even though the intellect understands things insofar as it becomes assimilated to them through the intelligible form by which it is put into act, it still is not necessary that a form should have the same mode of being in the intellect that it has in the thing known. For everything that exists in something else exists there according to the mode of the recipient.

Therefore, considering the nature of the intellect (which is other than the nature of the thing known) the mode of understanding by which the intellect understands must be one kind of mode, and the mode of being by which things exist must be another. For although the object which the intellect understands must exist in reality, it does not exist there according to the same mode.

Hence, even though the intellect understands mathematical entities without simultaneously understanding sensible substances, and understands universals without understanding particulars, it is not therefore necessary that the objects of mathematics should exist apart from sensible things, or that universals should exist apart from particulars.

For we also see that sight perceives color apart from flavor, even though flavor and color are found together in sensible substances.

159. And since the forms (987b18). Here he gives Plato’s opinion concerning the principles of things; and in regard to this he does two things.

First, he states the principles which Plato assigned to things;

second [169], the genus of cause to which they are reduced, at from the foregoing (988a8).

In regard to the first he does two things.

First, he tells us what kind of principles Plato had assigned to things.

Second [160], he shows in what respect Plato agreed with the Pythagoreans, and in what respect he differed from them, at yet Plato (987b22).

He first says that since the forms are the causes of all other beings according to Plato, the Platonists therefore thought that the elements of the forms are the elements of all beings. Hence, they assigned as the material principle of things the great and small, and said that the substance of things (that is, their form) is the one. They did this because they held these to be the principles of the forms. For they said that just as the forms are the formal principles of sensible things, in a similar way the one is the formal principle of the forms.

Therefore, just as sensible things are constituted of universal principles by participation in the forms, in a similar way the forms (which he said are numbers) are constituted from these, that is of the great and small. For the unit constitutes different species of numbers by addition and subtraction, in which the notion of the great and small consists.

Hence, since the one was thought to be the substance of being (because he did not distinguish between the one which is the principle of number and the one which is convertible with being), it seemed to him that a plurality of different forms might be produced from the one, which is their common substance, in the same way that a plurality of different species of numbers is produced from the unit.

160. Yet Plato (987b22). Here he compares the position of Plato with that of Pythagoras.

First, he shows in what respect they agreed;

second [162], in what respect they differed, at but to posit (987b25).

Now they agreed in two positions. The first is that the one is the substance of things. For the Platonists, like the Pythagoreans, said that what I call the one is not predicated of some other being as an accident is of a subject, but signifies a thing’s substance. They said this, as we have pointed out [159], because they did not distinguish between the one which is convertible with being and the one which is the principle of number.

161. The second position follows from the first, for the Platonists, like the Pythagoreans, said that numbers are the causes of the substance of all beings; they held this because number is just a collection of units. Hence if the one is substance, number must also be such.

162. But to posit (987b25). Here he shows in what respect they differed. In regard to this he does two things.

First, he states how they differed.

Second [164], he gives the reason for this difference, at therefore, his making (987b29).

Now this difference involves two things. First, the Pythagoreans, as has already been stated, posited two principles of which things are constituted—the limited and the unlimited—of which one, the unlimited, has the character of matter.

But in place of this one principle, the unlimited, which the Pythagoreans posited, Plato created a dyad, holding that the great and small have the character of matter. Hence the unlimited, which Pythagoras claimed to be one principle, Plato claimed to consist of the great and small. This is his own opinion in contrast with that of Pythagoras.

163. The second difference is that Plato held that numbers are separate from sensible things, and this in two ways. For he said that the forms themselves are numbers, as was pointed out above [159]. He also held, as was stated above [157], that the objects of mathematics are an intermediate genus between the forms and sensible things, and that they are numbers by their very essence.

But the Pythagoreans said that sensible things themselves are numbers, and did not make the objects of mathematics an intermediate species between the forms and sensible things. Nor again did they hold that the forms are separate from things.

164. Therefore, his making (987b29). Here he gives the reason for the difference.

First, he gives the reason for the second difference;

second [165], the reason for the first difference, at but his making (987b33).

He says, then, that the Platonists adopted the position that both the one and numbers exist apart from sensible things and not in sensible things, as the Pythagoreans claimed. They also introduced separate forms because of the investigation into the ideas of things, that is, because of their investigation of the definitions of things, which they thought could not be attributed to sensible substances, as has been stated [150]. This is the reason they were compelled to hold that there are certain things to which definitions are assigned. But the Pythagoreans, who came before Plato, were ignorant of dialectic, whose office it is to investigate definitions and universals of this kind, the study of which led to the introduction of the ideas.

165. But his making (987b33). Here he gives the reason for the other difference, the one concerning matter.

First, he gives the reason for such a difference.

Second [166], he shows that Plato was not reasonably motivated, at yet what happens is the contrary (988a1).

He accordingly says that the Platonists made the dyad to be a number of a different nature than the forms, because all numbers with the exception of prime numbers are produced from it. They called prime numbers those which are not measured by any other number (such as three, five, seven, eleven, and so on), for these are produced immediately from unity alone. But numbers which are measured by some other number are not called prime numbers, but composite ones (for example, the number four, which is measured by the number two). And in general every even number is measured by the number two. Hence even numbers are attributed to matter, since unlimitedness, which belongs to matter, is attributed to them, as has been stated above [125]. This is why he posited the dyad, from which as a matrix, or exemplar, all other even numbers are produced.

166. Yet what happens (988a1). Here he proves that Plato made unreasonable assumptions; in regard to this he does two things.

First, he proves this by an argument from nature.

Second [167], he gives the argument based on the nature of things, which led Plato to adopt this position, at and from one matter (988a3).

He says that although Plato posited a dyad on the part of matter, still what happens is the contrary of this, as the opinions of all the other natural philosophers testify; for they claimed that contrariety pertains to form and unity to matter, as is clear in Physics 1. For they held that the material principle of things is air or water or something of this kind, from which the diversity of things is produced by rarefaction and condensation, which they regarded as formal principles. For Plato’s position is not a reasonable one.

Now the natural philosophers adopted this position because they saw that many things are generated from matter as a result of a succession of forms in matter. For that matter which now supports one form may afterward support many forms as a result of one form being corrupted and another being generated.

But one species or form generates only once, that is, constitutes the thing which is generated. For when something is generated it receives a form, and the same form numerically cannot become the form of another thing that is generated, but ceases to be when that which was generated undergoes corruption. In this argument it is clearly apparent that one matter is related to many forms, and not the reverse (one form to many matters).

Thus it seems more reasonable to hold that unity pertains to matter but duality or contrariety to form, as the philosophers of nature claimed. This is the opposite of what Plato held.

167. And from one matter (988a3). Here he gives an opposite argument taken from sensible things according to the opinion of Plato. For Plato saw that each thing is received in something else according to the measure of the recipient. Hence receptions seem to differ according as the capacities of recipients differ. But one matter is one capacity for reception. And Plato also saw that the agent who induces the form, although he is one, causes many things to have this form; this comes about because of diversity on the part of matter. An example of this is evident in the case of male and female, for a male is related to a female as an agent and one who impresses a form on matter. But a female is impregnated by one action of a male, whereas one male can impregnate many females. This is why he held that unity pertains to form and duality to matter.

168. Now we must note that this difference between Plato and the philosophers of nature is a result of the fact that they considered things from different points of view.

For the philosophers of nature considered sensible things only insofar as they are subject to change, in which one subject successively acquires contrary qualities. Hence they attributed unity to matter and contrariety to form. But Plato, because of his investigation of universals, went on to give the principles of sensible things. Therefore, since the cause of the diversity of the many singular things that come under one universal is the division of matter, he held that diversity pertains to matter and unity to form. And such are the changes in these principles which Plato posited—that is, participations, or, as I may say, influences in the things generated. For Pythagoras understands the word “change” in this way. Or Aristotle says “changes” inasmuch as Plato changed the opinion which the first philosophers of nature had about principles, as is evident from the foregoing. Hence it is evident from the foregoing that Plato dealt thus with the causes which we are investigating.

169. From the foregoing (988a8). Here he shows to what genus of cause the principles given by Plato are referred. He says that it is evident from the foregoing that Plato used only two kinds of causes. For he used as one cause of a thing the cause of its whatness (that is, its quiddity, or its formal cause, which determines its quiddity), and he also used matter itself. This is also evident from the fact that the forms which he posited are the cause of the whatness in other things, that is, the causes of the whatness of sensible things (namely, their formal causes).

But the formal cause of the forms themselves is what I call the one, which seems to be the substance of which the forms are composed. And just as he holds that the one is the formal cause of the forms, in a similar fashion he holds that the great and small are their material cause, as was stated above [159]. And these causes—the formal and the material cause—are referred not only to the forms but also to sensible substances, because there is some subject of which the one is predicated in the forms. That is to say, that which is related to sensible substances in the same way as the one is to the forms is itself a form, because that duality which relates to sensible things as their matter is the great and small.

170. Furthermore, Plato indicated the cause of good and evil in the world, and he did this with reference to each of the elements which he posited. For he made form the cause of good and matter the cause of evil. However, some of the first philosophers attempted to investigate the cause of good and evil, such as Anaxagoras and Empedocles, who established certain causes in the world with end of giving the principles of good and evil by means of these causes. And in touching upon these causes of good and evil they came very close to positing the final cause, although they did not posit this cause directly, but only indirectly, as is stated below [177].

Summary of ancient opinions

We have examined, then, in a brief and summary way those philosophers who have spoken about the principles of things and about the truth, and the way in which they did this. Yet we have learned from them this much: none of those who have discussed principle and cause have said anything beyond the points established by us in the Physics.

Yet all have approached these causes obscurely.

For some speak of the principle as matter, whether they suppose it to be one or many, and whether they assume it to be a body or something incorporeal, as Plato speaks of the great and small; the Italians of the unlimited; Empedocles of fire, earth, water, and air; and Anaxagoras of an infinite number of like parts. All these have touched on this kind of cause, and so also have those who make the first principle air or fire or water or something denser than fire or rarer than air. For they have said that some such body is the primary element. These thinkers, then, have touched only on this cause.

But others have introduced the source of motion. For example, those who make friendship and strife, or intellect, or love, or something besides these, a principle of things.

But the quiddity or substance no one has presented clearly. Those who express it best are those who posit the ideas and the intelligible natures inherent in the ideas.

For they do not think of the ideas and the things inherent in them as the matter of sensible things; nor do they think of them as the source from which motion originates, for they say that these things are the causes rather of immobility and of that which is at rest. But the forms are responsible for the quiddity of all other things, and the one for the quiddity of the forms.

That for the sake of which there are actions and changes and motions they affirm in some way to be a cause, but not in the way we are determining causes, or in the way in which it is truly a cause.

For while those who speak of intellect or love posit these causes as good, they do not say that anything exists or comes to be because of them, but claim that the motion of things stems from them. In like manner, those who say that the one or being is such a reality say that it is the cause of substance, but not that things either are or come to be for the sake of this. Hence, it happens to them that in a way they both say and do not say that the good is a cause, for they do not speak of it in its principal aspect but in a secondary one.

Therefore, all these philosophers, being unable to touch on any other cause, seem to bear witness to the fact that we have dealt correctly with the causes, as to both their number and their kinds. Moreover, it is evident that all principles must be sought in this way or in some similar one. As to the way in which each of these philosophers has spoken, and how they have raised possible problems about the principles of things, let us discuss these points next.

171. Here he makes a summary of everything that the early philosophers have said about causes, and in regard to this he does three things.

First (988a18; [171]), he shows that the early philosophers were unable to add another kind of cause to the four genera of causes given above (983a24; [70]).

Second (988a22; [172]), he indicates the way in which they touched upon these causes, at yet all.

Third (988b16; [180]), he draws the conclusion at which he chiefly aims, at therefore, all these.

He first says (988a18) that in giving this brief and summary account he has stated who the philosophers are, and how they have spoken of the principles of things and of what is true of the substance itself of things. And from their statements this much can be learned: none of those who have spoken about causes and principles were able to mention any causes other than those distinguished in Physics 2.

172. Yet all (988a22). Here he gives the way in which they dealt with each of the causes.

He does this first (988a22) in a general way,

and second (988a23; [172]), in a special way, at for some speak.

Accordingly he says first that they not only have not added anything, but in the way in which they approached these causes they proceeded obscurely and not clearly. For they have not stated to what genus of cause the principles posited by them would belong, but they gave as principles things that can be adapted to some genus of cause.

173. For some speak (988a23). Here he shows in a special way how they touched on each of these causes.

He shows first (988a23) how they touched on the material cause;

second (988a32; [174]), on the efficient cause, at but others;

third (988a34; [175]), on the formal cause, at but the quiddity;

fourth (988b6; [177]), on the final cause, at that for the sake of which.

He says first (988a23) that those philosophers, the early ones, all agree insofar as they assign some material cause to things. Yet they differ in two respects.

First, they differ in that some, such as Thales, Diogenes, and the like, held that the material principle is one, whereas others, such as Empedocles, claimed that it is many.

Second, they differ in that some, such as the first group above, held that the material principle of things is a body, whereas others, such as Plato who posited a dyad, claimed that it is something incorporeal.

For Plato posited the great and small, which the Platonists do not speak of as a body. The Italians, or Pythagoreans, posited the unlimited, but neither is this a body. Empedocles, on the other hand, posited the four elements, which are bodies; Anaxagoras also posited an infinite number of like parts, or that the principles of things are an infinite number of like parts.

All of these thinkers have touched on this kind of cause, or the material cause, and so also have those who said that the principle of things is air or water or fire or something midway between these elements (that is, what is denser than fire and rarer than air). For all philosophers such as those just mentioned have claimed that some kind of body is the first element of things.

Thus Aristotle’s statement is evident: in the light of the foregoing remarks these philosophers have posited only the material cause.

174. But others (988a32). Here he gives their opinions about the efficient cause. He says that some of the foregoing philosophers have posited, in addition to the material cause, a cause from which motion begins—for example, those who made love or hate or intellect a cause of things, or those who introduced some other active principle distinct from these, as Parmenides, who made fire an efficient cause.

175. But the quiddity (988a34). Here he gives their opinions about the formal cause. He says that no one attributed the cause through which a thing’s substance is known (that is, the formal cause) to things with any clarity. And if the ancient philosophers touched on something that might pertain to the formal cause (as Empedocles did when he claimed that bone and flesh contain some proportion of the elements by which they are things of this kind), nevertheless they did not treat what belongs to the formal cause after the manner of a cause.

176. But among the other philosophers, those who posited the forms and those intelligible aspects which belong to the forms (such as unity, number, and the like) came closest to positing the formal cause.

For the forms and everything that belongs to the forms in the aforesaid way, such as unity and number, are not acknowledged or assumed by them to be the matter of sensible things, since they place matter rather on the side of sensible things; nor do they claim that the forms are the causes from which motion originates in the world, but rather that they are the cause of immobility in things.

For they said that whatever is found to be necessary in sensible things is caused by the forms, and that these, the forms, are immobile. For they claimed that the forms, because immobile, are uniform in being, as has been said (987a29; [156]), so that definitions can be given of them and demonstrations made about them. But according to the opinion of these men the forms are responsible for the quiddity of particular things after the manner of a formal cause, and the one is responsible for the quiddity of the forms.

All the foregoing weak on final cause

177. That for the sake of which (988b6). Here he gives the opinions of certain thinkers about the final cause. He says that in one sense the philosophers say that the goal for the sake of which motions, changes, and activities occur is a cause, and in another sense they do not. And they neither speak of it in the same way, nor in the way in which it is a true cause. For those who affirm that intellect or love is a cause posit these causes as good. For they said that things of this kind are the causes of things being well disposed, since the cause of good can only be good.

Hence it follows that they could make intellect and love to be causes, just as the good is a cause. But good can be understood in two ways: in one way as a final cause in the sense that something comes to be for the sake of some good, and in another way as an efficient cause, as we say that the good man does good.

Now these philosophers did not say that the foregoing causes are good in the sense that they are the reason for the existence or coming to be of some beings, which pertains to the intelligibility of the final cause, but in the sense that there proceeds from these causes—intellect and will—a kind of motion toward the being and coming-to-be of things. And this pertains to the intelligibility of the efficient cause.

178. In a similar way, the Pythagoreans and Platonists, who said that the substance of things is the one itself or being, also attributed goodness to the one or being. Thus they said that such a reality, the good, is the cause of the substance of sensible things, either in the manner of a formal cause (as the Platonists maintained), or in the manner of a material cause (as the Pythagoreans claimed).

However, they did not say that the being and coming-to-be of things exists for the sake of this (that is, the one or being); this is something that pertains to the intelligibility of the final cause.

Hence, just as the philosophers of nature claimed that the good is a cause in the manner of an efficient cause and not in that of a formal cause, in a similar way the Platonists claimed that the good is a cause in the manner of a formal cause, and not in that of a final cause. The Pythagoreans, on the other hand, considered it to be a cause in the manner of a material cause.

179. It is evident, then, that in one sense they happened to speak of the good as a cause and in another not. For they did not speak of it as a cause in its principal aspect, but in a secondary one, because according to its proper intelligible structure the good is a cause in the manner of a final cause. This is clear from the fact that the good is what all desire. Now that to which an appetite tends is a goal. Therefore, according to its proper intelligible structure the good is a cause in the manner of a goal.

Hence those who make the good a cause in its principal aspect claim that it is a final cause. But those who attribute a different mode of causality to the good claim that the good is a cause but only accidentally, because they do not hold that it is such by reason of being good, but by reason of that to which good happens to belong by reason of its being active or perfective. Hence it is clear that those philosophers posited a final cause only accidentally, because they posited as a cause something that is fitting to be an end—namely, the good. However, they did not claim that it is a cause in the manner of a final cause, as has been stated.

Conclusion

180. Therefore, all these (988b16). Here he draws the conclusion at which he chiefly aims: the things established about the causes, both as to their number and their kinds, are correct. For the foregoing philosophers seem to bear witness to this in being unable to add another genus of cause to those discussed above. This is one of the useful things resulting from the account of the foregoing views.

Another is that evidently the principles of things must be investigated in this science, either all or some of those which the ancient philosophers posited and which have been established above. For this science considers chiefly the formal and final cause, and also in a sense the efficient cause. Now it is not only necessary that the above views be discussed, but after this examination it is also necessary to describe the way in which each of these men has spoken (both in what sense their statements are acceptable and in what sense not), and how the statements which have been made about the principles of things contain a problem.

The number of material principles

Therefore, all those who hold that the whole is one and say that there is a certain single nature as matter, and that this is bodily and has measure, are clearly at fault in many ways. For they give only the elements of bodies and not those of incorporeal things, as if incorporeal things did not exist.

And in attempting to state the cause of generation and corruption, and in treating all things according to the method of natural philosophy, they do away with the cause of motion.

Furthermore, they did not claim that the substance or whatness of a thing is a cause of anything.

And they were wrong in holding that any of the simple bodies except earth is a principle, without considering how they are generated from each other.

I mean fire, earth, water and air; for some of these are generated from each other by combination and others by separation. Now it makes the greatest difference as to which of these is prior and which subsequent.

For in one way it would seem that the most basic element of all is that from which a thing first comes to be by combination. But such an element will be one which has the smallest parts and is the subtlest of bodies. Hence all those who posit fire as the first principle make statements that conform most closely to this theory. But each of the other thinkers admits that the primary element of bodies is something of this kind.

For none of the later thinkers, and none of those who spoke about the one, wanted earth to be an element, evidently because of the size of its particles. But each of the other three elements finds some supporter, for some say that this primary element is fire, others water, and others air. But why do they not say that it is earth, as in a sense most men do? For they say that everything is earth. And Hesiod says that earth is the first of bodies to be generated; for this happens to be the ancient and common view. Therefore, according to this theory, if anyone says that any of these bodies with the exception of fire is the primary element of things, or if anyone holds that it is something denser than air but rarer than water, he will not speak the truth.

However, if that which is later in generation is prior in nature, and if that which is condensed and compounded is later in generation, then the reverse will be true—water will be prior to air, and earth to water. Let these points suffice, then, regarding those who posit one cause such as we have described.

The same consequence will also be true if anyone posits many elements, as Empedocles says that the four bodies are the matter of things. For these same consequences must befall this man, as well as some which are peculiar to himself. For we see things being generated from each other in such a way that the same body does not always remain fire or earth. But we have spoken of these matters in our physical treatises.

And concerning the cause of things in motion, whether one or more than one must be posited, it must not be thought that what has been said is either entirely correct or reasonable.

And in general those who speak thus must do away with alteration, because the cold will not come from the hot, nor the hot from the cold. For what is it that undergoes these contraries and what is the one nature which becomes fire and water? Such a thing Empedocles does not admit.

But if anyone were to maintain that Anaxagoras speaks of two elements, they would acknowledge something fully in accord with a theory which he himself has not stated articulately, although he would have been forced to follow those who express this view.

For to say, as he did, that in the beginning all things are mixed together is absurd, both because it would be necessary to understand that things previously existed in an unmixed state, and because it is not fitting that anything should be mixed with just anything. Also because properties and accidents could be separated from substances (for there is both mixture and separation of the same things).

Yet, if anyone were to follow him up and articulate what he means, his statement would perhaps appear more astonishing. For when nothing was distinct from anything else, evidently nothing would be truly predicated of that substance. I mean that it would be neither white nor black nor tawny, nor have any color, but would necessarily be colorless; otherwise it would have one of these colors.

Similarly, it would be without humors. And for the same reason it would have no other similar attribute. For it could not have any quality or quantity or whatness, because, if it had, some of the attributes described as formal principles would inhere in it. But this is obviously impossible, since all things are mixed together; they would already be distinct from each other. But he said that all things are mixed together except intellect, and that this alone is unmixed and pure.

Now from these statements it follows for him that there are two principles, one being the intellect itself (for this is unmixed in an absolute sense), and the other being the kind of thing we suppose the indeterminate to be before it is limited and participates in a form. Hence, what he says is neither correct nor clear, although he intends something similar to what later thinkers said and what is now more apparent. But these thinkers are concerned only with theories proper to generation, corruption and motion, for usually it is only of this kind of substance that these men seek the principles and causes.

181. Having stated the opinions which the philosophers held about the principles of things, Aristotle begins here to criticize them. This is divided into two parts.

First, he criticizes each opinion.

Second [272], he summarizes his discussion and links it up with what follows, at from the foregoing (993a11).

The first is divided into two parts.

First, he criticizes the opinions of those who have treated things according to the method of natural philosophy.

Second [201], he criticizes the opinions of those, Pythagoras and Plato, who have not treated things according to the method of natural philosophy because they posited higher principles than the natural philosophers did, at but all those (989b24).

In regard to the first part he does two things.

First, he criticizes the opinions of those who posited one material cause;

and second [190], the opinions of those who posited many, at the same consequence (989a19).

In regard to the first he does two things.

First, he criticizes the foregoing opinions in a general way;

second [184], in a special way, at and they were wrong (988b29).

He criticizes these opinions in a general way by means of three arguments.

The first (988b22) is this: in the world there are not only bodies but also certain incorporeal things, as is clear from On the Soul. But these men posited only bodily principles, which is clear from the fact that they maintained that the whole is one, that is, that the universe is one thing substantially, and that there is a single nature as matter, and that this is bodily and has measure, or dimension. But a body cannot be the cause of an incorporeal thing. Therefore, it is evident that they were at fault in this respect that they treated the principles of things inadequately. And they were at fault not only in this respect but in many others, as is clear from the following arguments.

182. And in attempting (988b26). Here he gives the second argument, which runs thus: whoever feels obliged to establish the truth about motion must posit a cause of motion. But these philosophers felt obliged to treat motion, which is clear for two reasons: first, because they tried to state the causes of generation and corruption in the world, which do not occur without motion; second, because they wanted to treat things according to the method of natural philosophy.

But since a treatment of things according to this method involves motion (because nature is a principle of motion and rest, as is clear in Physics 2), they should therefore have dealt with that cause which is the source of motion. And since they did away with the cause of motion by saying nothing about it, obviously they were also at fault in this respect.

183. Furthermore, they did not (988b28). Here he gives the third argument: every natural being has a substance, that is, a form of the part, and whatness, or quiddity, which is the form of the whole. He says “form” inasmuch as it is a principle of subsistence, and “whatness” inasmuch as it is a principle of knowing, because “what a thing is” is known by means of this. But the foregoing philosophers did not claim that form is a cause of anything. They treated things inadequately, then, and were also at fault in neglecting the formal cause.

184. For none of the later (989a5). Here he criticizes their opinions in a special way; and he does this with respect to two things.

First, he criticizes them for maintaining that all the elements with the exception of fire are the principles of things.

Second [187], he criticizes them for omitting earth, at however, if (989a15).

First (989a5), he takes up once more the position of those who claimed that each of the simple bodies except earth is the primary element of things. The reason which he gives for this position is that these men saw that the simple bodies are generated from each other in such a way that some come from others by combination or compacting, as grosser things come from more refined ones.

185. He also explains how to proceed against their opinions from their own arguments. For they claimed that one of these elements is the principle of things by arguing that other things are generated from it either by combination or by separation. Now it makes the greatest difference as to which of these two ways is prior and which subsequent, for on this depends the priority or posteriority of that from which something is generated. For, on the one hand, that seems to be prior from which something is produced by combination. And he gives this argument first. Yet, on the other hand, that seems to be prior from which something is produced by rarefaction. And he bases his second argument on this.

186. For the fact that the primary element is that from which something is produced by combination supports the opinion which is now held, that the most basic element is that from which other things are produced by combination. This in fact is evident both from reason and from the things that they held. It is evident from reason because that from which other things are produced by combination is the most refined type of body, and the one having the smallest parts: this seems to be the simpler body. Hence, if the simple is prior to the composite, this body seems to be first. It is also evident from the things that they held, because all those who posited fire as the principle of things asserted that it is the first principle. Similarly, others have been seen to follow this argument, for they thought that the primary element of bodies is the one having the finest parts. This is evident from the fact that none of the later philosophers followed the theological poets, who said that earth is the primary element of things. Evidently they refused to do this because of the size of its parts, that is, because of the coarseness of its parts. However, it is a fact that each of the other three elements finds some philosopher who judges it to be the principle of things. But their refusal to make earth a principle is not to be explained by a refusal to reject a common opinion, for many men thought that earth is the substance of things. Hesiod, who was one of the theological poets, also said that earth is the first of all bodies to come into being. Thus the opinion that earth is the principle of things is evidently an ancient one, because it was maintained by the theological poets, who preceded the philosophers of nature. It was also the common opinion, because many men accepted it. It follows, then, that the later philosophers avoided the position that earth is a principle only because of the coarseness of its parts. But it is certain that earth has coarser parts than water, and water than air, and air than fire; if there is any intermediate element, it is evident that it is grosser than fire. Hence by following this argument it is clear that none of them spoke correctly, except he who held that fire is the first principle. For as soon as some element is held to be a principle by reason of its minuteness, the most minute element must be held to be the first principle of things.

187. However, if that which (989a15). Here he gives another argument, and according to it the opposite seems to be true, namely, that earth is the most basic element of things. For it is evident that whatever is subsequent in generation is prior in nature, because nature tends to the goal of generation as the first thing in its intention. But the denser and more composite something is, the later it appears in the process of generation; for the process of generation proceeds from simple things to composite ones, just as mixed bodies come from the elements, and the humors and members of a living body from mixed bodies. Hence, whatever is more composite and condensed is prior in nature. In this way a conclusion is reached which is the opposite of that following from the first argument: water is now prior to air and earth to water as the first principle of things.

188. It should be noted, however, that it is a different thing to look for what is prior in one and the same entity and for what is prior without qualification. For if one seeks what is prior without qualification, the perfect must be prior to the imperfect, just as act is prior to potency. For a thing is brought from a state of imperfection to one of perfection, or from potency to act, only by something completely actual. Therefore, if we speak of what is first in the whole universe, it must be the most perfect thing.

But in the case of one particular thing which goes from potency to complete act, potency is prior to act in time, although it is subsequent in nature. It is also clear that the first of all things must be one that is simplest, for the composite depends on the simple, and not the reverse. It was necessary, then, that the ancient philosophers should attribute both of these properties (the greatest perfection along with the greatest simplicity) to the first principle of the whole universe.

However, these two properties cannot be attributed simultaneously to any bodily principle, for in bodies subject to generation and corruption the simplest entities are imperfect. They were compelled, then, as by contrary arguments, to posit different principles. Yet they preferred the argument of simplicity, because they considered things only insofar as something passes from potency to act, and in this order it is not necessary that anything which is a principle should be more perfect. But this kind of opposition can be resolved only by maintaining that the first principle of things is incorporeal, because this principle will be the simplest one, as Aristotle will prove below [2548].

189. Last of all he concludes that for the purpose of the present discussion enough has been said about the positions of those who affirm one material cause.

190. The same consequence (989a19). Here he gives the arguments against those who posited many material causes.

First, he argues against Empedocles;

second [194], against Anaxagoras, but if anyone (989a30).

First (989a19), he says that the same consequence faces Empedocles, who held that the four bodies are the matter of things, because he experienced the same difficulty with regard to the above contrariety. For according to the argument of simplicity fire would seem to be the most basic principle of bodies; according to the other argument, earth would seem to be such, as has been stated [187].

And while Empedocles faced some of the same absurd conclusions as the preceding philosophers (namely, he did not posit either a formal cause or the aforesaid contrariety of simplicity and perfection in bodily things), there is no argument against him for doing away with the cause of motion. But he did face certain other absurd conclusions besides those that confronted the philosophers who posited one material cause.

191. This is shown by three arguments, of which the first is as follows. First principles are not generated from each other, because a principle must always remain in existence, as is pointed out in Physics 1. But we perceive that the four elements are generated from each other, and for this reason their generation is dealt with in natural philosophy. Hence his position that the four elements are the first principles of things is untenable.

192. And concerning the cause (989a25). Here he gives the second absurdity, which has to do with the cause of motion. For to posit many and contrary causes of motion is not at all correct or reasonable; because if the causes of motion are understood to be proximate ones, they must be contraries, since their effects seem to be contraries. But if the first cause is understood, then it must be unique, as is apparent in book 12 [2492] of this work, and in Physics 8. Therefore, since he intends to posit the first causes of motion, his position that they are contraries is untenable.

193. And in general (989a26). Here he gives the third argument which leads to an absurdity: in every process of alteration it must be the same subject which undergoes contraries. This is true because one contrary does not come from another in such a way that one is converted into the other. For example, the cold does not come from the hot in such a way that heat itself becomes cold or the reverse, although the cold does come from the hot when the underlying subject is one only inasmuch as the single subject which is now the subject of heat is afterwards the subject of cold. But Empedocles did not hold that contraries have one subject. In fact, he held that they are found in different subjects, as heat in fire and cold in water. Nor again did he hold that there is one nature underlying these two. Therefore, he could not posit alteration in any way. Yet it is absurd that alteration should be done away with altogether.

194. But if anyone (989a30). Here he deals with Anaxagoras’ opinion, and in regard to this he does two things.

First, he shows in general in what respect Anaxagoras’ opinion should be accepted as true, and in what respect not.

Second, he explains each of these in particular, at for to say (989a33).

He says, first, that if anyone wishes to maintain that Anaxagoras’ opinion is true insofar as he posited two principles—the material and the efficient cause—let him understand this according to the reasoning which Anaxagoras himself seems to have followed, as if compelled by some need for truth, inasmuch as he would have followed those who expressed this theory, which he himself has not stated articulately, that is, he has not expressed it distinctly. Therefore, with reference to what he has not expressly stated, his opinion is true; but with reference to what he has expressly stated his opinion is false.

195. This is made clear in particular as follows. If his opinion is taken in its entirety according to a superficial understanding of his statements, a greater absurdity will appear for four reasons.

First, his opinion that all things were mixed together at the beginning of the world is absurd, for in Aristotle’s opinion the distinction between the parts of the world is thought to be eternal.

The second reason is that what is unmixed is related to what is mixed as the simple to the composite. But simple bodies are prior to composite ones, and not the reverse. Therefore, what is unmixed must be prior to what is mixed. This is the opposite of what Anaxagoras said.

The third reason is this: in the case of bodies not anything at all is naturally disposed to be mixed with anything else, but only those things are naturally disposed to be mixed which are naturally inclined to pass over into each other by some kind of alteration. For a mixture is a union of the altered things that are capable of being mixed. But Anaxagoras held that anything is mixed with just anything.

The fourth reason is this: there is both mixture and separation of the same things, for only those things are said to be mixed which are naturally disposed to exist apart. But properties and accidents are mixed with substances, as Anaxagoras said. Therefore, it follows that properties and accidents can exist apart from substances. This is evidently false. These absurdities appear then, if Anaxagoras’ opinion is considered in a superficial way.

196. Yet if anyone were to follow him up and articulate, that is, investigate clearly and distinctly, the things that Anaxagoras means, or his intellect held, although he did not know how to express this, his statement would appear to be more astonishing and subtler than those of the preceding philosophers. This will be so for two reasons.

First, he came closer to a true understanding of matter. This is clear from the fact that in that mixture of things, when nothing was distinguished from anything else but all things were mixed together, nothing could be truly predicated of that substance which is so mixed, which he held to be the matter of things. This is clear in the case of colors, for no special color could be predicated of it so that it might be said to be white or black or have some other color, because, according to this, that color would necessarily be unmixed with other things. Similarly, neither could color in general be predicated of it so that it might be said to be colored, because everything of which a generic term is predicated must also have a specific term predicated of it, whether the predication be univocal or denominative. Hence, if that substance were colored, it would necessarily have some special color. But this is opposed to the foregoing statement. And the argument is similar with respect to humors (that is, flavors), and to all other things of this kind.

Hence the primary genera themselves could not be predicated of it in such a way that it would have quality or quantity or some attribute of this kind. For if these genera were predicated of it, some particular species would necessarily belong to it. But this is impossible, if all things are held to be mixed together. For this species which would be predicated of that substance would already be distinguished from the others.

And this is the true nature of matter: it does not have any form actually but is in potency to all forms. For the mixed body itself does not have actually any of the things that combine in its mixture, but has them only potentially. And it is because of this likeness between prime matter and what is mixed that he seems to have posited the above mixture, although there is some difference between the potency of matter and that of a mixture.

For even though the elements which constitute a mixture are present in the mixture potentially, they are still not present in a state of pure passive potency, for they remain virtually in the mixture. This can be shown from the fact that a mixture has motion and operations as a result of the bodies of which the mixture is composed. But this cannot be said of the things that are present potentially in prime matter.

And there is also another difference, namely, that even though a mixture is not actually any of the mixed bodies which it contains, yet it is something actual. This cannot be said of prime matter. But Anaxagoras seems to do away with this difference, because he has not posited any particular mixture but the universal mixture of all things.

197. The second reason is this: he spoke more subtly than the others because he came closer to a true understanding of the first active principle. For he said that all things are mixed together except intellect, and that this alone is unmixed and pure.

198. From these things it is clear that he posited two principles: one of these he claimed to be the intellect itself, insofar as it is simple and unmixed with other things; the other is prime matter, which we claim is like the indeterminate before it is limited and participates in a form. For since prime matter is the subject of an infinite number of forms, it is limited by a form and acquires some species by means of it.

199. It is clear, then, that, in regard to the things that he stated expressly, Anaxagoras neither spoke correctly nor clearly. Yet he would seem to say something directly which comes closer to the opinions of the later philosophers, which are truer (namely, to those of Plato and Aristotle, whose judgments about prime matter were correct) and which were then more apparent.

200. In concluding, Aristotle excuses himself from a more diligent investigation of these opinions, because the statements of these philosophers belong to the realm of physical discussions, which treat of generation and corruption. For these men usually posited principles and causes of this kind of substance (that is, of material and corruptible substance). He says usually because, while they did not treat other substances, certain of the principles laid down by them can also be extended to other substances. This is most evident in the case of intellect. Therefore, since they have not posited principles common to all substances, which pertains to this science, but only principles of corruptible substances, which pertains to the philosophy of nature, a diligent study of the foregoing opinions belongs rather to the philosophy of nature than to this science.

Critique of the Pythagoreans’ opinions

But all those who make a study of all existing things, and who claim that some are sensible and others not, evidently make a study of both genera. And for this reason one should dwell at greater length on the statements they have made, whether they be acceptable or not, for the purposes of the present study which we now propose to make.

Therefore, those who are called Pythagoreans used principles and elements which are foreign to the physicists. The reason is that they did not take them from sensible things. For the objects of mathematics, with the exception of those that pertain to astronomy, are devoid of motion. Nevertheless, they discuss and treat everything that has to do with the physical world, for they generate the heavens and observe what happens in regard to its parts, passions, and operations. And in doing this they use up their principles and causes, as though they agreed with the others (that is, the physicists) that whatever exists is sensible and is contained by the so-called heavens. But, as we have stated, the causes and principles are sufficient to extend even to a higher genus of beings, and are better suited to these than to their theories about the physical world.

Yet how there will be motion if only the limited and unlimited and even and odd are posited as principles, they do not say. But how can there be generation or corruption, or the activities of those bodies which traverse the heavens, if there is no motion or change?

And further, whether one grants them that continuous quantities come from these things, or whether this is demonstrated, how is it that some bodies are light and others heavy? For from what they suppose and state, they say nothing more about mathematical bodies than they do about sensible ones. Hence they have said nothing about fire, earth, and other bodies of this kind, since they have nothing to say that is proper to sensible things.

Further, how are we to understand that the attributes of number and number itself are the causes of what exists and comes to pass in the heavens, both from the beginning and now? And how are we to understand that there is no other number except that of which the world is composed?

For when they place opportunity and opinion in one part of the heavens, and a little above or below them injustice and separation or mixture, and when they state as proof of this that each of these is a number, and claim that there already happens to be in this place a plurality of quantities constituted of numbers, because these attributes of number correspond to each of these places, we may ask whether this number which is in the heavens is the same as that which we understand each sensible thing to be, or whether there is another kind of number in addition to this?

For Plato says there is another. In fact, he also thinks that both these things and their causes are numbers, but that some are intellectual causes and others sensible ones.

Regarding the Pythagoreans, then, let us dismiss them for the present, for it is enough to have touched upon them to the extent that we have.

201. Here he argues dialectically against the opinions of Pythagoras and Plato, who posited different principles from those which pertain to the philosophy of nature. In regard to this he does two things.

First, he shows that a study of these opinions rather than those mentioned above belongs to the present science.

Second [202], he begins to argue dialectically against these opinions, at therefore, those who (989b29).

He first says (989b24), then, that those who make a study (or an investigation) of all existing things, and hold that some are sensible and others non-sensible, make a study of both genera of beings. Hence an investigation of the opinions of those who spoke either correctly or incorrectly belongs rather to the study which we now propose to make in this science. For this science deals with all beings and not with some particular genus of being. Hence, the things that pertain to every genus of being are to be considered here rather than those which pertain to some particular genus of being.

202. Therefore, those who (989b29). Here he argues against the opinions of the foregoing philosophers.

First (989b29), he argues against Pythagoras;

second [208], against Plato, at but those who posited ideas (990a34).

In regard to the first he does two things.

First, he shows in what way Pythagoras agreed with the philosophers of nature, and in what way he differed from them.

Second [204], he argues against Pythagoras’ position, at yet how (990a8).

We must understand (989b29), then, that in one respect the Pythagoreans agreed with the philosophers of nature, and in another respect they differed from them.

They differed from them in their position regarding principles, because they employed principles of things in a way foreign to the philosophers of nature. The reason is that they did not take the principles of things from sensible beings, as the natural philosophers did, but from the objects of mathematics, which are devoid of motion, and are therefore not physical.

And the statement that the objects of mathematics are devoid of motion must be referred to those sciences which are purely mathematical, such as arithmetic and geometry. Astronomy considers motion because astronomy is a science midway between mathematics and natural philosophy. For astronomy and other intermediate sciences apply their principles to natural things, as is clear in Physics 2.

203. Now Pythagoras agreed with the philosophers of nature concerning the things whose principles he sought, for he discussed and treated all natural beings. He dealt with the generation of the heavens and observed everything that happens to the parts of the heavens (by which are meant the different spheres, or also the different stars). He also considered what happens to its passions, or to the eclipses of the luminous bodies; and what happens to the operations and motions of the heavenly bodies, and their effects on lower bodies. And he used up causes on particular things of this kind by applying to each one its proper cause. He also seemed to agree with the other philosophers of nature in thinking that that alone has being which is sensible and is contained by the heavens which we see. For he did not posit an infinite sensible body, as the other philosophers of nature did. Nor again did he hold that there are many worlds, as Democritus did.

He therefore seemed to think that there are no beings except sensible ones, because he assigned principles and causes only to such substances. However, the causes and principles which he laid down are not proper or limited to sensible things, but are sufficient for ascending to higher beings, that is, intellectual ones. And they were better fitted to these than the theories of the natural philosophers which could not be extended beyond sensible things, because these philosophers claimed that principles are bodily. But since Pythagoras posited incorporeal principles (namely, numbers), although he posited only principles of sensible bodies, he came very close to positing principles of intelligible beings, which are not bodies, as Plato did later.

204. Yet how (990a8). Here he gives three arguments against the opinion of Pythagoras.

The first is this. Pythagoras could not explain how motion originates in the world, because he posited as principles only the limited and unlimited and the even and odd, which he held to be principles as substance, or material principles. But he had to admit that there is motion in the world. For how could there be generation and corruption in bodies, and how could there be any activities of the heavenly bodies, which occur as a result of certain kinds of motion, unless motion and change existed? Evidently they could not exist in any way. Hence, since Pythagoras considered generation and corruption and the operations of the heavenly bodies without assigning any principle of motion, his position is clearly unsatisfactory.

205. And further (990a12). Here he gives the second argument. For Pythagoras claimed that continuous quantities are composed of numbers. But whether he proves this or takes it for granted, he could not give any reason on the part of numbers as to why some things are heavy and others light. This is clear from the fact that his arguments about numbers are no more adapted to sensible bodies than they are to the objects of mathematics, which are neither heavy nor light. Hence they obviously said nothing more about sensible bodies than they did about the objects of mathematics.

Therefore, since sensible bodies (such as earth and fire and the like) considered in themselves add something over and above the objects of mathematics, it is evident that they said nothing proper in any true sense about these sensible bodies. Thus it is also evident that the principles which they laid down are not sufficient, since they neglected to give the causes of those attributes which are proper to sensible bodies.

206. Further, how are we (990a18). Here he gives the third argument, which is based on the fact that Pythagoras seemed to hold two contrary positions.

For, on the one hand, he held that number and the attributes of number are the cause both of those events which occur in the heavens and of all generable and corruptible things from the beginning of the world.

Yet, on the other hand, he held that there is no other number besides that of which the substance of things is composed; for he held that number is the substance of things. But how is this to be understood, since one and the same thing is not the cause of itself?

For Pythagoras says that the former position may be demonstrated from the fact that each one of these sensible things is numerical in substance, because in this part of the universe there are contingent beings, about which there is opinion and which are subject to time inasmuch as they sometimes are and sometimes are not. But if generable and corruptible things were partly above or partly below, there would be disorder in the order of the universe, either after the manner of injustice (insofar as some being would receive a nobler or less noble place than it ought to have); or after the manner of separation (in the sense that, if a body were located outside its own place, it would be separated from bodies of a like nature); or after the manner of mixture and mingling, provided that a body located outside its proper place must be mixed with some other body (for example, if some part of water occupied a place belonging to air or to earth).

In this discussion he seems to touch on two ways in which a natural body conforms to its proper place. One pertains to the order of position, according to which nobler bodies receive a higher place, in which there seems to be a kind of justice. The other pertains to the similarity or dissimilarity between bodies in place, to which separation and mingling may be opposed.

Therefore, insofar as things have a definite position, they are fittingly situated in the universe. For if their position were fitting it would result that all parts of the universe are arranged in a definite proportion, as it has been stated and shown; for every definite proportion is numerical. And it was from this that Pythagoras showed that all things would be numbers.

But, on the other hand, we see that the continuous quantities established in different places are many and different, because the particular places in the universe correspond to the proper attributes by which bodies are differentiated. For the attributes of bodies which are above differ from those which are below.

Hence, since Pythagoras affirms that all sensible things are numbers by means of the above argument, and we see that the difference in sensible bodies is attributable to difference in place, the question arises whether the number which exists in the heavens (that is, in the whole visible body which comprises the heavens) is merely the same as that which must be understood to be the substance of each sensible thing, or whether besides this number which constitutes the substance of sensible things there is another number which is their cause.

Now Plato said that there is one kind of number which is the substance of sensible things, and another which is their cause. And while both Plato himself and Pythagoras thought that numbers are both sensible bodies themselves and their causes, Plato alone considered intellectual numbers to be the causes of things that are not sensible, and sensible numbers to be the causes and forms of sensible things. And since Pythagoras did not do this, his position is unsatisfactory.

207. In concluding, Aristotle says that these remarks about the Pythagoreans’ opinions will suffice; for it is enough to have touched upon them to this extent.

Critique of the Platonic Ideas

But those who posited ideas, and were the first to seek an understanding of the causes of sensible things, introduced other principles equal in number to these—as though one who wishes to count things thinks that this cannot be done when they are few, but believes that he can count them after he has increased their number.

For the separate forms are almost equal to, or not fewer than, these sensible things in the search for whose causes these thinkers have proceeded from sensible things to the forms.

For to each thing there corresponds some homogeneous entity bearing the same name, and with regard to the substances of other things there is a one-in-many, both in the case of these sensible things and in those which are eternal.

Furthermore, the forms do not become evident from any of the ways in which we prove that they exist. From some, no syllogism necessarily follows, but from others there does. According to these, there are forms of things of which we do not think there are forms.

According to those arguments from the sciences, there will be forms of all things of which there are sciences; according to the argument of the one-in-many there will also be forms of negations.

Again, according to the argument that there is some understanding of corruption, there will be forms of corruptible things; for of these there is some sensible image.

Again, according to the most certain arguments, some establish forms of relations, of which they deny there is any essential genus; but others lead to the third man.

And in general the arguments for the forms do away with the existence of the things that those who speak of the forms are more anxious to retain than the forms themselves. For it happens that the dyad is not first, but that number is, and that the relative is prior to that which exists of itself.

And all the other conclusions which some reach by following up the opinions about the ideas are opposed to the principles of the theory.

Again, according to the opinion whereby we claim that there are ideas, there will be forms not only of substances but also of many other things. For there is one concept not only of substances, but also of other things; and there are sciences not only of substance itself but also of other things. And a thousand other such difficulties face them.

But according to logical necessity and the opinions about the ideas, if the forms are participated in, there must be ideas only of substances.

For they are not participated in according to what is accidental. But things must participate in each form in this respect: insofar as each form is not predicated of a subject.

I mean that if anything participates in doubleness itself, it also participates in the eternal, but only accidentally; for it is an accident of doubleness to be eternal. Hence the forms will be substances.

But these things signify substance both here and in the ideal world; otherwise, why is it necessary that a one-in-many appear in addition to these sensible things? Indeed, if the form of the ideas and that of the things that participate in them are the same, there will be something in common.

For why should duality be one and the same in the case of corruptible twos and in those which are many but eternal, rather than in the case of this idea of duality and a particular two? But if the form is not the same, there will be pure equivocation; just as if one were to call both Callias and a piece of wood man, without observing any common attribute which they might have.

208. Here he argues disputatively against Plato’s opinion. This is divided into two parts.

First [208], he argues against Plato’s opinion with reference to his position about the substances of things;

second [217], with reference to his position about the principles of things, at and in general (990b17).

The first is divided into two parts.

First, he argues against Plato’s position that the forms are substances;

second (991b9; [239]), against the things that he posited about the objects of mathematics, at further, if the forms.

In regard to the first he does two things.

First, he argues against this position of Plato;

second [210], against the reasoning behind it, furthermore, the forms (990b8).

He first says (990a34) that the Platonists, in holding that the ideas are certain separate substances, seemed to be at fault in that when they sought for the causes of these sensible beings, they neglected sensible beings and invented certain other new entities equal in number to sensible beings.

This seems to be absurd, because one who seeks the causes of certain things ought to make these evident and not add other things, the premising of which only adds to the number of points which have to be investigated. For it would be similar if a man who wished to count certain things, which he did not think he was able to count because they are few, believed that he could count them by increasing their number through the addition of certain other things.

But it is evident that such a man acts foolishly, because the path is clearer when there are fewer things; it is better and easier to make certain of fewer things than of many. And the smaller a number is, the more certain it is to us, inasmuch as it is nearer to the unit, which is the most accurate measure. And just as the process of counting things is the measure we use to make certain of their number, in a similar fashion an investigation of the causes of things is the accurate measure for making certain of their natures. Therefore, just as the number of fewer numerable things is made certain of more easily, in a similar way the nature of fewer things is made certain of more easily.

Hence, when Plato increased the genera of beings to the extent that he did with a view to explaining sensible things, he added to the number of difficulties by taking what is more difficult in order to explain what is less difficult. This is absurd.

209. That the ideas are equal in number to, or not fewer than, sensible things, whose causes the Platonists seek (and Aristotle includes himself among their number because he was Plato’s disciple), and which they established by going from sensible things to the aforesaid forms, becomes evident if one considers by what reasoning the Platonists introduced the ideas. Now they reasoned thus: they saw that there is a one-in-many for all things having the same name. Hence they claimed that this one-in-many is a form.

Yet with respect to all substances of things other than the ideas, we see that there is found to be a one-in-many which is predicated of them univocally inasmuch as there are found to be many things that are specifically one. This occurs not only in the case of sensible things but also in that of the objects of mathematics, which are eternal; because among these there are also many things that are specifically one, as was stated above [157].

Hence it follows that some idea corresponds to each species of sensible things; and therefore each idea is something having the same name as these sensible things, because the ideas agree with them in name. For just as Socrates is called man, so also is the idea of man. Yet they differ conceptually; for the intelligible structure of Socrates contains matter, whereas that of the ideal man is devoid of matter. Or, according to another reading, each form is said to be something having the same name as these sensible things inasmuch as it is a one-in-many and agrees with the things of which it is predicated so far as the intelligible structure of the species is concerned.

Therefore he says that they are equal to, or not fewer than, these things. For either there are held to be ideas only of species, and then they would be equal in number to these sensible things (granted that things are counted here insofar as they differ specifically and not individually, for the latter difference is infinite); or there are held to be ideas not only of species but also of genera, and then there would be more ideas than there are species of sensible things, because all species would be ideas and in addition to these each and every genus would be an idea.

This is why he says that they are either not fewer than or more. Or, in another way, they are said to be equal inasmuch as he claimed that they are the forms of sensible things. And he says not “fewer than” but “more” inasmuch as he held that they are the forms not only of sensible things but also of the objects of mathematics.

210. Furthermore, the forms (990b8). Here he argues dialectically against the reasoning behind Plato’s position; in regard to this he does two things.

First, he gives a general account of the ways in which Plato’s arguments fail.

Second [211], he explains them in detail, at according to those arguments (990b11).

He says, first, that with regard to the ways in which we Platonists prove the existence of the forms, according to none of these are the forms seen to exist. The reason is that no syllogism follows necessarily from some of these ways—that is, from certain arguments of Plato—because they cannot demonstrate with necessity the existence of the ideas. However, from other arguments a syllogism does follow, although it does not support Plato’s thesis; for by certain of his arguments there are proved to be forms of certain things of which the Platonists did not think there are forms, just as there are proved to be forms of those things of which they think there are forms.

211. According to those arguments (990b11). Here he examines in detail the arguments by which the Platonists establish ideas.

First, he examines the second argument, and he does this by showing that from Plato’s argument it follows that there are forms of some things for which the Platonists did not posit forms.

Second [225], he examines the first argument, and he does this by showing that Plato’s arguments are not sufficient to prove that ideas exist, at but the most (991a8).

In regard to the first member of this division he gives seven arguments. The first is this. One of the arguments that induced Plato to posit ideas is taken from scientific knowledge. For, since science is concerned with necessary things, it cannot be concerned with sensible things, which are corruptible, but must be concerned with separate entities, which are incorruptible. According to the argument taken from the sciences, then, it follows that there are forms of every sort of thing of which there are sciences. Now there are sciences not only of that which is one-in-many, which is affirmative, but also of negations; for just as there are some demonstrations which conclude with an affirmative proposition, in a similar way there are demonstrations which conclude with a negative proposition. Hence it is also necessary to posit ideas of negations.

212. Again, according to the argument (990b13). Here he gives the second argument. In the sciences it is understood not only that some things always exist in the same way, but also that some things are destroyed; otherwise, the philosophy of nature, which deals with motion, would be destroyed. Therefore, if there must be ideas of all the things that are comprehended in the sciences, there must be ideas of corruptible things insofar as they are such, that is, insofar as these are singular sensible things; for thus are things corruptible.

But according to Plato’s theory, it cannot be said that those sciences by which we understand the processes of corruption in the world attain any understanding of the processes of corruption in sensible things, for there is no comprehension of these sensible things, but only imagination or phantasy, which is a motion produced by the senses in their act of sensing, as is pointed out in On the Soul 2.

213. Again, according to the most (990b15). Here he gives the third argument, which contains two conclusions that he says are drawn from the most certain arguments of Plato.

One conclusion is this: if there are ideas of all things of which there are sciences, and there are sciences not only of absolutes but also of things predicated relatively, then in giving this argument it follows that there are also ideas of relations. This is opposed to Plato’s view. For, since the separate ideas are things that exist of themselves, which is opposed to the intelligibility of a relation, Plato did not hold that there is a genus of ideas of relations, because the ideas are said to exist of themselves.

214. The second conclusion is one which follows from other most certain arguments, namely, that there is a third man. This phrase can be understood in three ways.

First, it can mean that the ideal man is a third man distinct from two men perceived by the senses, who have the common name “man” predicated of both of them. But this does not seem to be what he has in mind, granted that it is not mentioned in the Sophistical Refutations 2, because he argues against the position. Hence, according to this, it would not lead to an absurdity.

215. The second way in which this expression can be understood is this: the third man means one that is common to the ideal man and to one perceived by the senses.

For, since both a man perceived by the senses and the ideal man have a common intelligible structure (like two men perceived by the senses), then just as the ideal man is held to be a third man in addition to two men perceived by the senses, in a similar way there should be held to be another third man in addition to the ideal man and one perceived by the senses.

But neither does this seem to be what he has in mind here, because he leads us immediately to this absurdity by means of another argument. Hence it would be pointless to lead us to the same absurdity here.

216. The third way in which this expression can be understood is this. Plato posited three kinds of entities in certain genera of things, namely, sensible substances, the objects of mathematics, and the forms. He does this, for example, in the case of numbers, lines, and the like.

But there is no reason why intermediate things should be held to exist in certain genera rather than in others. Hence in the species of man it was also necessary to posit an intermediate man, who will be a third man midway between the man perceived by the senses and the ideal man. Aristotle also gives this argument in the later books of this work [2160].

217. And in general (990b17). Here he gives the fourth argument, which runs as follows. Whoever by his own reason does away with certain principles which are better known to him than the ones which he posits adopts an absurd position. But these theories about the forms which Plato held do away with certain principles whose reality the Platonists (when they said that there are ideas) were more convinced of than the existence of the ideas. Therefore, Plato’s position is absurd.

The minor premise is proved in this way. According to Plato the ideas are prior both to sensible things and to the objects of mathematics. But according to him the ideas themselves are numbers, and they are odd numbers rather than even ones, because he attributed odd number to form and even number to matter. Hence he also said that the dyad is matter. Therefore, it follows that other numbers are prior to the dyad, which he held to be the matter of sensible things, and identified with the great and small. Yet the Platonists asserted the very opposite of this, namely, that the dyad is first in the genus of number.

218. Again, if, as has been proved by the above argument [213], there must be ideas of relations, which are self-subsistent relations, and if the idea itself is prior to whatever participates in the idea, it follows that the relative is prior to the absolute, which is said to exist of itself. For sensible substances of this kind, which participate in ideas, are said to be in an unqualified sense. And in like manner whatever those who follow the opinion about the ideas say of all things is opposed to self-evident principles which even they themselves are most ready to acknowledge.

219. Again, according to the opinion (990b22). Here he gives the fifth argument, which is as follows. Ideas were posited by Plato in order that the intelligible structures and definitions of things given in the sciences might correspond to them, and in order that there could be sciences of them.

But there is one concept, a simple and indivisible concept, by which the quiddity of each thing is known—that is, not only the quiddity of substances but also of other things, namely, of accidents. And in a similar way there are sciences not only of substance and about substance, but there are also found to be sciences of other things, namely, of accidents. Hence, according to the opinion by which you, Platonists, acknowledge the existence of ideas, it evidently follows that there will be forms not only of substances but also of many other things, namely, of accidents.

This same conclusion follows not only because of definitions and the sciences, but there also happen to be many other such, or very many, reasons why it is necessary to posit ideas of accidents according to Plato’s arguments. For example, he held that the ideas are the principles of being and of becoming in the world, and of many such aspects which apply to accidents.

220. But, on the other hand, according to Plato’s opinion about the ideas and according to logical necessity, insofar as the ideas are indispensable to sensible things—namely, insofar as they are capable of being participated in by sensible things—it is necessary to posit ideas only of substances.

This is proved thus. Things that are accidental are not participated in. But an idea must be participated in by each thing insofar as it is not predicated of a subject.

This becomes clear as follows. If any sensible thing participates in doubleness itself, that is, in a separate doubleness (for Plato spoke of all separated things in this way, namely, as self-subsisting things), it must participate in the eternal. But it does not do this per se (because then it would follow that any double perceived by the senses would be eternal), but accidentally, insofar as doubleness itself, which is participated in, is eternal.

And from this it is evident that there is no participation in things that are accidental, but only in substances. Hence, according to Plato’s position a separate form was not an accident but only a substance. Yet according to the argument taken from the sciences there must also be forms of accidents, as was stated above [219].

221. But these things (990b34). Then he gives the sixth argument, which runs thus. These sensible things signify substance both in the case of things perceived by the senses and in that of those in the ideal world, namely, in the case of intelligible things, which signify substance (because they held that both intelligible things and sensible ones are substance). Therefore, it is necessary to posit in addition to both of these substances—intelligible and sensible ones—some common entity which is a one-in-many. For the Platonists maintained that the ideas exist on the grounds that they found a one-in-many which they believed to be separate from the many.

222. The need for positing a one apart from both sensible substances and the forms he proves thus. The ideas and the sensible things that participate in them either belong to one species or not. If they belong to one species, and it is necessary to posit, according to Plato’s position, one common separate form for all things having a common nature, then it will be necessary to posit some entity common to both sensible things and the ideas themselves which exists apart from both.

Now one cannot answer this argument by saying that the ideas, which are incorporeal and immaterial, do not stand in need of any higher forms. For the objects of mathematics, which Plato places midway between sensible substances and the forms, are similarly incorporeal and immaterial. Yet since many of them are found to belong to one species, Plato held that there is a common form for these things, in which not only the objects of mathematics participate but also sensible substances.

Therefore, if the two-ness which is the form or idea of two-ness is identical with that found in sensible twos, which are corruptible (just as a pattern is found in the things fashioned after it), and with that found in mathematical twos, which are many in one species (but are nevertheless eternal), then for the same reason in the case of the same two-ness (the idea two) and in that of the other two-ness (which is either mathematical or sensible), there will be another separate two-ness. For no reason can be given why the former should exist and the latter should not.

223. But if the other alternative is admitted—that sensible things, which participate in the ideas, do not have the same form as the ideas—it follows that the name which is predicated of both the ideas and sensible substances is predicated in a purely equivocal way. For those things are said to be equivocal which have only a common name and differ in their intelligible structure. And it follows that they are not only equivocal in every way but equivocal in an absolute sense, like those things on which one name is imposed without regard for any common attribute, which are said to be equivocal by chance—for example, if one were to call both Callias and a piece of wood man.

224. Now Aristotle added this because someone might say that a name is not predicated of an idea and of a sensible substance in a purely equivocal way, since a name is predicated of an idea per se and of a sensible substance by participation. For, according to Plato, the idea of man is called man in himself, whereas this man whom we apprehend by the senses is said to be a man by participation. However, such an equivocation is not pure equivocation. But a name which is predicated by participation is predicated with reference to something that is predicated per se; this is not pure equivocation, but the multiplicity of analogy. However, if an idea and a sensible substance were altogether equivocal by chance, it would follow that one could not be known through the other, as one equivocal thing cannot be known through another.

The destruction of the Platonists’ arguments for the ideas

But the most important problem of all that one might raise is what the forms contribute to sensible things, either to those which are eternal or to those which are generated and corrupted.

For they are not the cause of motion or of any change whatever in these things.

Nor are they of any assistance in knowing other things, for they are not the substance of other things, because if they were they would exist in them.

Nor do they contribute anything to the being of other things, for they are not present in the things that participate in them. For if they were they would perhaps seem to be causes, as whiteness mixed with some white thing.

But this theory, which was first stated by Anaxagoras and later by Hesiod and certain other thinkers, is easily disposed of. For it is easy to bring many absurd conclusions against such a view. In fact, other things are not derived from the forms in any of the customary ways.

Again, to say that they are exemplars, and that other things participate in them, is to speak with empty talk and to utter poetic metaphors.

For what is the work which looks toward the ideas? For one thing may both be and become similar to another thing and not be like it. So whether Socrates exists or not, a man like Socrates might come to be.

Similarly, it is evident that this will be the case even if Socrates is eternal. And there will be many exemplars of the same thing, and for this reason many forms, as animal and two-footed and man-in-himself will be the form of man.

Further, the forms will be the exemplars not only of sensible things but also of the forms themselves, as the genus of the species. Hence the same thing will be both an exemplar and a copy.

Again, it is thought to be impossible that the substance of a thing and that of which it is the substance should exist apart. Hence, if the forms are the substances of things, how will they exist apart from them?

But in the Phaedo it is stated that the forms are the causes both of being and of coming to be. Yet even if the forms do exist, still the things that participate in them will not come to be unless there is something which produces motion.

And many other things come to be, such as a house and a ring, of which we do not say that there are any forms. It is evident, then, that other things can exist and come to be because of such causes as those responsible for the things just mentioned.

225. Here Aristotle attacks the opinion of Plato insofar as he did not draw the conclusion which he intended to draw. For Plato intended to conclude that there are ideas by this argument that they are necessary in some way for sensible things. Hence, Aristotle, by showing that the ideas cannot contribute anything to sensible things, destroys the arguments by which Plato posits ideas. Thus he says (991a8) that of all the objections which may be raised against Plato the foremost is that the forms which Plato posited do not seem to contribute anything to sensible things, either to those which are eternal, as the celestial bodies, or to those which are generated and corrupted, as the elemental bodies. He shows that this criticism applies to each of the arguments by which Plato posited ideas, at for they are not (991a11).

226. Here (991a11) he begins to present five objections.

He argues, first [226], that they are useless in explaining motion;

second [227], that they are useless in explaining our knowledge of sensible things, at nor are they (991a12);

third [231], that they are of no value as exemplars, at again, to say (991a19);

fourth [236], that they are of no value as the substances of things, at again, it is thought (991b1);

and fifth [237] that they are of no value as causes of generation, at but in the Phaedo (991b3).

Accordingly, he says, first (991a11), that the forms cannot contribute anything to sensible things in such a way as to be the cause of motion or of any kind of change in them. He does not give the reason for this here but mentioned it above [237], because it is clear that the ideas were not introduced to explain motion but rather to explain immutability. For, since it seemed to Plato that all sensible things are always in motion, he wanted to posit something separate from sensible things that is fixed and immobile, of which there can be certain knowledge. Hence, according to him, the forms could not be held to be sensible principles of motion, but rather to be immutable things and principles of immutability; so that, undoubtedly, whatever is found to be fixed and constant in sensible things will be due to participation in the ideas, which are immutable in themselves.

227. Nor are they of any assistance (991a12). Second, he shows that the forms do not contribute anything to the knowledge of sensible things by the following argument. Knowledge of each thing is acquired by knowing its own substance, and not by knowing certain substances which are separate from it. But these separate substances, which they call forms, are altogether other than sensible substances. Therefore, a knowledge of them is of no assistance in knowing other sensible things.

228. Nor can it be said that the forms are the substances of these sensible things; for the substance of each thing is present in the thing whose substance it is. Therefore, if then forms were the substances of sensible things, they would be present in sensible things. This is opposed to Plato’s opinion.

229. Nor again can it be said that the forms are present in these sensible substances as in things that participate in them (for Plato thought that some forms are the causes of sensible things in this way). Just as we might understand whiteness itself existing of itself as a certain separate whiteness to be mingled with the whiteness in a subject, and to participate in whiteness, in a similar way we might say that man, who is separate, is mingled with this man who is composed of matter and the specific nature in which he participates. But this argument is easily disposed of, or destroyed; Anaxagoras, who also held that forms and accidents are mingled with things, was the first to state it. Hesiod and certain other thinkers were the second to mention it. Therefore, I say that it is easily disposed of, because it is easy to bring many absurd conclusions against such an opinion. For it would follow, as he pointed out above [194] against Anaxagoras, that accidents and forms could exist without substances. For only those things can exist separately which are naturally disposed to be mixed with other things.

230. It cannot be said, then, that the forms contribute in any way to our knowledge of sensible things as their substances. Nor can it be said that they are the principles of being in these substances by way of participation. Nor again can it be said that from these forms as principles other things—sensible ones—come to be in any of the ways in which we are accustomed to speak.

Therefore, if principles of being and principles of knowledge are the same, the forms cannot possibly make any contribution to scientific knowledge, since they cannot be principles of knowing. Hence he says in any of the customary ways of speaking, because Plato invented new ways of deriving knowledge of one thing from something else.

231. Again, to say (991a19). Here he gives the third objection against the arguments for separate forms. He says that the forms are of no value to sensible things as their exemplars.

First (991a19), he states his thesis;

second [232], he proves it, at for what is the work (991a22).

Accordingly he says, first (991a19), that to say that the forms are the exemplars both of sensible things and the objects of mathematics (because the latter participate in causes of this kind) is untenable for two reasons. First, because it is vain and useless to posit exemplars of this kind, as he will show; second, because this manner of speaking is similar to the metaphors which the poets introduce, which do not pertain to the philosopher. For the philosopher ought to teach by using proper causes.

Hence he says that this manner of speaking is metaphorical, because Plato likened the generation of natural substances to the making of works of art, in which the artisan, by looking at some exemplar, produces something similar to his artistic idea.

232. For what is the work (991a22). Here he proves his thesis by three arguments.

For the work (or use) of an exemplar seems to be this: the artisan by looking at an exemplar induces a likeness of the form in his own artifact. But in the operations of natural beings we see that like things are generated by like, as man is generated by man. Therefore, this likeness arises in things that are generated, either because some agent looks toward an exemplar or not. If not, then what is the work, or utility, of the agent’s so looking toward the ideas as exemplars? This is as if to say, none. But if the likeness results from looking at a separate exemplar, then it cannot be said that the cause of this likeness in the thing generated is the form of an inferior agent. For something similar would come into being with reference to this separate exemplar and not with reference to this sensible agent. And this is what he means when he says and not be like it, that is, like the sensible agent. From this the following absurdity results: someone similar to Socrates will be generated whether Socrates is held to exist or not. This we see is false, for unless Socrates plays an active part in the process of generation, no one similar to Socrates will ever be generated. Therefore, if it is false that the likeness of things that are generated does not depend on proximate agents, it is pointless and superfluous to posit separate exemplars of any kind.

233. However, it should be noted that, even though this argument does away with the separate exemplars postulated by Plato, it still does not do away with the fact that God’s knowledge is the exemplar of all things.

For, since things in the physical world are naturally inclined to induce their likeness in things that are generated, this inclination must be traced back to some directing principle which ordains each thing to its end. This can only be the intellect of that being who knows the end and the relationship of things to the end. Therefore, this likeness of effects to their natural causes is traced back to an intellect as their first principle. But it is not necessary that this likeness should be traced back to any other separate forms; because in order to have the above-mentioned likeness this direction of things to their end, according to which natural powers are directed by the first intellect, is sufficient.

234. Similarly, it is evident (991a26). Here he gives the second argument, which runs as follows. Just as Socrates adds something to man because he is Socrates, in a similar way man adds something to animal. And just as Socrates participates in man, so does man participate in animal. But if besides this Socrates whom we perceive there is held to be another Socrates who is eternal, as his exemplar, it will follow that there are several exemplars of this Socrates whom we perceive, namely, the eternal Socrates and the form man. And by the same reasoning the form man will have several exemplars; for its exemplar will be both animal and two-footed and also man-in-himself, or the idea of man. But that there should be several exemplars of a single thing made in likeness to an exemplar is untenable. Therefore, it is absurd to hold that things of this kind are the exemplars of sensible things.

235. Further, the forms (991a29). Here he gives the third argument, which runs thus. Just as a form is related to an individual, so also is a genus related to a species. Therefore, if the forms are the exemplars of individual sensible things, as Plato held, there will be also certain exemplars of these forms, namely, their genus. But this is absurd, because then it would follow that one and the same thing, form, would be an exemplar of one thing (namely, of the individual whom we perceive by the senses), and a copy made in likeness to something else (namely, a genus). This seems to be absurd.

236. Again, it is thought (991b1). Here he proves his fourth objection: the forms contribute nothing to sensible things as their substances or formal causes. For it is thought by him, that is to say, it is a matter of opinion (to put this impersonally), that it is impossible for a thing’s substance to exist apart from the thing whose substance it is. But the forms exist apart from the things of which they are the forms, that is, apart from sensible things. Therefore, they are not the substances of sensible things.

237. But in the Phaedo (991b3). Here he shows that the forms are of no value in accounting for the coming to be of sensible things, although Plato said in the Phaedo (that is, in one of his works), that the forms are the causes both of the being and of the coming to be of sensible things. But Aristotle disproves this by two arguments.

The first is as follows: to posit the cause is to posit the effect. However, even if the forms exist, the particular or individual things that participate in the forms will come into being only if there is some agent which moves them to acquire form. This is evident from Plato’s opinion that the forms are always in the same state.

Therefore, assuming that these forms exist, if individuals were to exist or come into being by participating in them, it would follow that individual substances of this kind would always be. This is clearly false. Therefore, it cannot be said that the forms are the causes of both the coming to be and the being of sensible things. The chief reason is that Plato did not hold that the forms are efficient causes, as was stated above [226].

For Aristotle holds that the being and coming to be of lower substances proceeds from immobile separate substances, inasmuch as these substances are the movers of the celestial bodies, by means of which generation and corruption are produced in these lower substances.

238. And many other (991b6). Here he gives the second argument, which runs thus. Just as artifacts are related to artificial causes, so are natural bodies to natural causes. But we see that many other things besides natural bodies come into being in the realm of these lower bodies, such as a house and a ring, for which the Platonists did not posit any forms. Therefore, other things (namely, natural things) can both be and come to be because of such proximate causes as those just mentioned (that is, artificial ones). Thus, just as artificial things come to be as a result of proximate agents, so also do natural things.

The ideas are not numbers

Further, if the forms are numbers, in what way will they be causes? Will it be because existing things are other numbers, so that this number is man, another Socrates, and still another Callias? In what respect, then, are the former the cause of the latter? For it will make no difference if the former are eternal and the latter are not.

But if it is because the things here are ratios of numbers, like a harmony, then clearly there will be one kind of thing of which they are the ratios. And if this is matter, evidently the numbers themselves will be certain ratios of one thing to something else. I mean that, if Callias is a numerical ratio of fire, water, earth, and air, his idea will also be a ratio of certain things, and man-in-himself, whether it be a number or not, will still be a numerical ratio of certain things and not just a number. Nor will it be any number besides these.

Again, one number will come from many numbers, but how or in what way can one form come from many forms?

But if one number is not produced from them but from the units which they contain, as the units in the number ten thousand, how are the units related? For if they are specifically the same, many absurdities will follow; and if they are not, neither will they be the same as one another nor all the others the same as all.

For in what way will they differ, if they have no attributes? For these statements are neither reasonable nor in accord with our understanding.

Further, if the forms are numbers, it is necessary to set up some other genus of number: that with which arithmetic deals.

And all the things that are said to be intermediate, from what things or what principles in an absolute sense will they come, or why will they be an intermediate class between the things at hand and those ideas?

Again, each of the units which are contained in the number two will come from a prior two. But this is impossible.

Further, why is a number something composed of these?

And, again, in addition to what has been said, if the units are different, it will be necessary to speak of them in the same way as do those who say that the elements are four or two. For none of them designates as an element what is common (namely, body), but fire and earth, whether body is something in common or not. But now we are speaking of the one as if it were one thing made up of like parts, as fire or water. But if this is the case, numbers will not be substances. Yet it is evident that, if the one itself is something common and a principle, then the one is used in different senses; otherwise, this will be impossible.

Now when we wish to reduce substances to their principles, we claim that lengths come from the long and short (that is, from a kind of great and small), and the plane from the wide and narrow, and body from the deep and shallow.

Yet how will a surface contain a line, or a solid a line or surface? For the wide and narrow is a different genus from the deep and shallow. Hence, just as number is not present in these, because the many and few differ from these, it is evident that no one of the other higher genera will be present in the lower. And the broad is not in the genus of the deep, for then the solid would be a kind of surface.

Further, from what will points derive being? Plato was opposed to this genus of objects as a geometrical fiction, but he called them the principle of a line. And he often holds that there are indivisible lines. Yet these must have some limit. Therefore, any argument that proves the existence of the line also proves the existence of the point.

239. Here he destroys Plato’s opinion about the forms inasmuch as Plato claimed that they are numbers. In regard to this he does two things.

First, he argues dialectically against Plato’s opinion about numbers,

and second [254], against his opinion about the other objects of mathematics, at now when we wish (992a10).

In regard to the first part he gives six arguments.

The first (991b9) is this. In the case of things that are substantially the same, one thing is not the cause of another. But sensible things are substantially numbers, according to the Platonists and Pythagoreans. Therefore, if the forms themselves are numbers, they cannot be the cause of sensible things.

240. But if it is said that some numbers are forms and others are sensible things, as Plato literally held (as though we were to say that this number is man and another is Socrates and still another is Callias), even this would not seem to be sufficient. For, according to this view, the intelligible structure of number will be common both to sensible things and the forms. But in the case of things that have the same intelligible structure, one does not seem to be the cause of another. Therefore, the forms will not be the causes of sensible things.

241. Nor again can it be said that they are causes for the reason that, if those numbers are forms, they are eternal. For this difference—namely, that some things differ from others in virtue of being eternal and non-eternal in their own being considered absolutely—is not sufficient to explain why some things are held to be the causes of others. Indeed, things differ from each other as cause and effect rather because of the relationship which one has to the other. Therefore, things that differ numerically do not differ from each other as cause and effect because some are eternal and some are not.

242. Again, it is said that sensible things are certain ratios or proportions of numbers, and that numbers are the causes of these sensible things, as we also observe to be the case in harmonies, that is, in the combinations of musical notes. For numbers are said to be the causes of harmonies insofar as the numerical proportions applied to sounds yield harmonies. Now if the above is true, then just as in harmonies there are found to be sounds in addition to numerical proportions, in a similar way it was obviously necessary to posit in addition to the numbers in sensible things something generically one to which the numerical proportions are applied, so that the proportions of those things that belong to that one genus would constitute sensible things.

However, if that to which the numerical proportion in sensible things is applied is matter, evidently those separate numbers, which are forms, had to be termed proportions of some one thing to something else. For this particular man, called Callias or Socrates, must be said to be similar to the ideal man, called man-in-himself, or humanity. Hence, if Callias is not merely a number, but is rather a kind of ratio or numerical proportion of the elements (that is, of fire, earth, water, and air), and if the ideal man-in-himself is a kind of ratio or numerical proportion of certain things, the ideal man will not be a number by reason of its own substance.

From this it follows that there will be no number besides these, that is, besides the things numbered. For if the number which constitutes the forms is separate in the highest degree, and if it is not separate from things but is a kind of proportion of numbered things, no other number will now be separate. This is opposed to Plato’s view.

243. It also follows that the ideal man is a proportion of certain numbered things, whether it is held to be a number or not. For according to those who held that substances are numbers, and according to the philosophers of nature, who denied that numbers are substances, some numerical proportions must be found in the substances of things. This is most evident in the case of the opinion of Empedocles, who held that each one of these sensible things is composed of a certain harmony or proportion of the elements.

244. Again, one number (991b22). Here he gives the second argument which runs thus: one number is produced from many numbers. Therefore, if the forms are numbers, one form is produced from many forms. But this is impossible.

For if from many things that differ specifically something specifically one is produced, this comes about by mixture, in which the natures of the things mixed are not preserved (just as a stone is produced from the four elements).

Again, from things of this kind which differ specifically, one thing is not produced by reason of the forms, because the forms themselves are combined in such a way as to constitute a single thing only in accordance with the intelligible structure of individual things, which are altered in such a way that they can be mixed together. And when the forms themselves of the numbers two and three are combined, they give rise to the number five, so that each number remains and is retained in the number five.

245. But since someone could answer this argument, in support of Plato, by saying that one number does not come from many numbers, but each number is immediately constituted of units, Aristotle is therefore logical in rejecting this answer, at but if one number (991b23). For if it is said that some greater number, such as ten thousand, is not produced from them (namely, from twos or many smaller numbers), but from the units (or ones), this question will follow: how are the units of which numbers are composed related to each other? For all units must either conform with each other or not.

246. But many absurd conclusions follow from the first alternative, especially for those who claim that the forms are numbers. For it will follow that different forms do not differ substantially but only insofar as one form surpasses another. It also seems absurd that units should differ in no way and yet be many, since difference is a result of multiplicity.

247. But if they do not conform, this can happen in two ways.

First, they can lack conformity because the units of one number differ from those of another number, as the units of the number two differ from those of the number three, although the units of one and the same number will conform with each other.

Second, they can lack conformity insofar as the units of one and the same number do not conform with each other or with the units of another number. He indicates this distinction when he says, neither will they be the same as one another (991b26), namely, the units which comprise the same number, nor all the others the same as all, namely, those which belong to different numbers.

Indeed, in whatever way there is held to be lack of conformity between units an absurdity is apparent. For every instance of non-conformity involves some form or attribute, just as we see that bodies which lack conformity differ insofar as they are hot and cold, white and black, or in terms of similar attributes. Now units lack qualities of this kind, because they have no qualities, according to Plato. Hence it will be impossible to hold that there is any non-conformity or difference between them of the kind caused by a quality. Thus it is evident that Plato’s opinions about the forms and numbers are neither reasonable (for example, those proved by an apodictic argument) nor in accord with our understanding (for example, those things that are self-evident and verified by intellect alone, as the first principles of demonstration).

248. Further, if the forms (991b27). Here he gives the third argument against Plato, which runs thus. All objects of mathematics, which Plato affirmed to be midway between the forms and sensible substances, are derived unqualifiedly from numbers, either as proper principles, or as first principles. He says this because in one sense numbers seem to be the immediate principles of the other objects of mathematics. For the Platonists said that the number one constitutes the point, the number two the line, the number three surface, and the number four the solid. But in another sense the objects of mathematics seem to be reduced to numbers as first principles and not as proximate ones. For the Platonists said that solids are composed of surfaces, surfaces of lines, lines of points, and points of units, which constitute numbers. But in either way it followed that numbers are the principles of the other objects of mathematics.

249. Therefore, just as the other objects of mathematics constituted an intermediate genus between sensible substances and the forms, in a similar way it was necessary to devise some genus of number which is other than the numbers that constitute the forms and other than those that constitute the substance of sensible things.

And arithmetic, which is one of the mathematical sciences, evidently deals with this kind of number as its proper subject, just as geometry deals with mathematical extensions.

However, this position seems to be superfluous, for no reason can be given why number should be midway between the things at hand, or sensible things, and those in the ideal world, or the forms, since both sensible things and the forms are numbers.

250. Again, each of the units (991b31). Here he gives the fourth argument, which runs thus. Those things that exist in the sensible world and those which exist in the realm of mathematical entities are caused by the forms. Therefore, if some number two is found both in the sensible world and in the realm of the objects of mathematics, each unit of this subsequent two must be caused by a prior two, which is the form of two-ness.

But it is impossible that unity should be caused by duality. For it would be most necessary to say this if the units of one number were of a different species than those of another number, because then these units would acquire their species from a form which is prior to the units of that number. And thus the units of a subsequent two would have to be produced from a prior two.

251. Further, why is (992a1). Here he gives the fifth argument, which runs thus: many things combine so as to constitute one thing only by reason of some cause, which can be considered to be either extrinsic, as some agent which unites them, or intrinsic, as some unifying bond. Or if some things are united of themselves, one of them must be potential and another actual. However, in the case of units none of these reasons can be said to be the one reason why a number (that is, the cause by which a number) will be a certain combination, or collection of many units. That is to say: it will be impossible to give any reason for this.

252. And, again, in addition (992a2). Here he gives the sixth argument, which runs thus. If numbers are the forms and substances of things, it will be necessary to say, as has been stated before [245], either that units are different, or that they conform. But if they are different, it follows that unity as unity will not be a principle. This is clarified by a similar case drawn from the position of the natural philosophers. For some of these thinkers held that the four elemental bodies are principles. But even though being a body is common to these elements, these philosophers did not maintain that a common body is a principle, but rather fire, earth, water, and air, which are different bodies. Therefore, if units are different, even though all have in common the intelligible constitution of unity, it will not be said that unity itself as such is a principle. This is contrary to the Platonists’ position; for they now say that the unit is the principle of things, just as the natural philosophers say that fire or water or some body with like parts is the principle of things. But if our conclusion against the Platonists’ theory is true—that unity as such is not the principle and substance of things—it will follow that numbers are not the substances of things. For number is held to be the substance of things only insofar as it is constituted of units, which are said to be the substances of things. This is also contrary to the Platonists’ position which is now being examined, namely, that numbers are forms.

253. But if you say that all units are undifferentiated, it follows that the whole, that is, the entire universe, is a single entity, since the substance of each thing is the one itself, and this is something common and undifferentiated. Further, it follows that the same entity is the principle of all things. But this is impossible by reason of the notion involved, which is inconceivable in itself—namely, that all things should be one according to the aspect of substance. For this view contains a contradiction, since it claims that the one is the substance of all things, yet maintains that the one is a principle. For one and the same thing is not its own principle, unless, perhaps, it is said that “the one” is used in different senses, so that when the senses of the one are differentiated all things are said to be generically one and not numerically or specifically one.

254. Now when we wish (992a10). Here he argues against Plato’s position with reference to his views about mathematical extensions.

First (992a10), he gives Plato’s position;

second [255], he advances an argument against it, at yet how will (992a13).

He says, first, that the Platonists, wishing to reduce the substances of things to their first principles, when they say that continuous quantities themselves are the substances of sensible things, thought they had discovered the principles of things when they assigned line, surface, and solid as the principles of sensible things. But in giving the principles of continuous quantities they said that lengths, or lines, are composed of the long and short, because they held that contraries are the principles of all things. And since the line is the first of continuous quantities, they first attributed to it the great and small, for inasmuch as these two are the principles of the line, they are also the principles of other continuous quantities. He says from a kind of great and small because the great and small are also placed among the forms, as has been stated [217]. But insofar as they are limited by position, and are thus particularized in the genus of continuous quantities, they constitute first the line and then other continuous quantities. And for the same reason they said that surface is composed of the wide and narrow, and body of the deep and shallow.

255. Yet how will a surface (992a13). Here he argues against the foregoing position by means of two arguments.

The first is as follows. Things whose principles are different are themselves different. But the principles of continuous quantities mentioned above are different, according to the foregoing position, for the wide and narrow, which are posited as the principles of surface, belong to a different genus than the deep and shallow, which are held to be the principles of body. The same thing can be said of the long and short, which differ from each of the above. Therefore, line, surface, and body all differ from each other. How then will one be able to say that a surface contains a line, and a body a line and a surface?

In confirmation of this argument he introduces a similar case involving number. For the many and few, which are held to be principles of things for a similar reason, belong to a different genus than the long and short, the wide and narrow, and the deep and shallow. Therefore, number is not contained in these continuous quantities but is per se separate. Hence, for the same reason, the higher of the above mentioned things will not be contained in the lower—for example, a line will not be contained in a surface or a surface in a body.

256. But because it could be said that certain of the foregoing contraries are the genera of the others—for example, that the long is the genus of the broad, and the broad the genus of the deep—he destroys this objection by the following argument. Things composed of principles are related to each other in the same way as their principles are. Therefore, if the broad is the genus of the deep, surface will also be the genus of body. Hence a solid will be a kind of plane—that is, a species of surface. This is clearly false.

257. Further, from what will (992a19). Here he gives the second argument, which involves points. In regard to this Plato seems to have made two errors.

First, Plato claimed that a point is the limit of a line, just as a line is the limit of a surface and a surface the limit of a body. Therefore, just as he posited certain principles of which the latter are composed, so too he should have posited some principle from which points derive their being. But he seems to have omitted this.

258. The second error is this. Plato seems to have held different opinions about points. For sometimes he maintained that the whole science of geometry treats this genus of things (namely, points), inasmuch as he held that points are the principles and substance of all continuous quantities. And he not only implied this but even explicitly stated that a point is the principle of a line, defining it in this way. But many times he said that indivisible lines are the principles of lines and other continuous quantities, and that this is the genus of things with which geometry deals (namely, indivisible lines). Yet by reason of the fact that he held that all continuous quantities are composed of indivisible lines, he did not avoid the consequence that continuous quantities are composed of points, and that points are the principles of continuous quantities. For indivisible lines must have some limits, and these can only be points. Hence, by whatever argument indivisible lines are held to be the principles of continuous quantities, by the same argument too the point is held to be the principle of continuous quantity.

The ideas are not principles

And, in general, even though wisdom investigates the causes of apparent things, we have neglected this study. For we say nothing about the cause from which motion originates. And while we think that we are stating the substance of these sensible things, we introduce other substances. But the way in which we explain how the latter are the substances of the former is empty talk, for to participate, as we have said before (991a20), signifies nothing.

Moreover, that which we see to be the cause in the sciences—that by reason of which all intellect and all nature operates—on that cause which we say is one of the principles, the forms do not touch in any way. But mathematics has been turned into philosophy by present-day thinkers (1028b16), although they say that mathematics must be treated for the sake of other things.

Further, one might suppose that the underlying substance which they consider as matter is too mathematical, and that it is rather a predicate and difference of substance and matter, like the great and small. This is just as the philosophers of nature speak of the rare and dense (985b10), which they say are the primary differences of the underlying subject, for these are a kind of excess and defect.

And with regard to motion, if these entities are motion, evidently the forms are moved; but if they are not, from what does motion come? For if it has no cause, the whole study of nature is destroyed.

And what seems easy to show is that all things are not one, for from their position all things do not become one. But if someone should assert that all things are some one thing, not even this is true unless one grants that the universal is a genus. In certain other cases this is impossible.

For they do not have any theory about the lengths, widths, and solids which come after the numbers, either as to how they now exist or will exist, or what importance they have. For it is impossible that they should be forms (since they are not numbers), or intermediate things (for those are the objects of mathematics), or corruptible things. On the contrary, it seems that they form a fourth genus.

And, in general, to look for the elements of existing things without distinguishing the different senses in which things are said to be makes it impossible to discover them.

And their view is unsatisfactory in another way—namely, in the way in which they seek for the elements of which things are composed. For it is impossible to understand of what things action or passion or straightness is composed.

But if this is possible only in the case of substances, then to look for the elements of all existing things, or to think that we have found them, is a mistake.

But how will one acquire knowledge of the elements of all things? For it is clearly impossible to have prior knowledge of anything. For just as one acquiring knowledge of geometry must have a prior knowledge of other things, but not of the things that this science investigates and which he is to learn, so it is in the case of the other sciences.

Hence, if there is a science of all things as some say (and there must be a science of these), the one learning this science does not have any prior knowledge of it.

But all learning proceeds from things previously known, either all or some of them, whether the learning be by demonstration or by definitions.

For the parts of which definitions are composed must already be known beforehand and be evident. The same thing is true in the case of things discovered by induction.

But if this science were connatural, it is a wonder how we could be unconscious of having the most important of the sciences.

Again, how is anyone to know the elements of which things are composed, and how is this to be made evident? For this also presents a difficulty, because one might argue in the same way as one does about certain syllables. For some say that SMA is made up of S, M, and A, whereas others say that it is a totally different sound and not any of those which are known to us.

Again, how could one know the things of which a sense is cognizant without having that sense? Yet this will be necessary if sensible things are the elements of which all things are composed, just as spoken words are composed of their proper elements.

From the foregoing, then, it is evident that they all seem to seek the causes mentioned in the Physics, and that we cannot state any other in addition to these. But they understood these obscurely, and while in one sense all causes have been mentioned before, in another sense they have not been mentioned at all.

Indeed, the earliest philosophy seems to speak in a faltering way about all subjects inasmuch as it was new as regards principles and the first of its kind. For even Empedocles says that ratios are present in bone, and that this is the quiddity or substance of a thing.

But if this is true, there must likewise be a ratio of flesh and of every other thing, or of nothing. For it is because of this that flesh and bone and every other thing exists, and not because of their matter, which he says is fire, earth, air, and water. But if someone else had said this, he would have been forced to agree to the same thing. But he has not said this. Such things as these, then, have been explained before. So let us return again to whatever problems one might raise about the same subject, for perhaps in the light of these we shall be able to make some investigation into subsequent problems.

259. Here Aristotle destroys Plato’s opinion about the principles of things.

First, he destroys Plato’s opinion about principles of being;

second [268], his opinion about principles of knowledge, at but how will one (992b24).

In regard to the first part he gives six arguments.

The first is based on the fact that Plato neglected to deal with the genera of causes. Thus he says that in general, wisdom, or philosophy, has as its aim to investigate the causes of apparent things, that is, things apparent to the senses. For men began to philosophize because they sought for the causes of things, as was stated in the prologue [53]. But the Platonists, among whom he includes himself, neglected the principles of things, because they said nothing about the efficient cause, which is the source of change. And by positing the ideas they thought they had given the formal cause of things.

But while they thought that they were speaking of the substance of sensible things, they posited the existence of certain other separate substances which differ from these. However, the way in which they assigned these separate substances as the substances of sensible things is empty talk, that is, it proves nothing and is not true. For they said that the forms are the substances of sensible things inasmuch as they are participated in by sensible things. But what they said about participation is meaningless, as is clear from what was said above [225].

Furthermore, the forms which they posited have no connection with the final cause, although we see that this is a cause in certain sciences which demonstrate by means of the final cause, and that it is by reason of this cause that every intellectual agent and every natural one operates, as has been shown in the Physics 2.

And just as they do not touch on that cause which is called an end when they postulate the existence of the forms [169], neither do they treat of that cause which is called the source of motion (namely, the efficient cause, which is like the opposite of the final cause).

But the Platonists, by omitting causes of this kind (since they did omit a starting-point and end of motion), have dealt with natural things as if they were objects of mathematics, which lack motion. Hence they said that the objects of mathematics should be studied not only for themselves but for the sake of other things (namely, natural bodies), inasmuch as they attributed the properties of the objects of mathematics to sensible bodies.

260. Further, one might (992b1). Here he gives the second argument, which runs thus: that which is posited as the matter of a thing is the substance of a thing, and is predicable of a thing to a greater degree than something which exists apart from it. But a form exists apart from sensible things. Therefore, according to the opinion of the Platonists, one might suppose that the underlying substance as matter is the substance of the objects of mathematics rather than a separate form. Furthermore, he admits that it is predicated of a sensible thing rather than the above form. For the Platonists held that the great and small is a difference of substance or matter, for they referred these two principles to matter just as the philosophers of nature [115] held that rarity and density are the primary differences of the underlying subject, or matter, by which matter is changed, and spoke of them in a sense as the great and small. This is clear from the fact that rarity and density are a kind of excess and defect. For the dense is what contains a great deal of matter under the same dimensions, and the rare is what contains very little matter. Yet the Platonists said that the forms are the substance of sensible things rather than the objects of mathematics, and that they are predicable of them to a greater degree.

261. And with regard (992b7). Here he gives the third argument, which runs thus. If those attributes which exist in sensible things are caused by separate forms, it is necessary to say either that there is an idea of motion among the forms or that there is not. If there is a form or idea of motion among the forms, and there cannot be motion without something that is moved, it also follows that the forms must be moved. But this is opposed to the Platonists’ opinion, for they claimed that the forms are immobile.

On the other hand, if there is no idea of motion, and these attributes which exist in sensible things are caused by the ideas, it will be impossible to assign a cause for the motion which occurs in sensible things. Thus the entire investigation of natural philosophy, which studies mobile things, will be destroyed.

262. And what seems easy (992b9). Then he gives the fourth argument, which runs thus. If unity were the substance of all things, as the Platonists assumed, it would be necessary to say that all things are one, just as the philosophers of nature also did in claiming that the substance of all things is water, and so on for the other elements. But it is easy to show that all things are not one. Hence the position that unity is the substance of all things is not held in high repute.

263. But let us assume that someone might say that it does not follow, from Plato’s position, that all things are one in an unqualified sense but in a qualified sense, just as we say that some things are one generically or specifically. And if someone wished to say that all things are one in this way, even this could be held only if what I call the one were a genus or universal predicate of all things. For then we could say that all things are one specifically, just as we say that both a man and an ass are animal substantially. But in certain cases it seems impossible that there should be one genus of all things, because the difference dividing this genus would necessarily not be one, as will be said in book 3 [432]. Therefore, in no way can it be held that the substance of all things is one.

264. For they do not have (992b13). Here he gives the fifth argument, which runs thus. Plato placed lengths, widths, and solids after numbers as the substances of sensible things, namely, as that of which they are composed. But, according to Plato’s position, there seems to be no reason why they should be held to exist either now or in the future. Nor does this notion seem to have any efficacy to establish them as the causes of sensible things. For things that exist now must mean immobile things (because these always exist in the same way), whereas things that will exist must mean those which are capable of generation and corruption, which acquire being after non-being.

This becomes clear in this way. Plato posited three genera of things: sensible things, the forms, and the objects of mathematics (which are an intermediate genus). But such lines and surfaces as those of which sensible bodies are composed cannot be forms, for the forms are essentially numbers, whereas these things come after numbers. Nor can such lines and surfaces be said to be an intermediate genus between the forms and sensible things. For the things in this intermediate genus are the objects of mathematics, and exist apart from sensible things, but this cannot be said of the lines and surfaces of which sensible bodies are composed. Nor again can such lines and surfaces be sensible things, for the latter are corruptible, but these lines and surfaces are incorruptible, as will be proved below in book 3 [466]. Therefore, either these things are nothing at all or they constitute a fourth genus of things, which Plato omitted.

265. And, in general (992b18). Here he gives the sixth argument, which runs thus. It is impossible to discover the principles of anything that is spoken of in many senses, unless these many senses are distinguished. Now those things that agree in name only and differ in their intelligible structure cannot have common principles, otherwise they would have the same intelligible structure, since the intelligible structure of a thing is derived from its own principles. But it is impossible to assign distinct principles for those things that have only the name in common, unless it be those whose principles must be indicated to differ from each other. Therefore, since being is predicated both of substance and of the other genera in different senses and not in the same sense, Plato assigned inadequate principles for things by failing to distinguish beings from each other.

266. But, since someone could assign principles to things that differ in their intelligible structure and have a common name by adjusting proper principles to each without distinguishing the many senses of the common name, and since the Platonists have not done this, then in another way, or by another argument, they assigned inadequate principles to things when they looked for the elements of which things are made—namely, in the way in which they sought for them, inasmuch as they did not assign principles which are sufficient for all things. For from their statements it is impossible to understand the principles of which either action and passion or curvature and straightness (or other such accidents) are composed. For they indicated only the principles of substances and neglected accidents.

267. But if in defense of Plato someone wished to say that it is possible for the elements of all things to have been acquired or discovered at the moment when the principles of substances alone happen to have been acquired or discovered, this opinion would not be true. For even if the principles of substances are also in a sense the principles of accidents, nevertheless accidents have their own principles. Nor are the principles of all genera the same in all respects, as will be shown below in book 11 [2173] and book 12 [2455] of this work.

268. But how will one (992b24). Here he argues dialectically against Plato’s position that the ideas are the principles of our scientific knowledge.

He gives four arguments, of which the first is this. If our scientific knowledge is caused by the ideas themselves, it is impossible for us to acquire knowledge of the principles of things. But it is evident that we do acquire knowledge. Therefore, our knowledge is not caused by the ideas themselves.

That it would be impossible to acquire knowledge of anything, he proves thus. No one has any prior knowledge of that object of which he ought to acquire knowledge. For example, even though in the case of geometry one has prior knowledge of other things that are necessary for demonstration, nevertheless the objects of which he ought to acquire knowledge he must not know beforehand. The same thing is also true in the case of the other sciences.

But if the ideas are the cause of our knowledge, men must have knowledge of all things, because the ideas are the intelligible structures of all knowable things. Therefore, we cannot acquire knowledge of anything unless one might be said to acquire knowledge of something which he already knew.

If it is held, then, that someone acquires knowledge, he must not have any prior knowledge of the thing which he comes to know, but only of certain other things through which he becomes instructed; that is, one acquires knowledge through things previously known, either of all, that is, of universals, or some of them, that is, of singular things. One learns through universals in the case of those things that are discovered by demonstration and definition, for in the case of demonstrations and definitions the things of which definitions or universals are composed must be known first. And in the case of things that are discovered by induction singular things must be known first.

269. But if this science (992b33). Here he gives the second argument, which runs thus. If the ideas are the cause of our knowledge, it must be connatural to us, for men grasp sensible things through this proper nature, because sensible things participate in ideas (according to the Platonists). But the most important knowledge or science is one that is connatural to us and which we cannot forget, as is evident of our knowledge of the first principles of demonstration, of which no one is ignorant. Hence there is no way in which we can forget the knowledge of all things caused in us by the ideas. But this is contrary to the Platonists’ opinion, who said that the soul forgets the knowledge which it has of all things by nature as a result of its union with the body, and that by teaching a man acquires knowledge of something that he previously knew, as though the process of acquiring knowledge were merely one of remembering.

270. Again, how is anyone (993a2). Here he gives the third argument, which runs thus. In order to know things, a man must acquire knowledge not only of the forms of things but also of the material principles of which they are composed. This is evident from the fact that occasionally questions arise regarding these. For example, with regard to the syllable SMA, some raise the question whether it is composed of the three letters S, M, and A, or whether it is one letter which is distinct from these and has its own sound. But only the formal principles of things can be known through the ideas, because the ideas are the forms of things. Hence the ideas are not a sufficient cause of our knowledge of things when material principles remain unknown.

271. Again, how could (993a7). Here he gives the fourth argument, which runs thus. In order to know reality, we must know sensible things, because sensible things are the apparent material element of which all things are composed, just as complex sounds (such as syllables and words) are composed of their proper elements. If, then, knowledge is caused in us by the ideas, our knowledge of sensible things must be caused by the ideas. But the knowledge which is caused in us by the ideas is grasped without the senses, because we have no connection with the ideas through the senses. Therefore, in the act of perception it follows that anyone who does not have a sense can apprehend the object of that sense. This is clearly false, for a man born blind cannot have any knowledge of colors.

272. From the foregoing (993a11). Here he summarizes the statements made by the ancient philosophers. He says that from what has been said above it is evident that the ancient philosophers attempted to investigate the cause which he dealt with in the Physics, and that in their statements we find no cause in addition to those established in that work.

However, these men discussed these causes obscurely, and while in a sense they have mentioned all of these causes, in another sense they have not mentioned any of them. For just as young children at first speak imperfectly and in a stammering way, in a similar fashion this philosophy, since it was new, seems to speak imperfectly and in a stammering way about the principles of all things. This is borne out by the fact that Empedocles was the first to say that bones have a certain ratio, or proportional mixture, and that this is a thing’s quiddity or substance. But the same thing must also be true of flesh and of every other single thing or of none of them, for all of these things are mixtures of the elements. And for this reason it is evident that flesh and bone and all things of this kind are not what they are because of their matter, which he identified with the four elements, but because of this principle—their form.

Empedocles, however, compelled as it were by necessity of truth, would have maintained this view if it had been expressed more clearly by someone else, but he did not express it clearly.

And just as the ancient philosophers have not clearly expressed the nature of form, neither have they clearly expressed the nature of matter, as was said above about Anaxagoras [90]. Nor have they clearly expressed the nature of any other principles.

Therefore, we have spoken before [190] concerning such things as have been stated imperfectly. And with regard to these matters we will restate again in book 3 [423] whatever difficulties can be raised on both sides of the question. For perhaps from such difficulties we will discover some useful information for dealing with the problems which must be examined and solved later on throughout this whole science.

The acquisition of truth

Theoretical or speculative knowledge of truth is in one sense difficult, and in another easy.

An indication of this is found in the fact that, while no one can attain an adequate knowledge of it, all men together do not fail, because each one is able to say something true about nature.

And while each one individually contributes nothing or very little to the truth, still as a result of the combined efforts of all a great amount of truth becomes known.

Therefore, if the situation in the case of truth seems to be like the one which we speak of in the proverb “Who will miss a door?,” then in this respect it will be easy to know the truth.

But the fact that we cannot simultaneously grasp a whole and its parts shows the difficulty involved.

However, since the difficulty is twofold, perhaps its cause is not in things but in us. For just as the eyes of owls are to the light of day, so is our soul’s intellective power to those things that are by nature the most evident of all.

Now it is only right that we should be grateful not merely to those with whose views we agree but also to those who until now have spoken in a superficial way, for they too have made some contribution because they have made use of the habit which we now exercise.

Thus if there had been no Timotheus, we would not have a great part of our music; and if there had been no Phrynis, there would have been no Timotheus.

The same is true of those who have made statements about the truth, for we have accepted certain opinions from some of them, and others have been the cause of them attaining their knowledge as they have been the cause of us attaining ours.

273. Having criticized the ancient philosophers’ opinions about the first principles of things, with which first philosophy is chiefly concerned, the Philosopher now begins to establish what is true. First philosophy considers truth in a different way from the particular sciences do. Each of the particular sciences considers a particular truth out a definite genus of beings—for example, geometry deals with the continuous quantities of bodies, and arithmetic with numbers—but first philosophy considers what is universally true of things. Therefore, it pertains to this science to consider in what respects man is capable of knowing the truth.

274. This part is divided into two sections.

In the first (993a30; [274]), he deals with the things that belong to a universal consideration of truth.

In the second (995a24; [338]) he begins to investigate what is true of first principles and of everything else with which this philosophy deals. He does this in book 3, which begins with the words with a view to the science under investigation.

The first part is again divided into three parts.

In the first of these he explains in what respects man is capable of knowing the truth.

In the second (993b19; [290]) he indicates to what science the knowledge of truth principally belongs, at it is only right to call.

In the third (994b32; [331]) he explains the method by which truth is investigated, at the way in which people are affected.

In regard to the first he does three things.

First, he shows in what respect it is easy to know the truth.

Second (993b7; [279]), he gives the reason for the difficulty involved, at however, since the difficulty is twofold.

Third (993b11; [287]), he shows how men assist each other to know the truth, at now it is only right.

In regard to the first he does two things.

First, he states what he intends to prove. He says that theoretical knowledge, that is, the contemplative or speculative understanding of truth, is in one sense difficult, and in another easy.

275. Second, at an indication of this (993a31), he explains what he intends to prove:

first, in what sense it is easy to know the truth;

second [278], in what sense it is difficult, at but the fact (993b6).

He shows in what sense it is easy to know the truth by giving three indications.

The first is this: while no man can attain a complete knowledge of the truth, still no man is so completely devoid of truth that he knows nothing about it. This is shown by the fact that anyone can make a statement about the truth and the nature of things, which is a sign of interior consideration.

276. And while each one individually (993b2). Here he gives the second indication. He says that while the amount of truth that one man can discover or contribute to the knowledge of truth by his own study and talents is small compared with a complete knowledge of truth, nevertheless what is known as a result of the combined efforts of all—that is, what is discovered and collected into one whole—becomes quite extensive. This can be seen in the case of the particular arts, which have developed in a marvelous manner as a result of the studies and talents of different men.

277. Therefore, if the situation (993b4). Third, he shows that the same thing is true by citing a common proverb. He concludes from the foregoing that if anyone can attain some knowledge of the truth, even though it be little, the situation in the case of knowledge is like the one that we speak of in the proverb, who will miss a door? that is, the outer door of a house. For it is difficult to know what the interior of a house is like, and a man is easily deceived in such matters.

But just as no one is mistaken about the entrance of a house, which is evident to all and is the first thing that we perceive, so too this is the case with regard to the knowledge of truth, for those truths through which we enter into a knowledge of others are known to all, and no man is mistaken about them.

Those first principles which are naturally apprehended are truths of this sort—for example, it is impossible to both affirm and deny something at the same time, and every whole is greater than each of its parts, and so on.

On the other hand, there are many ways in which error may arise with respect to the conclusions into which we enter through such principles as through an outer door. Therefore, it is easy to know the truth if we consider that small amount of it which is comprised of self-evident principles, through which we enter into other truths, because this much is evident to all.

278. But the fact that we cannot (993b6). Here he explains in what sense it is difficult to know the truth. He says that our inability to grasp the whole truth and a part of it shows the difficulty involved in the search for truth. In support of this we must consider his statement that the truth through which we gain admission to other truths is known to all. Now there are two ways in which we attain knowledge of the truth.

The first is the method of analysis, by which we go from what is complex to what is simple or from a whole to a part, as it is said in Physics 1 that the first objects of our knowledge are confused wholes. Now our knowledge of the truth is perfected by this method when we attain a distinct knowledge of the particular parts of a whole.

The other method is that of synthesis, by which we go from what is simple to what is complex; we attain knowledge of truth by this method when we succeed in knowing a whole. Thus the fact that man is unable to know perfectly a whole and a part in things shows the difficulty involved in knowing the truth by both of these methods.

279. However, since the difficulty is twofold (993b7). He gives the reason for this difficulty. Here too it must be noted that in all cases in which there is a certain relationship between two things, an effect can fail to occur in two ways, because of either one of the things involved. For example, if wood does not burn, this may happen either because the fire is not strong enough or because the wood is not combustible enough. And in a similar way, the eye may be prevented from seeing a visible object either because the eye is weak or because the visible object is in the dark. Therefore, in like manner, it may be difficult to know the truth about things either because things themselves are imperfect in some way or because of some weakness on the part of our intellect.

280. Now it is evident that we experience difficulty in knowing the truth about some things because of the things themselves, for, since each thing is knowable insofar as it is an actual being, as will be stated below in book 9 [1894] of this work, then those things that are deficient and imperfect in being are less knowable by their very nature. For example, matter, motion, and time are less knowable because of the imperfect being which they have, as Boethius says in his book The Two Natures.

281. Now there were some philosophers who claimed that the difficulty experienced in knowing the truth is wholly attributable to things themselves, because they maintained that nothing is fixed and stable in nature but that everything is in a state of continual change, as will be stated in book 4 [683] of this work. But the Philosopher denies this, saying that even though the difficulty experienced in knowing the truth can perhaps be twofold because of different things (that is, our intellect and things themselves), still the principal source of the difficulty is not things, but our intellect.

282. He proves this in the following way. If this difficulty were attributable principally to things, it would follow that we would know best those things that are most knowable by nature. But those things that are most knowable by nature are those which are most actual, namely, immaterial and unchangeable things, yet we know these least of all. Obviously, then, the difficulty experienced in knowing the truth is due principally to some weakness on the part of our intellect. From this it follows that our soul’s intellectual power is related to those immaterial beings which are by nature the most knowable of all as the eyes of owls are to the light of day, which they cannot see because their power of vision is weak, although they do see dimly lighted things.

283. But it is evident that this simile is not adequate, for, since a sense is a power of a bodily organ, it is made inoperative as a result of its sensible object being too intense. But the intellect is not a power of a bodily organ and is not made inoperative as a result of its intelligible object being too intelligible. Therefore, after understanding objects that are highly intelligible, our ability to understand less intelligible objects is not decreased but increased, as is stated in On the Soul 3.

284. Therefore, it must be said that a sense is prevented from perceiving some sensible object for two reasons. First, because a sensory organ is rendered inoperative as a result of its sensible object being too intense. This does not occur in the case of the intellect. Second, because of some deficiency in the ability of a sensory power to perceive its object, for the powers of the soul in all animals do not have the same efficacy. Thus, just as it is proper to man by nature to have the weakest sense of smell, in a similar way it is proper to an owl to have the weakest power of vision, because it is incapable of perceiving the light of day.

285. Therefore, since the human soul occupies the lowest place in the order of intellective substances, it has the least intellective power. As a matter of fact, just as it is by nature the act of a body, although its intellective power is not the act of a bodily organ, in a similar way it has a natural capacity to know the truth about bodily and sensible things. These are less knowable by nature because of their materiality, although they can be known by abstracting sensible forms from phantasms. And since this process of knowing truth befits the nature of the human soul insofar as it is the form of this kind of body (and whatever is natural always remains so), it is possible for the human soul, which is united to this kind of body, to know the truth about things only insofar as it can be elevated to the level of the things that it understands by abstracting from phantasms. However, by this process it cannot be elevated to the level of knowing the quiddities of immaterial substances because these are not on the same level as sensible substances. Therefore, it is impossible for the human soul, which is united to this kind of body, to apprehend separate substances by knowing their quiddities.

286. For this reason the statement which Averroes makes at this point in his Commentary is evidently false, namely, that the Philosopher does not prove here that it is just as impossible for us to understand abstract substances as it is for a bat to see the sun. The argument that he gives is wholly ridiculous, for he adds that if this were the case, nature would have acted in vain because it would have made something that is naturally knowable in itself to be incapable of being known by anything else. It would be the same as if it had made the sun incapable of being seen. This argument is not satisfactory for two reasons.

First, the end of separate substances does not consist in being understood by our intellect, but rather the converse. Therefore, if separate substances are not known by us, it does not follow that they exist in vain, for only that exists in vain which fails to attain the end for which it exists.

Second, even though the quiddities of separate substances are not understood by us, they are understood by other intellects. The same is true of the sun, for even though it is not seen by the eye of the owl, it is seen by the eye of the eagle.

287. Now it is only right (993b11). He shows how men assist each other to know the truth. One man assists another to consider the truth in two ways: directly and indirectly.

One is assisted directly by those who have discovered the truth, because, as has been pointed out, when each of our predecessors has discovered something about the truth (which is gathered together into one whole), he also introduces his followers to a more extensive knowledge of truth.

One is assisted indirectly insofar as those who have preceded us and who were wrong about the truth have bequeathed to their successors the occasion for exercising their mental powers, so that by diligent discussion the truth might be seen more clearly.

288. Now it is only fitting that we should be grateful to those who have helped us attain so great a good as knowledge of the truth. Therefore, he says that it is only right that we should be grateful not merely to those whom we think have found the truth and with whose views we agree by following them, but also to those who, in the search for truth, have made only superficial statements, even though we do not follow their views. For these men too have given us something because they have shown us instances of actual attempts to discover the truth. By way of an example he mentions the founders of music, for if there had been no Timotheus, who discovered a great part of the art of music, we would not have many of the facts that we know about melodies. But if Timotheus had not been preceded by a wise man named Phrynis, he would not have been as well off in the subject of music. The same thing must be said of those philosophers who made statements of universal scope about the truth of things, for we accept from certain of our predecessors whatever views about the truth of things we think are true and disregard the rest. Again, those from whom we accept certain views had predecessors from whom they in turn accepted certain views and who were the source of their information.

The supreme science of truth

It is only right to call philosophy the science of truth. For the end of theoretical knowledge is truth, whereas that of practical knowledge is action, for even when practical men investigate the way in which something exists, they do not consider it in itself but in relation to some particular thing and to the present moment.

But we know a truth only by knowing its cause.

Now anything which is the basis of a univocal predication about other things has that attribute in the highest degree. Thus fire is hottest and is actually the cause of heat in other things.

Therefore, that is also true in the highest degree which is the cause of all subsequent things being true. For this reason the principles of things that always exist must be true in the highest degree, because they are not sometimes true and sometimes not true.

Nor is there any cause of their being, but they are the cause of the being of other things. Therefore, insofar as each thing has being, to that extent it is true.

Further, it is evident that there is a principle, and that the causes of existing things are not infinite either in series or in species. For it is impossible that one thing should come from something else as from matter in an infinite regress—for example, flesh from earth, earth from air, air from fire, and so on to infinity. Nor can the causes from which motion originates proceed to infinity, as though man were moved by the air, the air by the sun, the sun by strife, and so on to infinity.

Again, neither can there be an infinite regress in the case of the reason for which something is done, as though walking were for the sake of health, health for the sake of happiness, and happiness for the sake of something else, so that one thing is always being done for the sake of something else. The same is true in the case of the quiddity.

289. Having shown how man is disposed for the study of truth, the Philosopher now shows that the knowledge of truth belongs preeminently to first philosophy. Regarding this he does two things.

First (993b19; [290]), he shows that knowledge of the truth belongs preeminently to first philosophy.

Second (994a1; [299]), he rejects a false doctrine that would render his proof untenable, at further, it is evident.

In regard to the first, he does two things.

First, he shows that knowledge of the truth belongs to first philosophy.

Second [290], that it belongs in the highest degree to this science, at but we know a truth (993b23).

He proves these two propositions from two things established above in the prologue of this book, namely, that wisdom is not a practical but a speculative science [53], and that it knows first causes [48].

290. He argues from the first of these to the first conclusion in this way. Theoretical or speculative knowledge differs from practical knowledge by its end, for the end of speculative knowledge is truth, because it has knowledge of the truth as its objective. But the end of practical knowledge is action, because, even though practical men, that is, men of action, attempt to understand the truth as it belongs to certain things, they do not seek this as an ultimate end. For they do not consider the cause of truth in and for itself as an end, but in relation to action, by applying it either to some definite individual or to some definite time. Therefore, if we add to the above the fact that wisdom or first philosophy is not practical but speculative, it follows that first philosophy is most fittingly called the science of truth.

291. But since there are many speculative sciences which consider the truth, such as geometry and arithmetic, therefore it was necessary to show that first philosophy considers truth in the highest degree inasmuch as it has been shown above that it considers first causes [48]. Hence he argues as follows. We have knowledge of truth only when we know a cause. This is apparent from the fact that the true things about which we have some knowledge have causes which are also true, because we cannot know what is true by knowing what is false, but only by knowing what is true. This is also the reason why demonstration, which causes science, begins with what is true, as is stated in Posterior Analytics 1.

292. Then he adds the following universal proposition. When a univocal predicate is applied to several things, in each case anything which is the basis of a univocal predication about other things has that attribute in the highest degree. Thus fire is the cause of heat in compounds. Therefore, since heat is predicated univocally both of fire and of compound bodies, it follows that fire is hottest.

293. Now he says “univocal” because sometimes it happens that an effect does not become like its cause so as to have the same specific nature, because of the excellence of that cause. For example, the sun is the cause of heat in these lower bodies, but the form which these lower bodies receive cannot be of the same specific nature as that possessed by the sun or any of the celestial bodies, since they do not have a common matter. This is why we do not say that the sun is hottest, as we say fire is, but that it is something superior to the hottest.

294. Now the term “truth” is not proper to one species of beings only, but is applied universally to all beings. Therefore, since the cause of truth is one having the same name and intelligible structure as its effect, it follows that whatever causes subsequent things to be true is itself most true.

295. From this he again concludes that the principles of things that always exist, namely, the celestial bodies, must be most true. He does this for two reasons.

First, they are not sometimes true and sometimes not true, and therefore surpass the truth of things subject to generation and corruption, which sometimes exist and sometimes do not.

Second, these principles have no cause, but are the cause of the being of other things. And for this reason they surpass the celestial bodies in truth and in being, and even though the latter are incorruptible, they have a cause not only of their motion, as some men thought, but also of their being, as the Philosopher clearly states in this place.

296. Now this is necessary because everything that is composite in nature and participates in being must ultimately have as its causes those things that have existence by their very essence. But all bodily things are actual beings insofar as they participate in certain forms. Therefore, a separate substance which is a form by its very essence must be the principle of bodily substance.

297. If we add to this conclusion the fact that first philosophy considers first causes, it then follows, as was said above [291], that first philosophy considers those things that are most true. Consequently, this science is preeminently the science of truth.

298. From these conclusions he draws a corollary: since those things that cause the being of other things are true in the highest degree, it follows that each thing is true insofar as it is a being. For things that do not always have being in the same way do not always have truth in the same way, and those which have a cause of their being also have a cause of their truth. The reason for this is that a thing’s being is the cause of any true judgment which the mind makes about a thing, for truth and falsity are not in things, but in the mind, as will be said in book 6 [1230] of this work.

299. At further, it is evident (994a1), he rejects a position that would render the above proof untenable, for this proof proceeded on the supposition that first philosophy considers first causes. But if there were an infinite regress in causes, this proof would be destroyed, for then there would be no first cause. So his aim here is to refute this position. Concerning this he does two things.

First (994a1), he points out what he intends to prove.

Second [301], he proceeds to do so, at for intermediate things (994a11).

He says, first, that from what has been said it can clearly be shown that there is some first principle of the being and truth of things. He states that the causes of existing things are not infinite in number because we cannot proceed to infinity in a series of causes belonging to one and the same species (for example, the species of efficient causes). Nor again are causes infinite in species, as though the species of causes were infinite in number.

300. Then he explains his statement about an infinite number of causes in a series.

He first does this in regard to the genus of material causes. For it is impossible to have an infinite series in the sense that one thing always comes from something else as its matter (for example, that flesh comes from earth, earth from air, and air from fire), and that this does not terminate in some first entity but goes on to infinity.

Second, he gives an example of this in the genus of efficient cause. He says that it is impossible to have an infinite series in the genus of cause which we define as the source of motion—for example, when we say that a man is moved to put aside his clothing because the air becomes warm, the air having been heated in turn by the sun, the sun having been moved by something else, and so on to infinity.

Third, he gives an example of this in the genus of final causes. He says that it is also impossible to proceed to infinity in the case of the reason for which something is done (that is, the final cause)—for example, if we were to say that a journey or a walk is undertaken for the sake of health, health for the sake of happiness, happiness for the sake of something else, and so on to infinity.

Finally, he mentions the formal cause. He says that it is also impossible to proceed to infinity in the case of the quiddity, or the formal cause, which the definition signifies. However, he omits examples because these are evident, and because it was shown in Posterior Analytics 1 that it is impossible to proceed to infinity in the matter of predication, as though animal were predicated quidditatively of man, living of animal, and so on to infinity.

The existence of first efficient and material causes

For intermediate things in a series limited by some first and last thing must have as their cause the first member of the series, which they follow, because if we had to say which one of these three is the cause of the others, we would say that it is the first.

What is last is not the cause, since what is last is not a cause of anything. Neither is the intermediate the cause, because it is the cause of only one; for it makes no difference whether one or several intermediates exist, or an infinite or finite number.

Indeed, in series that are infinite in this way or in the infinite in general, all parts are intermediates to the same degree right down to the present one. Therefore, if there is nothing first in the whole series, nothing in the series is a cause.

Neither is it possible to proceed to infinity in a downward direction, where there is a starting point in an upward direction, so that water comes from fire, earth from water, and some other genus of things always being generated in this way.

Now there are two ways in which one thing comes from another. I do not mean “from” in the sense of “after,” as the Olympian games are said to come from the Isthmian, but as a man comes from a boy as a result of a boy changing, or as air comes from water.

We say, then, that a man comes from a boy in the sense that what has come into being comes from what is coming into being, or in the sense that what has been completed comes from what is being completed.

For generation is always midway between being and non-being, and thus whatever is coming into being is midway between what is and what is not.

Now a learner is one who is becoming learned, and this is the meaning of the statement that the man of science comes from the learner. But water comes from air in the sense that it comes into being when the latter ceases to be.

This is why changes of the former kind are not reversible, and thus a boy does not come from a man. The reason is that what has come into being does not come from generation, but exists after generation.

This is the way in which the day comes from the dawn, namely, in the sense that it exists after the dawn: because of this the dawn cannot come from the day. On the other hand, changes of the latter sort are reversible.

Now in neither way is it possible to proceed to infinity; for existing intermediaries must have some end, and one thing may be changed into the other because the corruption of one is the generation of the other.

At the same time it is impossible that an eternal first cause should be corrupted, for, since generation is not infinite in an upward direction, then a first principle by whose corruption something else is produced could not be eternal.

301. Having assumed above that the causes of beings are not infinite in number, the Philosopher now proves this.

First (994a11; [301]), he proves that there are not an infinite number of causes in a series;

and second (994b27; [330]), that the species of causes are not infinite in number, at again, if the species of causes.

In regard to the first he does four things.

First, he proves his assumption in the case of efficient or moving causes;

second (994a19; [305]), in the case of material causes, at neither is it possible;

third (994b9; [316]), in the case of final causes, at again, that for the sake of which;

and fourth (994b16; [320]), in the case of formal causes, at nor can the quiddity.

In regard to the first he proceeds as follows.

First, he lays down this premise. In the case of all those things that lie between two extremes, one of which is last and the other first, the first is necessarily the cause of those which come after it (namely, what is intermediate and what is last).

302. Then he proves this premise by a process of division. For if we had to say which of the three—that is, the first, the intermediate, or the last—is the cause of the others, we would have to say that the first is the cause. We could not say that what is last is the cause of all the others, because it is not a cause of anything. For in other respects what is last is not a cause, since an effect follows a cause. Nor could we say that the intermediate is the cause of all the others, because it is the cause of only one of them, namely, what is last.

303. And lest someone should think that an intermediate is followed by only one thing, namely, what is last (for this occurs only when there is a single thing between two extremes), in order to exclude this interpretation he adds that it makes no difference to the premise given above whether there is only one intermediate or several, because all intermediates are taken together as one insofar as they have in common the character of an intermediate.

Nor again does it make any difference whether there are a finite or infinite number of intermediates, because so long as they have the nature of an intermediate they cannot be the first cause of motion.

Further, since there must be a first cause of motion prior to every secondary cause of motion, then there must be a first cause prior to every intermediate cause, which is not an intermediate in any sense, as though it had a cause prior to itself.

But if we were to hold that there is an infinite series of moving causes in the above way, then all causes would be intermediate ones. Thus we would have to say without qualification that all parts of any infinite thing, whether of a series of causes or of continuous quantities, are intermediate ones. For if there were a part that was not an intermediate one, it would have to be either a first or a last, and both of these are opposed to the nature of the infinite, which excludes every limit, whether it be a starting point or a terminus.

304. Now there is another point that must be noted—namely, that if there are several intermediate parts in any finite thing, not all parts are intermediate to the same degree, for some are closer to what is first, and some to what is last. But in the case of some infinite thing in which there is neither a first nor a last part, no part can be closer to or farther away from either what is first or what is last. Therefore, all parts are intermediates to the same degree right down to the one you designate now. Consequently, if the causes of motion proceed to infinity in this way, there will be no first cause. But a first cause is the cause of all things. Therefore, it will follow that all causes are eliminated, for when a cause is removed the things of which it is the cause are also removed.

305. Neither is it possible (994a19). He shows that it is impossible to proceed to infinity in the case of material causes.

First (994a19; [300]), he states what he intends to prove.

Second (994a22; [308]), he proceeds with his proof, at now there are two ways.

In regard to the first, it must be noted that a patient is subjected to the action of an agent. Therefore, to pass from agent to agent is to proceed in an upward direction, whereas to pass from patient to patient is to proceed in a downward direction.

Now just as action is attributed to the cause of motion, so is undergoing action attributed to matter. Therefore, among the causes of motion the process is in an upward direction, whereas among material causes the process is in a downward direction.

Consequently, since he showed among moving causes that it is impossible to proceed to infinity in an upward direction (as it were), he adds that it is impossible to proceed to infinity in a downward direction (that is, in the process of material causes), granted that there is a starting point in an upward direction among the causes of motion.

306. He illustrates this by way of the process of natural bodies, which proceeds in a downward direction, as if we were to say that water comes from fire, earth from water, and so on to infinity. He uses this example in accordance with the opinion of the ancient philosophers of nature, who held that one of these elements is the source of the others in a certain order.

307. However, this can also be explained in another way, inasmuch as we understand that in the case of moving causes there are evident to the senses certain ultimate effects which do not move anything else. Therefore, we do not ask if there is an infinite regress in the lower members of that genus, but if there is an infinite regress in the higher ones.

But in regard to the genus of material causes, he assumes that there is one first cause which is the foundation and basis of the others; and he inquires whether there is an infinite regress in a downward direction in the process of those things that are generated from matter.

The example which he gives illustrates this, because he does not say that fire comes from water and this in turn from something else, but the converse, namely, that water comes from fire, and something else again from this. For this reason first matter is held to exist, and he asks whether the things that are generated from matter proceed to infinity.

308. Now there are two ways in which (994a22). He proves his original thesis. Concerning this he does four things.

First (994a22; [308]), he distinguishes between the two ways in which one thing comes from something else.

Second (994a25; [310]), he shows that these two ways differ in two respects, at we say, then, that a man.

Third (994b3; [312]), he shows that it is impossible to proceed to infinity in either of these ways, at now in neither way.

Fourth (994b6; [314]), he shows in which of these ways other things come from the first material principle, at at the same time.

He says, first, that one thing comes from another properly and per se in two ways. He speaks thus in order to exclude that way in which something is said in an improper sense to come from something else only by reason of the fact that it comes after it, as when it is said that certain feasts of the Greeks called the Olympian come from those called the Isthmian, or as if we were to say that the feast of Epiphany comes from the Nativity. But this is an improper use of the word, because the process of coming to be is a change, and in a change it is necessary not only that an order exist between the two limits of the change but also that both limits have the same subject. Now this is not the case in the above example, but we speak in this way insofar as we think of time as the subject of different feasts.

309. Now, properly speaking, it is necessary to say that one thing comes from something else when some subject is changed from this into that. This occurs in two ways: first, as when we say that a man comes from a boy in the sense that a boy is changed from boyhood to manhood; second, as when we say that air comes from water as a result of substantial change.

310. We say, then, that a man (994a25). He explains the twofold sense in which these two ways differ.

First, we say that a man comes from a boy in the sense that what has already come into being comes from what is coming into being, or in the sense that what has already been completed comes from what is being completed. For anything in a state of becoming and of being completed is midway between being and non-being, just as generation is midway between existence and nonexistence.

Therefore, since we reach an extreme through an intermediate, we say that what has been generated comes from what is being generated, and that what has been completed comes from what is being completed. Now this is the sense in which we say that a man comes from a boy, or a man of science from a learner, because a learner is one who is becoming a man of science.

But in the other sense—the one in which we say that water comes from fire—one of the limits of the change is not related to the other as a passage or intermediate, as generation is to being, but rather as the limit from which a thing starts in order to reach another limit. Therefore, one comes from the other when the other is corrupted.

311. This is why changes (994a31). He infers another difference from the foregoing one. Since, in the first way, one thing is related to the other as generation is to being, and as an intermediate to a limit, it is evident that one is naturally ordained to the other. Therefore, they are not reversible so that one comes from the other indifferently. Consequently, we do not say that a boy comes from a man, but the reverse.

The reason for this is that those two things, of which one is said to come from the other in this way, are not related to each other in the same way as the two limits of a change, but as two things one of which comes after the other in sequence.

And this is what he means when he says that what has come into being (that is, the terminus of generation or being) does not come from generation as though generation itself were changed into being, but is that which exists after generation, because it follows generation in a natural sequence. This is in the same way that one’s destination comes after a journey, and as what is last comes after what is intermediate.

Therefore, if we consider these two things—generation and being—the way in which they are related does not differ from the one we have excluded in which sequence alone is considered, as when we say that the day comes from the dawn because it comes after the dawn. Moreover, this natural sequence prevents us from saying in an opposite way that the dawn comes from the day, that is, after the day. For the same reason, a boy cannot come from a man.

But in the other sense in which one thing comes from another, the process is reversible; just as water is generated by reason of air being corrupted, in a similar way air is generated by reason of water being corrupted. The reason is that these two are not related to each other in a natural sequence as an intermediate to a limit, but as two limits, either one of which can be first or last.

312. Now in neither way (994b3). He shows that it is impossible to proceed to infinity in either of these ways.

First, in the way in which we say that a man comes from a boy. For the thing from which we say something else comes as a man comes from a boy has the position of an intermediary between two limits (that is, between being and non-being). But an infinite number of intermediates cannot exist when certain limits are held to exist, since limits are opposed to infinity. Therefore, it is impossible to have an infinite series in this way.

313. In like manner, it is impossible to have an infinite series in the other way, for in that way one limit is converted into the other because the corruption of one is the generation of the other, as has been explained.

Now, wherever a reversible process exists, there is a return to some first thing in the sense that what was at first a starting-point is afterwards a terminus. This cannot occur in the case of things that are infinite, in which there is neither a starting-point nor a terminus. Consequently, there is no way in which one thing can come from another in an infinite regress.

314. At the same time it is impossible (994b6). He shows in which of these ways something comes from first matter. Now it must be noted that in this place Aristotle uses two common suppositions accepted by all of the ancient philosophers.

First, that there is a primary material principle, and therefore that in the process of generation there is no infinite regress on the part of the higher, namely, of that from which a thing is generated.

Second, that matter is eternal. Therefore, from this second supposition he immediately concludes that nothing comes from first matter in the second way—that is, in the way in which water comes from air as a result of the latter’s corruption, because what is eternal cannot be corrupted.

315. But since someone could say that the philosophers did not hold that the first material principle is eternal because it remains numerically one eternally, but because it is eternal by succession (as if the human race were held to be eternal), he therefore excludes this from the first supposition. He says that since generation is not infinite in an upward direction but stops at a first material principle, then if there is a first material principle by reason of whose corruption other things come into being, it must not be the eternal principle of which the philosophers speak. The reason is that the first material principle cannot be eternal if other things are generated by reason of its corruption and it in turn is generated by the corruption of something else. It is evident, then, that a thing comes from this first material principle as something imperfect and potential which is midway between pure non-being and actual being, but not as water comes from air by reason of the latter’s corruption.

The existence of first final and formal causes

Again, that for the sake of which something comes to be is an end. Now such a thing is not for the sake of something else, but other things are for its sake.

Therefore, if there is such a thing as an ultimate end, there will not be an infinite regress; but if there is no ultimate end, there will be no reason for which things come to be.

Now those who posit infinity do away with the nature of the good without realizing it.

But no one will attempt to do anything unless he thinks he can carry it through to its term.

Nor will there be any intelligence in such matters, because one who has intelligence always acts for the sake of something, since this limit is the end of a thing.

Nor can the quiddity be reduced to a definition which adds to the defining notes.

For a prior definition is always more of a definition, whereas a subsequent one is not. Where the first does not apply, neither does a later one.

Again, those who speak in this way do away with science, because it is impossible to have science until we reach what is undivided.

Nor will knowledge itself exist; for how can one understand things that are infinite in this way?

This case is not like that of a line, whose divisibility has no limit, for it would be impossible to understand a line if it had no limits. This is why no one will count the sections, which proceed to infinity.

But it is necessary to understand that there is matter in everything that is moved, and that the infinite involves nothingness, but essence does not. But if there is no infinite, what essence does the infinite have?

Again, if the species of causes were infinite in number, it would also be impossible to know anything. For we think that we have scientific knowledge when we know the causes themselves of things, but what is infinite by addition cannot be traversed in a finite period of time.

316. Having shown that there is no infinite regress either among the causes of motion or among material causes, the Philosopher now shows that the same thing is true of the final cause, which is called that for the sake of which something comes to be (994b9). He proves this by four arguments.

The first is as follows. That for the sake of which something comes to be has the character of an end. But an end does not exist for the sake of other things, but others exist for its sake. Now such a thing either exists or not. If there is something of such a kind that all things exist for its sake and not it for the sake of something else, it will be the last thing in this order; and thus there will not be an infinite regress. However, if no such thing exists, no end will exist; thus the genus of final cause will be eliminated.

317. Now those who posit infinity (994b12). He gives the second argument, which is derived from the foregoing one, for from the first argument he concluded that those who posit an infinite regress in final causes do away with the final cause. Now when the final cause is removed, so also is the nature and notion of the good, because “good” and “end” have the same meaning, since the good is that which all desire, as is said in Ethics 1. Therefore, those who hold that there is an infinite regress in final causes do away completely with the nature of the good, although they do not realize this.

318. But no one will attempt (994b13). He gives the third argument, which is as follows. If there were an infinite number of final causes, no one could reach a last terminus, because there is no last terminus in an infinite series. But no one will attempt to do anything unless he thinks he is able to accomplish something as a final goal. Therefore, those who hold that final causes proceed to infinity do away with every attempt to operate and even with the activities of natural bodies, for a thing’s natural movement is only toward something which it is naturally disposed to attain.

319. Nor will there be (994b14). He states the fourth argument, which is as follows. One who posits an infinite number of final causes does away with a limit, and therefore with the end for the sake of which a cause acts. But every intelligent agent acts for the sake of some end. Therefore, it would follow that there is no intellect among causes which are productive. Thus the practical intellect is eliminated. But since these things are absurd, we must reject the first position, from which they follow—namely, that there is an infinite number of final causes.

320. Nor can the quiddity (994b16). He shows that there is not an infinite number of formal causes. In regard to this he does two things.

First (994b16; [320]), he states what he intends to prove.

Second (994b18; [322]), he proves it, at for a prior definition.

Regarding the first we must understand that each thing derives its particular species from its proper form, and this is why the definition of a species signifies chiefly a thing’s form. Therefore, we must understand that a procession of forms is consequent upon a procession of definitions, for one part of a definition is prior to another just as genus is prior to difference and one difference is prior to another. Therefore, an infinite regress in forms and an infinite regress in the parts of a definition are one and the same.

Now since Aristotle wishes to show that it is impossible to proceed to infinity in the case of formal causes, he holds that it is impossible to proceed to infinity in the parts of a definition. Hence he says that it is impossible for a thing’s quiddity to be reduced to another definition, and so on to infinity, so that the defining notes are always increased in number. For example, one who defines man gives animal in his definition, and therefore the definition of man is reduced to that of animal, and this in turn to the definition of something else, thereby increasing the defining notes. But to proceed to infinity in this way is absurd.

321. Now we do not mean by this that there are the same number of forms in each individual as there are genera and differences (so that in man there is one form by which he is man, another by which he is animal, and so on), but we mean that there must be as many grades of forms in reality as there are orders of genera and differences in knowledge. For we find in reality one form which is not the form of a body, another which is the form of a body but not of an animated body, and so on.

322. For a prior definition (994b18). He proves his premise by four arguments.

The first is this. Wherever there are a number of forms or defining notes, a prior definition is always more of a definition. This does not mean that a prior form is more complete (for specific forms are complete), but that a prior form belongs to more things than a subsequent form, which is not found wherever a prior form is found (for example, the definition of man is not found wherever that of animal is found). From this he argues that if the first thing does not fit the thing defined, neither does a later one. But if there were an infinite regress in definitions and forms, there would be no first definition or definitive form. Hence all subsequent definitions and forms would be eliminated.

323. Again, those who speak (994b20). He gives the second argument, which is as follows. It is impossible to have scientific knowledge of anything until we come to what is undivided. Now in this place “undivided” cannot mean the singular, because there is no science of the singular.

However, it can be understood in two other ways. First, it can mean the definition itself of the last species, which is not further divided by essential differences. In this sense his statement can mean that we do not have complete knowledge of a thing until we reach its last species, for one who knows the genus to which a thing belongs does not yet have a complete knowledge of that thing.

According to this interpretation, we must say that just as the first argument concluded that it is impossible to have an infinite regress in an upward direction among formal causes, in a similar fashion this second argument concludes that it is impossible to have an infinite regress in a downward direction, otherwise it would be impossible to reach a last species. Therefore, this position destroys any complete knowledge.

324. Now a formal division exists not only when a genus is divided by differences (and when such division is no longer possible the last species can be said to be undivided), but also when the thing defined is divided into its definitive parts, as is evident in Physics 1. Therefore, in this place “undivided” can also mean a thing whose definition cannot be resolved into any definitive parts.

Now, according to this the supreme genus is undivided, and from this point of view his statement can mean that we cannot have scientific knowledge of a thing by definition unless we reach its supreme genera, because when these remain unknown it is impossible to know its subsequent genera. And according to this, the second argument concludes (as the former one did) that it is impossible to proceed to infinity in an upward direction among formal causes.

325. Or, in order to reach the same conclusion, “undivided” can be explained in another way, namely, in the sense that an immediate proposition is undivided. For if it were possible to proceed to infinity in an upward direction in the case of definitions, there would be no immediate proposition, and thus science as such (which is about conclusions derived from immediate principles) would be destroyed.

326. Nor will knowledge (994b21). He gives the third argument, which proceeds to show that such an infinite regress would destroy not only science but any kind of human knowing whatsoever. In regard to this argument he does two things.

First (994b21; [326]), he gives his argument.

Second (994b23; [327]), he refutes an objection raised against it, at this case is not like.

The argument is as follows. We know each thing by understanding its form. But if there were an infinite regress in forms, these forms could not be understood, because the intellect is incapable of understanding the infinite as infinite. Therefore, this position destroys knowing in its entirety.

327. This case is not like (994b23). He disposes of an objection, for someone could say that a thing having an infinite number of forms can be understood in the same way as a line which is divided to infinity. But he denies this. He says that this case is not the same as that of a line, whose divisions do not stop but go on to infinity. For it is impossible to understand anything unless some limit is set to it. Therefore, a line can be understood inasmuch as some actual limit is given to it by reason of its extremes. However, it cannot be understood insofar as its division does not terminate. Hence no one can count the divisions of a line insofar as they are infinite.

But as applied to forms “infinite” means actually infinite, and not potentially infinite as it does when applied to the division of a line. Therefore, if there were an infinite number of forms, there would be no way in which a thing could be known either scientifically or in any way at all.

328. But it is necessary (994b25). He gives the fourth argument, which runs thus. Matter must be understood to exist in everything that is moved, for whatever is moved is in potency, and what is in potency is matter. But matter itself has the character of the infinite, and nothingness belongs to the infinite in the sense of matter, because matter taken in itself is understood without any of kind of form. And since nothingness belongs to the infinite, it follows contrariwise that the principle by which the infinite is a being is itself not infinite, and that it does not belong to the infinite (or to matter) to be infinite in being. But things are by virtue of their form. Hence there is no infinite regress among forms.

329. However, it must be noted that in this place Aristotle holds that the infinite involves the notion of nothingness, not because matter involves the notion of privation (as Plato claimed when he failed to distinguish between privation and matter), but because the infinite involves the notion of privation. For a potential being contains the notion of the infinite only insofar as it comes under the nature of privation, as is evident in Physics 3.

330. Again, if the species (994b27). He shows that the species of causes are not infinite in number, and he uses the following argument. We think that we have scientific knowledge of each thing when we know all its causes. But if there were an infinite number of causes in the sense that one species of cause may be added to another continuously, it would be impossible to traverse this infinity in such a way that all causes could be known. Hence in this way too the knowing of things would be destroyed.

The method of metaphysics

The way in which people are affected by what they hear depends upon the things to which they are accustomed. For it is in terms of such things that we judge statements to be true, and anything over and above these does not seem similar, but less intelligible and more remote. For it is the things to which we are accustomed that are better known.

The great force which custom has is shown by the laws, in which legendary and childish elements prevail over our knowledge of them, because of custom.

Now some men will not accept what a speaker says unless he speaks in mathematical terms; others, unless he gives examples; while others expect him to quote a poet as an authority.

Again, some want everything stated with certitude, while others find certitude annoying, either because they are incapable of comprehending anything or because they consider exact inquiry to be quibbling—for there is some similarity.

Hence it seems to some men that just as liberality is lacking when a fee is charged for a banquet, so also is it lacking in arguments.

For this reason one must be trained how to meet every kind of argument, and it is absurd to search simultaneously for knowledge and for the method of acquiring it. Neither of these is easily attained.

But the exactness of mathematics is not to be expected in all cases, but only in those which have no matter. This is why its method is not that of natural philosophy; for perhaps the whole of nature contains matter. Hence we must first investigate what nature is, for in this way it will become evident what the things are with which natural philosophy deals, and whether it belongs to one science or to several to consider the causes and principles of things.

331. Having shown that the study of truth is in one sense difficult and in another easy, and that it belongs preeminently to first philosophy, the Philosopher now exposes the proper method of investigating the truth. In regard to this he does two things.

First (994b32; [331]), he gives the different methods which men follow in the study of truth.

Second (995a12; [335]), he shows which method is the proper one, at for this reason one must.

In regard to the first he does two things.

First, he shows how powerful custom is in the study of truth.

Second (995a6; [334]), he concludes that the different methods which men employ in the study of truth depend on the different things to which they are accustomed, at now some men.

In regard to the first he does two things.

First, he shows how powerful custom is in the study of truth.

Second (995a3; [333]), he makes this clear by an example, at the great force.

He first says that the way in which people are affected by what they hear depends upon the things to which they are accustomed, because such things are more willingly heard and more easily understood. For things spoken of in a manner to which we are accustomed seem to us to be acceptable; and if any things are said to us over and above what we have been accustomed to hear, these do not seem to have the same degree of truth. As a matter of fact they seem less intelligible to us and further removed from reason just because we are not accustomed to them. For it is the things that we are accustomed to hear that we know best of all.

332. Now the reason for this is that things that are customary become natural. Hence a habit, which disposes us in a way similar to nature, is also acquired by customary activity. And from the fact that someone has some special sort of nature or special kind of habit, he has a definite relationship to one thing or another. But in every kind of cognition there must be a definite relationship between the knower and the object of cognition. Therefore, to the extent that natures and habits differ, there are diverse kinds of cognition. For we see that there are innate first principles in men because of their human nature, and that what is proper to some special virtue appears good to one who has this habit of virtue. Again, something appears palatable to the sense of taste because of its disposition. Therefore, since custom produces a habit which is similar to nature, it follows that what is customary is better known.

333. The great force (995a3). Here he makes his previous statement clear by giving a concrete case. He says that the laws which men pass are positive evidence of the force of custom, for the legendary and childish elements in these laws are more effective in winning assent than is knowledge of the truth.

Now the Philosopher is speaking here of the laws devised by men, which have as their ultimate end the preservation of the political community. Therefore, the men who have established these laws have handed down in them (in keeping with the diversity of peoples and nations involved) certain directives by which human souls might be drawn away from evil and persuaded to do good, although many of them, which men had heard from childhood and of which they approved more readily than of what they knew to be true, were empty and foolish. (But the law given by God directs men to that true happiness to which everything false is opposed. Therefore, there is nothing false in the divine law.)

334. Now some men (995a6). Here he shows how men as a result of custom use different methods in the study of truth. He says that some men listen to what is said to them only if it is mathematical in character, and this is acceptable to those who have been educated in mathematics because of the habits which they have.

Now, since custom is like nature, the same thing can also happen to certain men because they are poorly disposed in some respect, such as those who have a strong imagination but little intelligence.

Then there are others who do not wish to accept anything unless they are given a concrete example, either because they are accustomed to this or because their sensory powers dominate and their intellect is weak.

Again, there are some who think that nothing is convincing enough unless a poet or some authority is cited. This is also a result either of custom or of poor judgment, because they cannot decide for themselves whether the conclusion of an argument is certain; therefore, having no faith in their own judgment, as it were, they require the judgment of some recognized authority.

Again, there are others who want everything said to them with certitude, that is, by way of careful rational investigation. This occurs because of the superior intelligence of the one making the judgment and the arguments of the one conducting the investigation, provided that one does not look for certitude where it cannot be had.

On the other hand, there are some who are annoyed if some matter is investigated in an exact way by means of a careful discussion. This can occur for two reasons.

First, they lack the ability to comprehend anything; since their reasoning power is poor, they are unable to understand the order in which premises are related to conclusions.

Second, it occurs because of quibbling—that is, reasoning about the smallest matters— which bears some resemblance to the search for certitude since it leaves nothing undiscussed down to the smallest detail. Then there are some who think that, just as liberality is lacking when the smallest details are taken into account in computing the fee for a banquet, in a similar way there is a lack of civility and liberality when a man also wishes to discuss the smallest details in the search for truth.

335. For this reason one must be trained (995a12). He exposes the proper method of investigating the truth. Concerning this he does two things.

First [335], he shows how a man can discover the proper method of investigating the truth.

Second [336], he explains that the method which is absolutely the best should not be demanded in all matters, at but the exactness of mathematics (995a14).

He first says that since different men use different methods in the search for truth, one must be trained in the method which the particular sciences must use to investigate their subject. And since it is not easy for a man to undertake two things at once (indeed, so long as he tries to do both he can succeed in neither), it is absurd for a man to try to acquire a science and at the same time to acquire the method proper to that science. This is why a man should learn logic before any of the other sciences, because logic considers the general method of procedure in all the other sciences. Moreover, the method appropriate to the particular sciences should be considered at the beginning of these sciences.

336. But the exactness of mathematics (995a14). He shows that the method which is absolutely the best should not be demanded in all the sciences. He says that the exactness (namely, the careful and certain demonstrations) found in mathematics should not be demanded in the case of all things of which we have science, but only in the case of those things that have no matter. For things that have matter are subject to motion and change, and therefore in their case complete certitude cannot be had. In the case of these things, we do not look for what exists always and of necessity, but only for what exists in the majority of cases.

Now immaterial things are most certain by their very nature because they are unchangeable, although they are not certain to us because our intellectual power is weak, as was stated above [279]. The separate substances are things of this kind. But while the things with which mathematics deals are abstracted from matter, they do not surpass our understanding; therefore, in their case most certain reasoning is demanded. Again, because the whole of nature involves matter, this method of most certain reasoning does not belong to natural philosophy. However, he says perhaps because of the celestial bodies, since they do not have matter in the same sense that lower bodies do.

337. Now since this method of most certain reasoning is not the method proper to natural science, in order to know which method is proper to that science we must investigate first what nature is. In this way, we will discover the things that natural philosophy studies. Further, we must investigate whether it belongs to one science (that is, to natural philosophy) or to several sciences to consider all causes and principles. In this way we will be able to learn which method of demonstration is proper to natural philosophy. He deals with this method in Physics 2, as is obvious to anyone who examines it carefully.

Necessity of considering all difficulties

With a view to the science under investigation we must attack first those subjects which must first be investigated. These are all the subjects about which some men have entertained different opinions, and any other besides these which has been omitted.

Now for those who wish to investigate the truth it is worth the while to ponder these difficulties well. For the subsequent study of truth is nothing else than the solution of earlier problems. For it is impossible to untie a knot without knowing it.

But a perplexity on the part of the mind makes this evident in regard to the matter at hand. Insofar as the mind is perplexed, to that extent it experiences something similar to men who are bound—in both cases it is impossible to move forward. For this reason, then, it is first necessary to consider all the difficulties and the reasons for them.

This is also necessary for another reason, namely, that those who make investigations without first recognizing the problem are like those who do not know where they ought to go.

Again, one would not even know when he finds the thing which he is seeking, for the goal is not evident to such a man, but it is evident to one who previously discussed the difficulties.

Furthermore, one who has heard all the arguments of the litigants, as it were, and of those who argue the question, is necessarily in a better position to pass judgment.

338. Having indicated in book 2 [331] the method of considering the truth, the Philosopher now proceeds with his study of the truth.

First, he proceeds disputatively, indicating those points which are open to question so far as the truth of things is concerned.

Second [529], he begins to establish what is true, and he does this in book 4, which begins: there is a certain science (1003a21).

The first part is divided into two sections.

In the first, he states what he intends to do.

In the second [346], he proceeds to do it, at the first problem (995b4).

In regard to the first he does two things.

First, he states what he intends to do.

Second [339], he gives the reasons for this, at now for those (995a27).

He first says, then, that with a view to this science which we are seeking about first principles and what is universally true of things, we must first attack those subjects about which it is necessary to raise questions before the truth is established.

Now there are disputed points of this kind for two reasons: either because the ancient philosophers entertained a different opinion about these things than is really true, or because they completely neglected to consider them.

339. Now for those (995a27). Here he gives four arguments in support of this thesis:

first, he says that for those who wish to investigate the truth it is worth the while, that is, worth the effort, to ponder these difficulties well, that is, to examine carefully those matters which are open to question. This is necessary because the subsequent study of truth is nothing else than the solution of earlier difficulties. Now in loosening a physical knot it is evident that one who is unacquainted with this knot cannot loosen it. But a difficulty about some subject is related to the mind as a physical knot is to the body, and manifests the same effect. For insofar as the mind is puzzled about some subject, it experiences something similar to those who are tightly bound. For just as one whose feet are tied cannot move forward on an earthly road, in a similar way one who is puzzled, and whose mind is bound, as it were, cannot move forward on the road of speculative knowledge. Therefore, just as one who wishes to loosen a physical knot must first of all inspect the knot and the way in which it is tied, in a similar way one who wants to solve a problem must first survey all the difficulties and the reasons for them.

340. This is also necessary (995a34). Here he gives the second argument. He says that those who wish to investigate the truth without first considering the problem are like those who do not know where they are going. This is true for this reason: just as the end of a journey is the goal intended by one who travels on foot, in a similar way the solution of a problem is the goal intended by one who is seeking the truth. But it is evident that one who does not know where he is going cannot go there directly, except perhaps by chance. Therefore, neither can one seek the truth directly unless he first sees the problem.

341. Again, one would (995a35). Here he gives the third argument. He says that just as one who is ignorant of where he is going does not know whether he should stop or go further when he reaches his appointed goal, in a similar way one who does not know beforehand the problem whose solution marks the terminus of his search cannot know when he finds the truth which he is seeking and when not. For he does not know what the goal of his investigations is. But this is evident to one who knew the problem beforehand.

342. Furthermore (995b2). He gives the fourth argument, which is taken from the viewpoint of a judge. For a judge must pass judgment on the things that he hears. But just as one can pass judgment in a lawsuit only if he hears the arguments on both sides, in a similar way one who has to pass judgment on a philosophy is necessarily in a better position to do so if he will hear all the arguments, as it were, of the disputants.

343. Now it must be noted that it was for these reasons that Aristotle was accustomed, in nearly all his works, to set forth the problems which emerge before investigating and establishing what is true. But while in other works Aristotle sets down the problems one at a time in order to establish the truth about each one, in this work he sets forth all the problems at once, and afterwards in the proper order establishes the things that are true. The reason for this is that other sciences consider the truth in a particular way, and therefore it belongs to them to raise problems of a particular kind about individual truths. But just as it belongs to this science to make a universal study of truth, so also does it belong to it to discuss all the problems which pertain to the truth. Therefore, it does not discuss its problems one at a time, but all at once.

344. There can also be another reason for this—namely, that those problems on which he touches are chiefly those about which the philosophers have held different opinions. However, he does not proceed to investigate the truth in the same order as the other philosophers did. For he begins with things that are sensible and evident and proceeds to those which are separate from matter, as is evident below in book 7 [1566].

But the other philosophers wanted to apply intelligible and abstract principles to sensible things. Hence, because he did not intend to establish the truth in the same order as that followed by the other philosophers, and from whose views these problems arise, he therefore decided to give first all the problems in a separate section, and afterwards to solve these problems in their proper order.

345. Averroes gives another reason. He says that Aristotle proceeds in this way because of the relationship of this science to logic, which will be touched on below in book 4 [588]. Therefore, he made dialectical discussion a principal part of this science.

Questions on metaphysical method

The first problem concerns the things about which we raised questions in our introductory statements, namely, whether it belongs to one science or to many to speculate about the causes.

And there is also the problem of whether it belongs to this science to know only the principles of substance, or also the principles on which all sciences base their demonstrations (for example, whether it is possible to affirm and deny one and the same thing at the same time or not, and other such principles).

And if this science deals with substance, there is the question of whether one science deals with all substances, or many sciences. And if many, whether all are cognate, or whether some should be called wisdom and others something else.

It is also necessary to inquire whether sensible substances alone must be said to exist, or whether there are other substances in addition to these.

Also, whether they are unique, or whether there are many kinds of substances, as was said by those who put forms and mathematical objects between these and sensible things. As we said, then, this must be examined.

There is also the problem of whether this speculation has to do with substances alone or also with the proper accidents of substances. And we must inquire about sameness and difference, likeness and unlikeness, contrariety, priority and posteriority, and all other such things that the dialecticians attempt to treat (basing their investigations only on probabilities). For to them too it belongs to theorize about all these things. Furthermore, we must investigate all those per se accidents of these same things, and not only what each one of them is, but also whether there is one contrary for each one.

Does this science make use of all four causes?

346. Following his announced plan, the Philosopher begins to set down the problems which are encountered in establishing the truth. He divides this into two parts.

In the first, he gives these problems;

and in the second [369], he gives the reasons for these problems, by indicating the arguments on either side of the question, at therefore, let us discuss (996a18).

Now it was stated in book 2 [335] that it is necessary to seek the method of a science before seeking the science itself.

Therefore, he first gives the problems which pertain to this science’s method of investigation.

Second [355], he gives the problems which pertain to the first principles with which this science deals, as has been stated in book 1 [36]; and this is at and we must inquire (995b27).

Now a science is concerned with two things, as was said in book 2 [336], namely, a study of the causes by which it demonstrates and the things with which it deals.

Hence in regard to the first point he does two things.

First, he presents a problem concerning the investigation of causes.

Second [347], he presents several problems concerning the things with which this science deals, at and there is also the problem (995b6).

He says, then, that the first problem is one which we proposed in the issues raised at the end of book 2 [336], which is, so to speak, the prologue to the whole of science. It is whether a study of the four causes in their four genera belongs to one science or to many different sciences And this is to ask whether it belongs to one science, and especially to this science, to demonstrate by means of all the causes, or rather whether some sciences demonstrate by one cause and some by another.

Does it consider both principles of substance and principles of knowledge?

347. And there is also the problem (995b6). Here he raises problems about the things that this science considers.

First, he inquires about the things that this science considers about substances;

second, about the things that this science considers about accidents, at there is also (995b18).

Concerning the first he does two things.

First, he raises questions about the science itself, which is about substance;

second [350], about substances themselves, at it is also necessary (995b13).

In regard to the first he raises three questions.

For if it is supposed, from what was said in book 1 [35], that this science considers first principles, the first question here will be whether it belongs to this science only to know the first principles of substances, or also to consider the first principles of demonstration, by means of which all sciences demonstrate. For example, should this science consider whether it is possible to affirm and deny one and the same thing at the same time or not? And the same thing applies to the other first and self-evident principles of demonstration.

Is its subject all substances, or do different sciences consider different substances?

348. And if this science considers substance as the primary kind of being, the second question is whether there is one science which considers all substances, or whether there are many sciences which consider different substances. For it seems that there should be many sciences which consider many substances.

Is it distinct from other sciences?

349. And if there are many sciences which consider many substances, the third question is whether all are cognate, that is, whether all belong to one genus, as geometry and arithmetic belong to the genus of mathematical science, or whether they do not, but some to the genus of wisdom and some to another genus (for example, to the genus of natural philosophy or to that of mathematical science). For, according to the first point of view, it seems that they do not belong to one genus, since material and immaterial substances are not known by the same method.

Are there immaterial substances, and of what kind?

350. It is also necessary (995b13). Here he adds to the number of questions about substance, and he does this by raising two questions.

The first question is whether sensible substances alone must be held to exist, as the philosophers of nature claimed, or whether there are in addition to sensible substances other immaterial and intelligible substances, as Plato claimed.

351. And if there are some substances separate from sensible things, the second question is whether they are unique, that is, whether they belong only to one genus, or whether there are many genera of such substances. For certain men, understanding that there is a twofold abstraction (namely, of the universal from the particular, and of the mathematical form from sensible matter) held that each genus is self-subsistent. Thus they held that there are separate substances which are subsisting abstract universals, and between these and particular sensible substances they placed the objects of mathematics—numbers, continuous quantities, and figures—which they regarded as separate subsisting things.

Concerning the questions which have now been raised, then, it is necessary to investigate them below.

He does this first by arguing both sides of the question,

and second by determining its truth.

Does this science consider accidents or properties of substance?

352. There is also the problem (995b18). Here he asks whether this science’s investigations extend to accidents, and he raises three questions.

The first is whether this science, seeing that it is called the philosophy of substance, speculates about substance alone, or whether it also speculates about the proper accidents of substance. For it seems to be the office of the same science to consider a subject and the proper accidents of that subject.

How does it differ from logic in considering these things?

353. The second question is whether this science considers certain things that seem to be proper accidents of being and which belong to all beings, namely, sameness and difference, likeness and unlikeness, contrariety, priority and posteriority, and all others of this kind which are treated by the dialecticians, who deal with all things. However, they do not examine such things according to necessary premises but according to probable ones. For from one point of view it seems that, since these accidents are common ones, they pertain to first philosophy. But from another point of view it seems that, since they are considered by the dialecticians (whose office it is to argue from probabilities), an examination of them does not belong to the consideration of the philosopher (whose office it is to demonstrate).

Does it consider how these accidents are inter-related?

354. And since certain proper attributes naturally flow from these common accidents of being, the third question is whether it is the function of the philosopher to consider in regard to the common accidents only their quiddity, or also their properties (for example, whether there is one opposite for each one).

Questions on metaphysics’ object

And we must inquire whether it is genera that constitute the principles and elements of things, or the parts into which each existing thing is divided. And if it is genera, whether it is those that are predicated of individuals first or last. And we must also inquire whether animal or man is a principle, and exists more truly than the singular.

But most of all it is necessary to investigate and treat the question of whether, besides matter, there is any cause in the proper sense or not, whether it is separable or not, and whether it is numerically one or many.

And we must ask whether there is anything besides the synolon (and by synolon I mean matter when something is predicated of it), or nothing; or whether this is true of some things but not of others.

Further, we must inquire whether the principles of things are limited in number or in kind, both those in the intelligible structures of things and those in the underlying subject.

Also, whether the principles of corruptible and of incorruptible things are the same or different. Also, whether they are all incorruptible, or whether those of corruptible things are corruptible.

And the most difficult question of all, and the most disputed one, is whether unity and being are not something different from the substances of existing things, as the Pythagoreans and Plato say, or whether this is not the case, but the underlying subject is something different, as Empedocles holds of love, another thinker of fire, another of water, and another of air. And we must inquire whether the principles of things are universals or singular things.

Again, we must inquire whether they exist potentially or actually. And also whether they are principles of things in reference to motion or in some other way. For these questions present great difficulty.

And in addition to these questions we must inquire whether numbers or lengths and points are somehow substances or not. And if they are substances, whether they are separate from sensible things or are found in them. Concerning all these matters, not only is it difficult to discover what is true, but it is not even easy to state the problems well.

How are substances to be analyzed, into elements or into genera?

355. Having raised questions pertaining to the method of investigation which this science uses, the Philosopher now raises questions pertaining to the things that this science considers. And since this science considers first principles, as has been stated in book 1 [35], he therefore raises here questions pertaining to the principles of things. Now both the forms and the objects of mathematics were held to be the first principles of things.

Therefore, first he raises questions concerning species;

second [366], concerning the objects of mathematics, at and in addition to these (996a12).

In regard to the first he does two things.

First, he asks what things are principles;

second [361], what sort of beings they are, at further, we must inquire (996a1).

And since separate universals were held to be the principles of things, he asks first whether universals are the principles of things;

second [357], whether separate entities are the principles of things, at but most of all (995b31).

Concerning the first he asks two questions.

The first is whether genera constitute the principles and elements of things, or the ultimate parts into which each individual thing is divided. This question arises because an element is that of which a thing is first composed and into which it is ultimately divided.

Now we find a twofold mode of composition and dissolution.

One has to do with the intelligible constitution, in which species are resolved into genera, and according to this mode genera seem to be the principles and elements of things, as Plato claimed.

The other mode of composition and dissolution has to do with the real order. For example, natural bodies are composed of fire, air, water, and earth, and are dissolved into these. It was for this reason that the natural philosophers claimed that the elements constitute the first principles of things.

356. And assuming that genera are the principles of things, the second question is whether the principles of things are to be identified with the universals which are predicated of individual things (that is, the lowest species, which he calls genera, after the usage of the Platonists), because the lowest species contain under themselves many individuals, just as genera contain many species.

Or is it rather the first and most common genera that constitute principles? For example, which of the two is more of a principle, animal or man? For man is a principle according to the Platonists, and is more real than any singular man.

Now this problem arises because of two divisions which reason makes. One of these is that whereby we divide genera into species, and the other is that whereby we resolve species into genera. For it seems that whatever is the last term in a process of division is always the first principle and element in a process of composition.

Is there an immaterial principle? Is it one or many?

357. But most of all (995b31). Here he inquires whether separate entities are the principles of things, and he raises four questions.

Since the first philosophers of nature posited only a material cause, the first question is whether, besides matter, there is anything else that is a cause in the proper sense or not.

358. And granted that there is some other cause besides matter, the second question is whether it is separable from matter, as Plato or Pythagoras held.

359. And if there is something separable from matter, the third question is whether it is a single thing, as Anaxagoras claimed, or many, as Plato and Aristotle himself claimed.

Is individuality distinct from the specific form?

360. The fourth question is whether there is anything besides the synolon (that is, the concrete whole), or nothing; or whether there is something in certain cases and not in others; and what kind of things they are in those cases in which there is something else, and what kind of things they are in those in which there is not. And he explains what a synolon, or concrete whole, is. Namely, it is matter when something is predicated of it.

Now in order to understand this, we must note that Plato claimed that man and horse (and universals which are predicated in this way) are certain separate forms; and that man is predicated of Socrates or Plato by reason of the fact that sensible matter participates in a separate form. Hence Socrates or Plato is called a synolon, or concrete whole, because each is constituted as a result of matter participating in a separate form. And each is, as it were, a kind of predicate of matter.

Hence the Philosopher asks here whether the whatness of the individual thing is something else in addition to the individual thing itself, or not; or also whether it is something else in the case of some things and not in that of others. The Philosopher will answer this question in book 7 [7356].

361. Further, we must inquire (996a1). Here he raises questions about the way in which principles exist.

And since being is divided by the one and many, and by act and potency, he asks first whether these principles are one or many.

Second [365], whether they are actual or potential, at again, we must inquire (996a10).

In regard to the first he asks four questions,

the first of which is whether the principles are limited according to number or to kind. We say, for example, that there are three principles of nature. Now the statement that they are limited in number can mean that the principle of nature is numerically a single form and a single matter and privation. And the statement that they are limited in kind can mean that there are many material principles which have in common the specific nature of material principle, and so on for the rest. Since some of the philosophers, such as the Platonists, attributed formal causes to things, while others, such as the ancient natural philosophers, attributed only material causes to things, he adds that this question is applicable both in the intelligible structures, that is, in formal causes, and in the underlying subject, that is, in material causes.

Are the principles of corruptible and incorruptible things the same or different?

362. The second question is whether the principles of corruptible and of incorruptible things are the same or different. And if they are different, whether all are incorruptible, or whether the principles of corruptible things are corruptible and those of incorruptible things are incorruptible.

Are “one” and “being” the same as or distinct from specific natures?

363. The third question is whether unity and being signify the very substance of things and not something added to the substance of things (as the Pythagoreans and Platonists claimed), or whether they do not signify the substance of things, but something else is the subject of unity and being (for example, fire or air or something else of this kind, as the ancient philosophers of nature held). Now he says that this question is the most difficult and most puzzling one, because on this question depends the entire thought of Plato and Pythagoras, who held that numbers are the substance of things.

364. The fourth question is whether the principles of things are somehow universals or singular things, that is, whether those things that are held to be principles have the character of a principle in the sense of a universal intelligible nature, or according as each is a particular and singular thing.

365. Again, we must inquire (996a10). Here he asks whether these principles exist potentially or actually. This question seems to refer especially to material principles, for it can be a matter of dispute whether the first material principle is some actual body, such as fire or air, as the ancient philosophers of nature held, or something which is only potential, as Plato held. And since motion is the actualization of something in potency, and is, in a sense, midway between potency and act, he therefore also asks whether the principles of things are causes only in reference to motion (as the philosophers of nature posited only material or efficient principles of motion), or whether they are principles which act also in some other way than by motion (as Plato claimed that sensible things are caused by immaterial entities by a certain participation in these). Furthermore, he says that these questions have been raised because they present the greatest difficulty, as is clear from the manner in which the philosophers have disagreed about them.

366. And in addition to these (996a12). Here he raises questions concerning the objects of mathematics, which are posited as the principles of things. He raises two questions.

The first is whether numbers, lengths, figures, and points are somehow substances, as the Pythagoreans or Platonists held, or whether they are not, as the philosophers of nature held.

367. And if they are substances, the second question is whether they are separate from sensible things, as the Platonists held, or exist in sensible things, as the Pythagoreans held.

368. Now these questions are raised as problems which must be debated and settled below, because in these matters, not only is it difficult to discover the truth, but it is not even easy to debate the matter adequately by finding probable arguments for either side of the question.

How many sciences study all causes?

Therefore, let us discuss first the problem about which we first spoke (995b4): whether it is the office of one science or of many to study all the genera of causes.

For how will it be the office of one science to come to principles since they are not contrary?

Furthermore, in the case of many existing things not all the principles are present. How can a principle of motion be present in all immobile things, or how can the nature of the good be found there?

For everything which is a good in itself and by reason of its own nature is an end and thus a cause, because it is for its sake that other things come to be and exist. Further, the end and that for the sake of which something comes to be is the terminus of some action.

But all actions involve motion. Therefore, it would be impossible for this principle to be present in immobile things, nor could there be an autoagathon, that is, a good in itself.

Hence in mathematics too nothing is proved by means of this cause, nor is there any demonstration on the grounds that a thing is better or worse. Nor does anyone make any mention at all of anything of this kind. And for this reason some of the Sophists, for example, Aristippus, disregarded these. For in the other arts, even in the servile ones, such as the art of building and cobbling, all things are to be explained on the grounds that they are better or worse; but the mathematical sciences give no account of things that are good or evil.

But on the other hand, if there are many sciences of the causes, and different sciences for different principles, which of these must be said to be the one that is being sought, or which one of those who have them is best informed about the subject under investigation?

For it is possible for the same thing to have all the kinds of causes. For example, in the case of a house the source of motion is the art and the builder, the final cause is its function, the matter is earth and stones, and the form is the plan.

Therefore, from the things established a little while ago (982a4–982b7; [36–51]), which of the sciences should be called wisdom?

For there is a reason for calling each one of them such. For inasmuch as wisdom takes precedence and is a more authoritative science, and one which the others, like slaves, have no right to contradict, then the science that deals with the end and the good is such a science, because other things are for the sake of this.

But insofar as wisdom has been defined (982a30; [49]) as the science of first causes and of what is most knowable, such a science will be about substance. For while a subject may be known in many ways, we say that he who knows what a thing is in its being knows it better than he who knows it in its non-being.

And in the former case one knows better than another, especially he who knows what a thing is, and not how great it is or of what sort it is or anything that it is naturally disposed to do or to undergo. Further, in the case of other things, too, we think that we know every single thing (and those of which there are demonstrations) when we know what each is—for example, what squaring is, because it is finding the middle term. The same thing is true in other cases.

But with regard to processes of generation and actions and every change, we think that we know these perfectly when we know the principle of motion. But this differs from and is opposite to the end of motion. And for this reason it seems to be the province of a different science to speculate about each one of these causes.

Can one science consider many causes?

369. Having raised the questions which cause difficulty in this science, Aristotle begins here to treat them dialectically. This is divided into three parts.

In the first part, he treats the questions which pertain to the method of investigation of this science.

In the second [403], he treats the questions which pertain to substances, at furthermore, there is (997a34).

In the third [423], he treats the questions which pertain to the principles of substances, at concerning the principles (998a21).

In regard to the first he does three things.

First, he argues dialectically about this science’s method of investigation, with reference to the causes by means of which it demonstrates;

second [379], with reference to the first principles of demonstration, at but insofar (996b13);

third [393], with reference to substances themselves, at and there is the problem (997a15).

In regard to the first he does two things.

First, he takes up again the question about which he plans to argue dialectically, concluding from the order in which the questions have been listed that it is necessary first to debate those issues which were stated first in the list of questions—namely, whether it is the function of one science or of many to investigate all the genera of causes. In this way the order of argument corresponds to the order in which the questions have been raised.

370. For how will it be (996a20). Second, he gives the arguments relating to this question, and in regard to this he does three things.

First (996a20), he gives an argument for the purpose of showing that it is not the office of a single science to consider all the genera of causes.

Second (996b1; [376]), assuming that it belongs to different sciences to consider the different genera of causes, he asks which genus of cause it is that is investigated by first philosophy. He argues on both sides of this question, at but on the other hand.

Third (996b22; [382]), he draws from this second dispute the conclusion of the first arguments, at but with regard to.

In regard to the first (996a20) he gives two arguments.

He asks, since it belongs to one science to consider contraries, how it will belong to one science to consider principles, since they are not contrary? This view, if it is considered superficially, seems to be of no importance, for it appears to follow from the destruction of the antecedent, as if one were to argue thus. If principles are contraries, they belong to one science; therefore, if they are not contraries, they do not belong to one science.

371. Therefore, it can be said that in these disputes the Philosopher not only uses probable arguments, but sometimes also uses sophistical ones when he gives arguments introduced by others. But it does not seem reasonable that in such an important matter so great a Philosopher would have introduced an argument which is both trifling and insignificant. Hence a different explanation must be given, namely, that if one rightly considers the nature of the various things that belong to the same science, some belong to a single science insofar as they are different, but others insofar as they are reduced to some one thing. Hence many other different things are found to belong to one science insofar as they are reduced to one thing (for example, to one whole, one cause, or one subject). But contraries and all opposites belong essentially to one science by reason of the fact that one is the means of knowing the other. And from this comes this probable proposition that all different things that are contraries belong to one science. Therefore, if principles were different and were not contraries, it would follow that they would not belong to one science.

372. Furthermore, in the case (996a21). Here he gives the second argument, which runs thus. In the case of different things that belong to one science, whatever science considers one also considers another. This is evident in the case of contraries, which are different and belong essentially to one science without being reduced to some other unity. But not every science which considers one cause considers all causes. Therefore, the study of all the causes does not belong to a single science.

373. He proves the minor premise thus. Different sciences deal with different beings, and there are many beings to which all the causes cannot be assigned. He makes this clear, first, with regard to that cause which is called the source of motion, for it does not seem that there can be a principle of motion in immobile things. Now certain immobile things are posited, especially by the Platonists, who claim that numbers and substances are separate entities. Hence, if any science considers these, it cannot consider the cause which is the source of motion.

374. Second, he shows that the same thing is true of the final cause, which has the character of good. For it does not seem that the character of goodness can be found in immobile things, if it is conceded that everything which is good in itself and by reason of its own nature is an end. And it is a cause in the sense that all things come to be and exist because of it and for its sake.

However, he says everything which is a good in itself and by reason of its own nature in order to exclude the useful good, which is not predicated of the end, but of the means to the end. Hence those things that are said to be good only in the sense that they are useful for something else are not good in themselves and by reason of their own nature. For example, a bitter medicine is not good in itself, but only insofar as it is directed to the end, health, which is a good in itself. But an end, or that for the sake of which something comes to be, seems to be the terminus of an action. But all actions seem to involve motion.

Therefore, it seems to follow that this principle—that is, the final cause, which has the character of goodness—cannot exist in immobile things. Further, since those things that exist of themselves apart from matter must be immobile, it therefore does not seem possible that an autoagathon (or a good-in-itself) exists, as Plato held. For he called all immaterial and unparticipated things entities which exist of themselves, just as he called the idea of man “man-in-himself,” as though not something participated in matter. Hence he also called the good-in-itself that which is its own goodness unparticipated—namely, the first principle of all things.

375. Moreover, with a view to strengthening this argument he introduces an example. From the fact that there cannot be an end in the case of immobile things, it seems to follow that, in the mathematical sciences (which abstract from matter and motion), nothing is proved by means of this cause, as in the science of nature (which deals with mobile things) something is proved by means of the notion of good. For example, we may give as the reason why man has hands that by them he is more capable of executing the things that reason conceives.

But in the mathematical sciences no demonstration is made by saying that something is so because it is better for it to be so, or worse if it were not so—as if one were to say that the angle in a semi-circle is a right angle because it is better that it should be so than be acute or obtuse. And because there can be, perhaps, another way of demonstrating by means of the final cause (for example, if one were to say that if an end is to be, then what exists for the sake of an end must first be), he therefore adds that in the mathematical sciences no one makes any mention at all of any of those things that pertain to the good or to the final cause.

And for this reason certain sophists, as Aristippus, who belonged to the Epicurean school, completely disregarded any demonstrations which employ final causes, considering them to be worthless in view of the fact that in the servile or mechanical arts, for example, in the art of building, that is, in carpentry, and in that of cobbling, all things are explained on the grounds that something is better or worse. But in the mathematical sciences, which are the noblest and most certain of the sciences, no mention is made of things good and evil.

376. But on the other hand (996b1). Here he interjects another question.

First, he states this question, which has two parts.

The first part of the question is this. If different causes are considered by many sciences, so that a different science considers a different cause, then which of these sciences should be called the one that is being sought, that is, first philosophy? Is it the one which considers the formal cause, or the one which considers the final cause, or the one which considers one of the other causes?

The second part of the question is this. If there are some things that have many causes, which one of those who consider those causes knows that subject best?

377. For it is possible (996b5). He clarifies the second part of the question by the fact that one and the same thing is found to have every type of cause. For example, in the case of a house, the source of motion is the art and the builder; the reason for which, or the final cause of the house, is its function, or its use, which is habitation; its material cause is the earth, from which the walls and floor are made; and its species or form is the plan of the house, which the architect, after first conceiving it in his mind, gives to matter.

378. Therefore, from the things (996b8). Here he takes up again the question as to which of the aforesaid sciences we can call wisdom on the basis of the points previously established about wisdom at the beginning of this work (982a4; [36])—namely, whether it is the science which considers the formal cause, or the one which considers the final cause, or the one which considers one of the other causes.

And he gives, in order, arguments relating to each of the three causes, saying that there seems to be some reason why each one of the sciences (that is, any one which proceeds by means of any cause at all) should be called by the name of wisdom.

First, he speaks of that science which proceeds by means of the final cause. For it was stated at the beginning of this work that this science, which is called wisdom, is the most authoritative one, and the one which directs others as subordinates.

Therefore, inasmuch as wisdom takes precedence, or is prior in the order of dignity and more influential in its authoritative direction of the other sciences (because it is not right that the others should contradict it but they should take their principles from it as its servants), it seems that that science that deals with the end and the good, that is, the one which proceeds by means of the final cause, is worthy of the name of wisdom. And this is true because everything else exists for the sake of the end, so that in a sense the end is the cause of all the other causes.

Thus the science which proceeds by means of the final cause is the most important one. This is indicated by the fact that those arts which are concerned with ends are more important than and prior to the other arts. For example, the art of navigation is more important than and prior to the art of ship-building. Hence, if wisdom is preeminent and regulative of the other sciences, it seems that it proceeds especially by means of the final cause.

379. But insofar as wisdom (996b13). Here he introduces the arguments relating to the formal cause. For it was said in the prologue of this work (982b7; [51]) that wisdom is concerned with first causes and with whatever is most knowable and most certain.

And according to this it seems to be concerned with substance; that is, it proceeds by means of the formal cause. For among the different ways of knowing things, we say that he who knows that something exists knows more perfectly than he who knows that it does not exist.

Hence in the Posterior Analytics the Philosopher proves that an affirmative demonstration is preferable to a negative demonstration. And among those who know something affirmatively, we say that one knows more perfectly than another.

But we say that he knows more perfectly than any of the others who knows what a thing is, and not he who knows how great it is, or what it is like, or what it can do or undergo. Therefore, to know a thing itself in the most perfect way absolutely is to know what it is, and this is to know its substance. But even in knowing other things (for example, a thing’s properties), we say that we know best every single thing about which there are demonstrations when we also know the whatness of their accidents and properties. For whatness is found not only in substance but also in accidents.

380. He gives the example of squaring—that is, squaring a surface of equally distant sides which is not square but which we say is squared when we find a square equal to it. But since every rectangular surface of equally distant sides is contained by the two lines which contain the right angle, so that the total surface is simply the product of the multiplication of one of these lines by the other, then we find a square equal to this surface when we find a line which is the proportional mean between these two lines. For example, if line A is to line B as line B is to line C, the square of line B is equal to the surface contained by C and A, as is proved in Euclid’s Elements 6.

381. This becomes quite evident in the case of numbers. For six is the proportional mean between nine and four; for nine is related to six in the ratio of one to one and a half, and so also is six to four. Now the square of six is thirty-six, which is also produced by multiplying four by nine, for four times nine equals thirty-six. And it is similar in all other cases.

382. But with regard to processes (996b22). Here he gives an argument pertaining to the cause of motion. For in processes of generation and actions and in every change, we can say we know a thing when we know its principle of motion, and that motion is nothing else than the act of something mobile produced by a mover, as is stated in Physics 3. He omits the material cause, however, because that cause is a principle of knowing in the most imperfect way, for the act of knowing is not caused by what is potential but by what is actual, as is stated below in book 9 (1051a21; [1894]).

383. Then after having given those arguments which pertain to the second question, he introduces an argument which is based on the same reasons as were given above (996a20; [370]) in reference to the first question—namely, that it is the office of a different science to consider all these causes, because in different subject matters different causes seem to have the principal role. For example, the source of motion has this in mobile things, the quiddity in demonstrable things, and the end in things directed to an end.

384. However, we do not find that Aristotle explicitly solves this question later on, though his solution can be ascertained from the things that he establishes below in different places. For in book 4 [533] he establishes that this science considers being as being, and therefore that it also belongs to it (and not to the philosophy of nature) to consider first substances, for there are other substances besides mobile ones. But either every substance is a being of itself (granted that it is only a form) or it is a being by its form (granted that it is composed of matter and form).

Hence inasmuch as this science considers being, it considers the formal cause before all the rest. But the first substances are not known by us in such a way that we know what they are, as can be understood in some way from the things established in book 9 [1904]. Thus in our knowledge of them the formal cause has no place. But even though they are immobile in themselves, they are nevertheless the cause of motion in other things after the manner of an end.

Hence inasmuch as this science considers first substances, it belongs to it especially to consider the final cause, and also in a way the efficient cause. But to consider the material cause in itself does not belong to it in any way, because matter is not properly a cause of being, but of some definite kind of being, namely, of mobile substance. However, such causes belong to the consideration of the particular sciences, unless perhaps they are considered by this science inasmuch as they are contained under being. For it extends its analysis to all things in this way.

385. Now when these things are seen it is easy to answer the arguments which have been raised.

First, nothing prevents the different causes in this science from belonging to a single existing thing, even though they are not contraries, because they are reducible to one thing—being in general—as has been stated [384].

And in a similar way, even though not every science considers all of the causes, still nothing prevents one science from being able to consider all of the causes or several of them insofar as they are reducible to some one thing. But to be more specific, it must be said that in the case of immobile things nothing prevents the source of motion and the end or good from being investigated. By immobile things I mean here those which are still causes of motion, as the first substances.

However, in the case of those things that are neither moved nor cause motion, there is no investigation of the source of motion, or of the end in the sense of the end of motion, although an end can be considered as the goal of some operation which does not involve motion.

For if there are held to be intellectual substances which do not cause motion, as the Platonists claimed, still insofar as they have an intellect and a will it is necessary to hold that they have an end and a good which is the object of their will. However, the objects of mathematics neither are moved nor cause motion nor have a will. Hence in their case the good is not considered under the name of good and end, although in them we do consider what is good (namely, their being and what they are). Hence the statement that the good is not found in the objects of mathematics is false, as he proves below in book 9 [1888].

386. The reply to the second question is already clear, for a study of the three causes, about which he argued dialectically, belongs to this science.

How many sciences study the principles of demonstration and substance?

But with respect to the principles of demonstration there is also the problem of whether they are studied by one science or by many. By principles of demonstration I mean the common opinions from which demonstrations proceed—for example, everything must either be either affirmed or be denied, and it is impossible both to be and not to be at the same time, and all other such propositions.

Now it would be unreasonable that these things should be studied by one science. For why should the study of these be proper to geometry rather than to any other science? In a similar way, then, if this study pertains to any science but cannot pertain to all, an understanding of these principles is no more proper to the science which studies substance than it is to any other science.

But at the same time, how will there be a science of these principles? For we already know what each one of them is; therefore, the other arts use them as something known. However, if there is demonstration of them, there will have to be some subject genus, and some of the principles will have to be properties and others axioms. For there cannot be demonstration of all things, since demonstration must proceed from something, and be about something, and be demonstration of certain things. It follows, then, that there is a single genus of demonstrable things, for all demonstrative sciences use axioms.

But on the other hand, if the science which considers substance differs from the one which considers axioms, which of these sciences is the more important and prior one? For axioms are most universal and are the principles of all things. And if it does not belong to the philosopher to establish truth and falsity, to what other person will it belong?

Is the science of substance also that of first principles?

387. Having debated the first question which had to do with the study of causes, Aristotle’s intention here is to argue dialectically about the science which is concerned with the study of the first principles of demonstration; in regard to this he does three things.

First, he raises the question.

Second (996b33; [388]), he argues one side of the question, at now it would be unreasonable.

Third (997a11; [391]), he argues on the other side of the question, at but on the other hand.

Accordingly, he first states the problem relating to the principles of demonstration (996b26), namely, whether they are studied by one science or by many. Further, he explains what the principles of demonstration are, saying that they are the common conceptions of all men on which all demonstrations are based—that is, inasmuch as the particular principles of the proper demonstrated conclusions derive their stability from these common principles. And he gives an example of first principles, especially this one: everything must either be affirmed or be denied. Another principle which he mentions is that it is impossible for the same thing both to be and not to be at the same time. Hence the question arises as to whether these principles and similar ones pertain to one science or to many. And if they pertain to one science, whether they pertain to the science which investigates substance or to another science. And if to another science, then which of these must be called wisdom, or first philosophy, which we now seek.

388. Now it would be (996b33). Here he argues one side of the question with a view to showing that it is not the office of one science to consider all first principles, that is, the first principles of demonstration and substance.

He gives two arguments, of which the first runs thus. Since all sciences employ these principles of demonstration, there seems to be no reason why the study of them should pertain to one science rather than to another. Nor again does it seem reasonable that they should be studied by all sciences, because then it would follow that the same thing would be treated in different sciences, which would be superfluous. Hence it seems to follow that no science considers these principles. Therefore, for the very same reason that it does not belong to any of the other sciences to give us a knowledge of such principles, for this reason too it follows that it does not belong to the science whose function it is to consider substance.

389. But at the same time (997a2). Here he gives the second argument, which runs thus. In the sciences there are two methods by which knowledge is acquired. One is that by which the whatness of each thing is known, and the other is that by which knowledge is acquired through demonstration. But it does not belong to any science to give us a knowledge of the principles of demonstration by means of the first method, because such knowledge of principles is assumed to be prior to all the sciences. For we already know what each one of them is; that is, we know from the very beginning what these principles signify, and by knowing this, the principles themselves are immediately known. And since such knowledge of principles belongs to us immediately, he concludes that all the arts and sciences which are concerned with other kinds of cognitions make use of these principles as things naturally known by us.

390. But it is proved in the same way that a knowledge of these principles is not presented to us in any science by means of demonstration, because if there was demonstration of them, then three principles would have to be considered: namely, the subject genus, its properties, and the axioms. In order to clarify this he adds that there cannot be demonstration of all things, for subjects are not demonstrated but properties are demonstrated of subjects. Concerning subjects, however, it is necessary to know beforehand whether they exist and what they are, as is stated in Posterior Analytics 1.

The reason is that demonstration must proceed from certain things as principles, which are the axioms, and be about something, which is the subject, and be demonstrative of certain things, which are properties. Now according to this it is immediately evident of one of these three, the axioms, that they are not demonstrated. Otherwise there would have to be certain axioms prior to the axioms, which is impossible. Therefore, having dismissed this method of procedure as obvious, he proceeds to consider the subject genus. For since one science has one subject genus, then that science which would demonstrate axioms would have one subject genus. Thus there would have to be one subject genus for all demonstrative sciences, because all demonstrative sciences use axioms of this kind.

391. But on the other hand (997a11). Here he argues the other side of the question. For if it is said that there is one science which deals with such principles and another which deals with substance, the problem will remain as to which of these sciences is the more important and prior one.

For, on the one hand, since the axioms are most universal and are the principles of everything that is treated in any of the sciences, it seems that the science which deals with such principles is the most important one. Yet, on the other hand, since substance is the first and principal kind of being, it is evident that first philosophy is the science of substance. And if it is not the same science which deals with substance and with the axioms, it will not be easy to state to which of the other sciences it belongs to consider the truth and falsity of these axioms if it does not belong to first philosophy, which considers substance.

392. The Philosopher answers this question in book 4 [590] of this work. He says that the study of the axioms belongs chiefly to the philosopher inasmuch as it pertains to him to consider being in general, to which first principles of this kind belong per se, as is most evident in the case of the very first principle: it is impossible for the same thing both to be and not to be [at the same time]. Hence all the particular sciences use principles of this kind just as they use being itself, although it is the first philosopher who is chiefly concerned with this. And the first argument is solved in this way.

But the second argument is solved thus: the philosopher does not consider principles of this kind in such a way as to make them known by defining them or by demonstrating them in an absolute sense, but by refutation, that is, by arguing disputatively against those who deny them, as is stated in book 6 [608].

Are all substances considered by one science or by many?

And there is the problem of whether there is one science or many sciences which deal with all substances.

If there is not one science, then with what substances must this science deal?

But it is unreasonable that there should be one science of all substances, for then one science would demonstrate all per se accidents (if it is true that every demonstrative science speculates about the per se accidents of some subject by proceeding from common opinions).

Hence it is the office of the same science to study the per se accidents of the same subject genus by proceeding from the same opinions.

For it belongs to one science to consider that something is so, and it belongs to one science (whether to the same science or to another) to consider the principles.

Hence it belongs to one science to consider accidents, whether they are studied by these sciences or by one derived from them.

Further, there is the problem of whether this science is concerned only with substances, or also with accidents.

I mean, for example, that if a solid is a kind of substance, and also lines and surfaces, the question arises as to whether it is the function of the same science to know these and also the accidents of each genus of things about which the mathematical sciences make demonstrations, or whether it is the concern of a different science.

For if it is the concern of the same science, a particular one will undertake these demonstrations and this will be the one which deals with substance. However, there does not seem to be any demonstration of the quiddity.

But if it is the concern of a different science, which science will it be that studies the accidents of substances? For to solve this is very difficult.

Does the science of substance consider all substances as well as accidents?

393. Having debated two questions which pertain to the scope of investigation of this science, he now treats the third question which is about the study of substances and accidents.

This is divided into two parts inasmuch as he discusses two questions on this point.

The second (997a34; [403]) begins where he says, furthermore, there is.

In regard to the first he does three things.

First, he raises the question of whether there is one science that considers all substances, or whether there are many sciences that consider different substances.

394. If there is not (997a16). Second, he argues the first side of the question with a view to showing that there is one science of all substances. For if there were not one science of all substances, then apparently it would be impossible to designate the substance which this science considers, because substance as substance is the primary kind of being. Hence it does not seem that one substance rather than another belongs to the consideration of the basic science.

395. But it is unreasonable (997a17). Third, he argues the other side of the question, saying that it is unreasonable to hold that there is one science of all substances. For it would follow that there would be one demonstrative science of all per se accidents. And this is true because every science which demonstrates certain accidents speculates about the per se accidents of some particular subject, and it does this from certain common conceptions. Therefore, since a demonstrative science considers the accidents only of some particular subject, it follows that the study of some subject genus belongs to the same science that is concerned with the study of the per se accidents of that genus, and vice versa, so long as demonstrations proceed from the same principles.

396. But sometimes it happens to be the function of some science to demonstrate from certain principles that a thing is so, and sometimes it happens to be the function of some science to demonstrate the principles from which it was demonstrated that a thing is so. This sometimes belongs to the same science and sometimes to a different one.

An example of its being the function of the same science is seen in the case of geometry, which demonstrates that a triangle has three angles equal to two right angles in virtue of the principle that the exterior angle of a triangle is equal to the two interior angles opposite to it. For to demonstrate this belongs to geometry alone.

An example of its being the function of a different science is seen in the case of music, which proves that a tone is not divided into two equal semitones because a ratio of nine to eight (which is superparticular) cannot be divided into two equal parts. But to prove this does not pertain to the musician, but to the arithmetician. It is evident, then, that sometimes sciences differ because their principles differ, so long as one science demonstrates the principles of another science by means of certain higher principles.

397. But if it is assumed that the principles are identical, sciences could not differ so long as the accidents are the same and the subject genus is the same, as if one science considered the subject and another its accidents. Hence it follows that that science which considers a substance will also consider its accidents, so that if there are many sciences which consider substances, there will be many sciences which consider accidents. But if there is only one science which considers substances, there will be only one science which considers accidents. But this is impossible, because it would then follow that there would be only one science, since there is no science which does not demonstrate the accidents of some subject. Therefore, it is not the function of one science to consider all substances.

398. This is treated in book 4 [546] of this work, where it is shown that the examination of substance as substance belongs to the first science, whose province it is to consider being as being. Thus it considers all substances according to the common aspect of substance. Therefore, it belongs to this science to consider the common accidents of substance. But it belongs to the particular sciences, which deal with particular substances, to consider the particular accidents of substances, just as it belongs to the science of nature to consider the accidents of mobile substance. However, among substances there is also a hierarchy, for the first substances are immaterial ones. Hence the study of them belongs properly to first philosophy, just as the philosophy of nature would be first philosophy if there were no other substances prior to mobile bodily substances, as is stated below in book 6 [1170].

399. Further, there is the problem (997a25). Here he raises another question regarding the study of substance and accidents. Concerning this he does three things.

First, he raises the question of whether the investigation of this science is concerned with substance alone or also with the attributes that are accidents of substances. For example, if we say that lines, surfaces, and solids are substances of some sort, as some held, the question arises whether it belongs to the same science to consider such things and also their proper accidents, which are demonstrated in the mathematical sciences, or whether it belongs to another science.

400. For if it is the concern (997a30). Second, he argues one side of the question. For if it belongs to the same science to consider accidents and substances, then, since a science which considers accidents demonstrates accidents, it follows that a science which considers substance demonstrates substances. But this is impossible, for the definition of a substance, which expresses the quiddity, is indemonstrable. Hence it will not belong to the same science to consider substances and accidents.

401. But if it is the concern (997a32). Third, he argues the other side of the question. If different sciences consider substance and accident, it will not be possible to state which science it is that speculates about the accidents of substance, because the science which would do this would consider both, although this would seem to pertain to all sciences. For every science considers the per se accidents of its subject, as has been explained.

402. The Philosopher answers this question in book 4 [570] of this work, saying that it is also the office of that science which is concerned with the study of substance and being to consider the proper accidents of substance and being. Yet it does not follow that it would consider each in the same way, that is, by demonstrating substance as it demonstrates accidents, but by defining substance and by demonstrating that accidents either belong to or do not belong to it. This is explained more fully at the end of book 9 [1895] of this work.

Are there substances separate from sensible things?

Furthermore, there is the problem whether sensible substances alone must be said to exist, or others besides these. And whether there is one genus or many genera of substances, as is held by those who speak of the forms and the intermediate entities with which they say the mathematical sciences deal.

Now the way in which we say that the forms are both causes and substances in themselves has been treated in our first discussions concerning all of these things (987a29).

But while they involve difficulty in many respects, it is no less absurd to say that there are certain other natures besides those which exist in the heavens, and that these are the same as sensible things, except that the former are eternal whereas the latter are corruptible.

For they say nothing more or less than that there is a man-in-himself and horse-in-itself and health-in-itself, which differ in no respect from their sensible counterparts. In this they act like those who say that there are gods and that they are of human form. For just as the latter made nothing else than eternal men, in a similar way the former make the forms nothing else than eternal sensible things.

Furthermore, if anyone holds that there are intermediate entities in addition to the forms and sensible substances, he will face many problems. For evidently there will be, in like manner, lines in addition to ordinary sensible lines, and the same will be true of other genera of things.

Therefore, since astronomy is one of these mathematical sciences, there will be a heaven in addition to the one we perceive, and a sun and moon, and the same will be true of the other celestial bodies. And how are we to accept these things?

For it is unreasonable that a heaven should be immobile, but that it should be mobile is altogether impossible. The same thing is true of the things with which the science of perspective is concerned, and of harmonics in mathematics, because for the same reasons it is also impossible that these should exist apart from sensible things.

For if there are intermediate sensible objects and senses, evidently there will be intermediate animals between animals-in-themselves and those which are corruptible.

Again, one might also raise the question as to what things these sciences must investigate.

For if geometry, the art of measuring the earth, differs from geodesy, the art of dividing the earth, only in that the latter deals with things that we sense, whereas the former deals with what is not sensible, evidently there will be, besides the science of medicine, another science between the science of medicine itself and this particular science of medicine; and this will be true of the other sciences.

But how is this possible? For then there will be certain healthy things besides those which are sensible and besides health-in-itself.

Similarly, neither does it seem that geodesy is concerned with continuous quantities which are sensible and corruptible. For in this case it would be destroyed when they are destroyed.

Nor again will astronomy deal with sensible continuous quantities, or with this heaven. For the lines we perceive by the senses are not such as those of which geometry speaks, since none of the things perceived by the senses are straight or round in this way.

For the circle does not touch the rule at a point, but in the way in which Protagoras spoke in arguing against the geometricians. Neither are the motions or revolutions of the heavens similar to the things of which geometry speaks, nor do points have the same nature as the stars.

However, there are also some who say that these intermediate entities, which are below the forms and above sensible things, do not exist outside of sensible things, but in them. But to enumerate all the impossible consequences which follow from this theory would require too long a discussion. It will be sufficient to propose the following consideration.

It is unreasonable that this should be so only in the case of such things, but evidently it is also possible for the forms to exist in sensible things, because both of these views depend on the same argument.

Furthermore, it would be necessary for two solids to occupy the same place.

And the objects of mathematics would not be immobile, since they exist in sensible things, which are moved.

Moreover, on the whole, to what end would anyone hold that they exist but exist in sensible things? For the same absurdities as those described will apply to these suppositions. For there will be a heaven in addition to the one which we perceive, although it will not be separate, but in the same place. But this is quite impossible.

In these matters, then, it is difficult to see how it is possible to have any positive truth.

Are there substances besides sensible ones?

403. Having debated the questions which pertain to the scope of this science, the Philosopher now treats dialectically the questions which pertain to the substances themselves with which this science is chiefly concerned. In regard to this he does three things.

First, he raises the questions.

Second (997b3; [406]), he indicates the source from which arguments can be drawn in support of one side of the question, at now the way.

Third (997b5; [407]), he argues on the other side of the question, at but while they involve.

In regard to the first part of this division he raises two questions.

The first question is whether sensible substances alone are found in the universe, as certain of the ancient philosophers of nature claimed, or whether besides sensible substances there are certain others, as the Platonists claimed.

404. And assuming that besides sensible substances there are certain others, the second question is whether these substances belong to one genus, or whether there are many genera of substances. For he considers both opinions. For some thinkers held that, in addition to sensible substances, there are only separate forms: an immaterial man-in-himself and horse-in-itself and so on for the other species of things, whereas others held that there are certain other substances midway between the forms and sensible things, namely, the objects of mathematics, with which they said the mathematical sciences deal.

405. The reason for this view is that they posited on the part of the intellect a twofold process of abstracting things: one whereby the intellect is said to abstract the universal from the particular, and according to this mode of abstraction they posited separate forms, which subsist of themselves.

They posited another whereby the intellect is said to abstract from sensible matter certain forms whose definition does not include sensible matter, as a circle is abstracted from brass. And according to this mode of abstraction they posited separate objects of mathematics, which they said are midway between the forms and sensible substances, because they have something in common with both:

with the forms inasmuch as they are separate from sensible matter, and with sensible substances inasmuch as many of them are found in one species, as many circles and many lines.

406. Now the way in which (997b3). Then he shows how it is possible to argue one side of the question, saying that it has been stated in our first discussions, that is, in book 1 (987a29; [151]), how the forms are held to be both the causes of sensible things and substances which subsist of themselves. Hence, from the things that have been said there in presenting the views of Plato, arguments can be drawn in support of the affirmative side of the question.

407. But while they involve (997b5). Here he advances reasons for the negative side.

He does this first (997b5) for the purpose of showing that the forms are not separate from sensible things;

second (997b12; [410]), for the purpose of showing that the objects of mathematics are not separate, at furthermore, if anyone.

Now above in book 1 (990a12; [208]) he gave many arguments against those who posited separate forms; therefore, passing over those arguments, he gives the line of reasoning which seems most effective. He says (997b5) that while the position of those who posit separate forms contains many difficulties, the position of those which is now given is no less absurd than any of the others—namely, that someone should say that there are certain natures in addition to the sensible ones which are contained beneath the heavens. For the heavens constitute the limit of sensible bodies, as is proved in On the Heavens 1. But those who posited the forms did not place them below the heavens or outside of it, as is stated in Physics 3.

Hence, in accordance with this, he says that they posited certain other natures in addition to those which exist in the heavens. And they said that these contrary natures are the same as these sensible things both in kind and in their intelligible constitution, and that they exist in these sensible things—or rather, they said that those natures are the forms of these sensible things.

For example, they said that a separate man constitutes the humanity of this particular man who is perceived by the senses, and that a man who is perceived by the senses is a man by participating in that separate man. Yet they held that these differ in this respect: those immaterial natures are eternal, whereas these sensible natures are corruptible.

408. That they hold those natures to be the same as these sensible things is clear from the fact that just as man, horse, and health are found among sensible things, in a similar way they posited among these natures a man-in-himself, or one lacking sensible matter. They did the same with regard to horse and health.

Moreover, they claimed that nothing else existed in separate substances except the counterpart of what existed materially in the sensible world. This position seems to be similar to that of those who held that the gods are of human form, which was the position of the Epicureans, as Cicero states in The Nature of the Gods. For just as those who held that the gods are of human form did nothing else than make men eternal in nature, in a similar way those who claimed that there are forms do nothing else than hold that there are eternal sensible things, such as horse, ox, and the like.

409. But it is altogether absurd that what is naturally corruptible should be specifically the same as what is naturally incorruptible. It is rather the opposite that is true, namely, that corruptible and incorruptible things differ in kind to the greatest degree, as is said below in book 10 (1058b26; [2137]) of this work. Yet it can happen that what is naturally corruptible is kept in being perpetually by divine power.

410. Furthermore, if anyone (997b12). Then he argues against those who claimed that the objects of mathematics are midway between the forms and sensible things.

First (997b12; [410]), he argues against those who held that the objects of mathematics are intermediate entities and are separate from sensible things;

second (998a7; [417]), against those who held that the objects of mathematics exist but exist in sensible things, at however, there are.

In regard to the first, he does two things.

First, he introduces arguments against the first position.

Second (997b34; [416]), he argues in support of this position, at nor again.

He brings up three arguments against the first position.

The first argument is this. Just as there is a mathematical science about the line, in a similar way there are certain mathematical sciences about other subjects. If, then, there are certain lines in addition to the sensible ones with which geometry deals, by the same token there will be certain things in addition to those perceived by the senses in all other genera of things with which the other mathematical sciences deal. But he shows that it is impossible to hold this with regard to two of the mathematical sciences.

411. He does this first in the case of astronomy, which is one of the mathematical sciences and which has as its subject the heavens and the celestial bodies. Hence, according to what has been said, it follows that there is another heaven besides the one perceived by the senses, and similarly another sun and another moon, and so on for the other celestial bodies. But this is incredible, because that other heaven would be either mobile or immobile. If it were immobile, this would seem to be unreasonable, since we see that it is natural for the heavens to be always in motion. Hence the astronomer also makes some study of the motions of the heavens. But to say that a heaven should be both separate and mobile is impossible, because nothing separate from matter can be mobile.

412. Then he shows that the same view is unacceptable in the case of other mathematical sciences (for example, in that of perspective, which considers visible lines, and in harmonics, that is, in that of music, which studies the ratios of audible sounds).

Now it is impossible that there should be intermediate entities between the forms and sensible things. For if these sensible things—sounds and visible lines—were intermediate entities, it would also follow that there are intermediate senses. And since senses exist only in an animal, it would follow that there are also intermediate animals between the form animal and corruptible animals. But this is altogether absurd.

413. Again, one might (997b25). The second argument is as follows. If in those genera of things with which the mathematical sciences deal there are three degrees of things—sensible substances, forms, and intermediate entities—then, since the intelligible structure of all sensible things and of all forms seems to be the same, it appears to follow that there are intermediate entities between any sensible things at all and their forms.

Hence there remains the problem as to what genera of things are included in the scope of the mathematical sciences. For if a mathematical science such as geometry differs from geodesy (the science of sensible measurements) only in the respect that geodesy deals with sensible measurements while geometry deals with intermediate things that are not sensible, there will be in addition to all the sciences which consider sensible things certain other mathematical sciences which deal with these intermediate entities. For example, if the science of medicine deals with certain sensible bodies, there will be in addition to the science of medicine (and any like science) some other science which will be intermediate between the science of medicine which deals with sensible bodies and the science of medicine which deals with the forms.

But this is impossible, for since medicine is about healthy things (or things that are conducive to health), then it will also follow, if there is an intermediate science of medicine, that there will be intermediate health-giving things in addition to the health-giving things perceived by the senses and absolute health (or health-in-itself), which is the form of health separate from matter. But this is clearly false.

Hence it follows that these mathematical sciences do not deal with certain things that are intermediate between sensible things and the separate forms.

414. Similarly, neither (997b32). Then he gives the third argument, and here one of the points in the foregoing position is destroyed. Namely, this is that there would be a science of continuous quantities which are perceptible; thus, if there were another science of continuous quantities, it would follow from this that there would be intermediate continuous quantities. Hence he says that it is not true that geodesy is a science of perceptible continuous quantities, because such continuous quantities are corruptible. It would follow, then, that geodesy is concerned with corruptible continuous quantities. But it seems that a science is destroyed when the things with which it deals are destroyed, for when Socrates is not sitting, our present knowledge that he is sitting will not be true. Therefore, it would follow that geodesy (or geosophics, as other readings say) is destroyed when sensible continuous quantities are destroyed. But this is contrary to the character of science, which is necessary and incorruptible.

415. Yet this argument can be brought in on the opposite side of the question, inasmuch as one may say that he intends to prove by this argument that there are no sciences of sensible things, so that all sciences must be concerned with either the intermediate entities or the forms.

416. Nor again will (997b34). Here he argues in support of this position as follows. It belongs to the very notion of science that it should be concerned with what is true. But this would not be the case unless it were about things as they are. Therefore, the things about which there are sciences must be the same in themselves as they are shown to be in the sciences.

But sensible lines are not such as geometry says they are. He proves this on the grounds that geometry demonstrates that a circle touches the rule, that is, a straight line, only at a point, as is shown in Euclid’s Elements 3. But this is not found to be true of a circle and a line in sensible things. Protagoras used this argument when he destroyed the certainties of the sciences against the geometricians.

Similarly, the movements and revolutions of the heavens are not such as the astronomers describe them, for it seems to be contrary to nature to explain the movements of the celestial bodies by means of eccentrics and epicycles and other different movements which the astronomers describe in the heavens.

Similarly, neither are the quantities of the celestial bodies such as the astronomers describe them to be, for they use stars as points even though they are still bodies having extension.

It seems, then, that geometry does not deal with perceptible continuous quantities, and that astronomy does not deal with the heaven which we perceive. Hence it remains that these sciences are concerned with certain other things, which are intermediate.

417. However, there are (998a7). Here he argues against another position.

First, he states the point at issue.

Second (998a11; [418]), he brings in arguments to his purpose, at it is unreasonable.

Accordingly, he says, first (998a7), that some thinkers posit natures midway between the forms and sensible things, yet they do not say that these natures are separate from sensible things, but exist in sensible things themselves. This is clear regarding the opinion of those who held that there are certain self-subsistent dimensions which penetrate all sensible bodies, which some thinkers identify with the place of sensible bodies, as is stated in Physics 4 and is disproved there. Hence he says here that to pursue all the absurd consequences of this position is a major undertaking, but that it is now sufficient to touch on some points briefly.

418. It is unreasonable (998a11). Then he brings four arguments against this position.

The first runs as follows. It seems to be for the same reason that in addition to sensible things the forms and objects of mathematics are posited, because both are held by reason of abstraction on the part of the intellect. If, then, the objects of mathematics are held to exist in sensible things, it is fitting that not only they but also the forms themselves should exist there. But this is contrary to the opinion of those who posit the existence of the forms. For they hold that these are separate, and not that they exist anywhere in particular.

419. Furthermore, it would be (998a13). Here he gives the second argument, which runs thus. If the objects of mathematics differ from sensible things yet exist in them, since a body is an object of mathematics, it follows that a mathematical body exists simultaneously with a sensible body in the same subject. Therefore, two solids, or two bodies, will exist in the same place. This is impossible not only for two sensible bodies but also for a sensible body and a mathematical one, because each has dimensions, by reason of which two bodies are prevented from being in the same place.

420. And the objects of mathematics (998a14). Here he gives the third argument. For when something is moved, anything that exists within it is moved. But sensible things are moved. Therefore, if the objects of mathematics exist in sensible things, it follows that the objects of mathematics are moved. But this is contrary to the intelligible constitution of mathematical objects, which abstract not only from matter but also from motion.

421. Then he gives the fourth argument, at moreover, on the whole (998a15), which runs thus. No position is thought to be reasonable unless it is based on one of the causes, and especially if a more untenable conclusion follows from such a position. But this position is held without a cause. For the same absurdities face those who hold the objects of mathematics to be intermediate entities and to exist in sensible things as face those who hold that they do not exist in sensible things, as well as certain other peculiar and greater difficulties, as is clear from what has been said above. Hence, this position is an unreasonable one. In concluding, he states that the questions mentioned above involve much difficulty as to what is true in these matters.

422. Now the Philosopher treats these questions below in books 12, 13, and 14 of this work, where he shows that there are neither separate mathematical substances nor forms. The reasoning which moved those who posited the objects of mathematics and the forms, which are derived from an abstraction of the intellect, is given at the beginning of book 13. For nothing prevents a thing which has some particular attribute from being considered by the intellect without its being viewed under this aspect, and yet being considered truly, just as a white man can be considered without white being considered.

Thus the intellect can consider sensible things not inasmuch as they are mobile and material, but inasmuch as they are substances or continuous quantities. This is to abstract the thing known from matter and motion.

However, so far as the thing known is concerned, the intellect does not abstract in such a way that it understands continuous quantities and forms to exist without matter and motion. For then it would follow either that the intellect of the one abstracting is false or that the things that the intellect abstracts are separate in reality.

Are genera principles of things?

Concerning the principles of things there is the problem of whether genera must be regarded as the elements and principles of things, or rather the first things of which each thing is composed inasmuch as they are intrinsic.

Just as the elements and principles of a word seem to be those things of which all words are first composed, but not word in common. And just as we say that the elements of diagrams are those things whose demonstrations are found in the demonstrations of others, either of all or of most of them.

Furthermore, those who say that the elements of bodies are many, and those who say that they are one, call the things of which bodies are composed and constituted their principles, as Empedocles says that fire and water and those things that are included with these are the elements from which existing things derive their being. But he does not speak of them as the genera of existing things.

And again if anyone wished to speculate about the nature of other things, in finding out in regard to each (a bed, for example) of what parts it is made and how it is put together, he will come to know its nature. And according to these arguments, genera are not the principles of existing things.

But if we know each thing through definitions, and genera are the principles of definitions, genera must be the principles of the things defined.

And if in order to acquire scientific knowledge of existing things it is necessary to acquire scientific knowledge of their species, according to which they are said to be beings, then genera are the principles of species.

Moreover, some of those who say that the elements of existing things are the one or being or the great and small seem to use these as genera.

But it is not possible to speak of principles in both ways; for the meaning of substance is one. Therefore, a definition by means of genera will differ from one which gives the intrinsic constituents.

Again, if genera are the principles of things in the fullest sense, there is the question of whether the first genera must be thought to be principles, or those which are lowest and are predicated of individual things. For this also raises a problem.

For if universals are the principles of things to a greater degree, evidently these must be the highest genera, because it is most properly these which are predicated of all existing things. Therefore, there will be as many principles of existing things as there are first genera. Hence being and unity will be principles and substances, for it is these especially which are predicated of all existing things. It is impossible, however, that unity or being should be a single genus of existing things, for it is necessary both that the differences of each genus exist and that each be one. But if unity and being are not genera, neither will they be principles, if genera are principles.

Further, those things that are intermediate and are taken along with differences will be genera down to individuals. But some seem to be such, whereas others do not. Again, differences are principles to a greater degree than genera. If they are principles, principles will be infinite in number, so to speak. And this will appear in another way also if one holds that the first genus is a principle.

But, on the other hand, if unity is a specific principle to a greater degree, and unity is indivisible, and everything indivisible is such either in quantity or in species, and what is indivisible in species is prior, and genera are divisible into species, then it will be rather the lowest predicate which is one. For man is not the genus of particular men.

Further, in the case of those things to which prior and subsequent apply, it is not possible in their case that there should be something which exists apart from them.

For example, if the number two is the first of numbers, there will not be any number apart from the species of numbers, nor, likewise, any figure apart from the species of figures.

But if the genera of these things do not exist apart from the species, then in the case of other things the teaching will be that there are genera apart from the species; for of these things there seem especially to be genera. But among individual things one is not prior and another subsequent.

Further, where one thing is better and another worse, that which is better is always prior; so that there will be no genus of these things. From these considerations, then, it seems that it is the terms predicated of individuals, rather than genera, which are principles.

But again it is not easy to state how one must conceive these to be the principles of things. For a principle or cause must be distinct from the things of which it is the principle or cause, and must be able to exist apart from them. But why should one think that anything such as this exists apart from singular things, except that it is predicated universally and of all things? But if this is the reason, then the more universal things are, the more they must be held to be principles. Hence the first genera will be principles of things.

What is the difference between genera and elements?

423. Having debated the questions which were raised about substances, the Philosopher now treats dialectically the questions which were raised about principles. This is divided into two parts.

In the first, he discusses the questions which asked what the principles of things are;

in the second (1044b29; [456]), the questions which asked what kind of things the principles are, at again, there is the problem.

In the first part of this division he discusses two questions:

first, whether universals are the principles of things;

second (999a24; [443]), whether any principles are separate from matter, at but there is a problem.

In regard to the first he discusses two questions,

of which the first is whether genera are the principles of things.

The second (998b14; [431]) asks which genera these are, whether the first genera or the others, at again, if genera.

In regard to the first he does two things:

first, he raises the question;

second (998a23; [424]), he treats it dialectically, at just as the elements.

The first question has to do with the principles of things. Is it necessary to accept or believe that those genera which are predicated of many things are the elements and principles of things, or rather that those parts of which every single thing is composed must be called the elements and principles of things?

But he adds two conditions, one of which is inasmuch as they are intrinsic, which is given in order to distinguish these parts from a contrary and a privation. For white is said to come from black or the non-white, although these are not intrinsic to white. Hence they are not its elements.

The other condition is what he calls the first things, which is given in order to distinguish them from secondary components. For the bodies of animals are composed of flesh and nerves, which exist within the animal, yet these are not called the elements of animals, because they are not the first things of which an animal is composed, but rather fire, air, water, and earth, from which flesh and nerves derive their being.

424. Just as the elements (998a23). Here he treats this question dialectically, and in regard to this he does three things.

First, he shows that the first things of which anything is composed are its principles and elements.

Second (998b4; [427]), he argues the opposite side of the question, at but if we know.

Third (998b11; 430), he rejects one answer by which it could be said that both of these¹ are the principles and elements of things, at but it is not.

In regard to the first he gives three arguments.

The first of these proceeds from natural phenomena, in which he makes his thesis evident by two examples.

He first gives the example of a word, whose principle and element is not said to be the common term “word,” but rather the first constituents of which all words are composed, which are called letters.

He gives diagrams (the demonstrative descriptions of geometrical figures) as a second example. For the elements of these diagrams are not said to be the common term “diagram,” but rather those theorems whose demonstrations are found in the demonstrations of other geometrical theorems, either of all or of most of them, because the other demonstrations proceed from the supposition of the first demonstrations. Hence Euclid’s book is called The Elements, because the first theorems of geometry, from which the other demonstrations proceed, are demonstrated therein.

425. Furthermore, those who (998a28). Here he gives the second argument, which also employs certain examples drawn from nature. He says that those who hold that the elements of bodies are either one or many say that the principles and elements of bodies are those things of which bodies are composed and made up as intrinsic constituents.

Thus Empedocles says that the elements of natural bodies are fire and water and other things of this kind, which along with these he calls the elements of things. Natural bodies are constituted of these first things inasmuch as they are intrinsic. Moreover, the early philosophers held that in addition to these two principles there are four others—air, earth, strife, and friendship—as was stated in book 1 (984b32; [104]). But neither Empedocles nor the other philosophers of nature said that the genera of things are the principles and elements of these natural bodies.

426. And again if anyone (998a32). Here he gives the third argument, which involves things made by art. He says that if someone wished to speculate about the nature, that is, about the definition which indicates the essence of other bodies than natural ones (namely, of bodies made by human art)—for example, if one wished to know a bed—it would be necessary to consider of what parts it is made and how they are put together. In this way he would know the nature of a bed. And after this he concludes that genera are not the principles of existing things.

427. But if we know (998b4). Here he argues the other side of the question.

He gives three arguments, the first of which is as follows. Each thing is known through its definition. Therefore, if a principle of being is the same as a principle of knowing, it seems that anything which is a principle of definition is also a principle of the thing defined. But genera are principles of definitions, because definitions are first composed of them. Hence genera are the principles of the things defined.

428. And if in order to (998b6). Here he gives the second argument, which runs thus. Scientific knowledge of each thing is acquired by knowing the species from which it gets its being, for Socrates can be known only by understanding that he is man. But genera are principles of species, because the species of things are composed of genera and differences. Therefore, genera are the principles of existing things.

429. Moreover, some of those (998b9). Here he gives a third argument, which is based on the authority of the Platonists, who held that the one and being are the principles of things, and also the great and small, which are used as genera. Therefore, genera are the principles of things.

430. But it is not possible (998b11). Here he excludes one answer which would say that both of these are principles. He says that it is impossible to say that both of these are principles, that is, both the elements (or the parts of which something is composed) and genera. He proves this by the following argument.

Of each thing there is one definite concept which manifests its substance, just as there is also one substance of each thing. But the definitive concept which involves genera is not the same as the one which involves the parts of which a thing is composed. Hence it cannot be true that each definition indicates a thing’s substance. But the definitive concept which indicates a thing’s substance cannot be taken from its principles. Therefore, it is impossible that both genera and the parts of which things are composed should be simultaneously the principles of things.

431. Again, if genera (998b14). Then he treats the second question dialectically.

First, he raises the question;

second (998b17; [432]), he brings up arguments relative to this question, at for if universals.

Accordingly, he asks: if we hold that genera are the principles of things in the fullest sense, which of these genera should be considered to be the principles of things to a greater degree? Must we consider those genera which are first in number (namely, the most common), or also the lowest genera, which are proximately predicated of the individual (namely, the lowest species)? For this is open to question, as is clear from what follows.

432. For if universals (998b17). Here he argues about the question which was proposed, and in regard to this he does three things.

First, he introduces arguments to show that the first genera cannot be principles.

Second (999a1; [436]), he introduces arguments to show that the last species should rather be called the principles of things, at but, on the other hand.

Third (999a16; [441]), he debates the proposed question, at but again it is.

In regard to the first (998b17) he gives three arguments, of which the first runs thus. If genera are principles to the extent that they are more universal, then those which are most universal (namely, those which are predicated of all things) must be the first genera and the principles of things in the highest degree. Hence there will be as many principles of things as there are most common genera of this kind. But the most common of all genera are unity and being, which are predicated of all things. Therefore, unity and being will be the principles and substances of all things.

But this is impossible, because unity and being cannot be genera of all things. For, since unity and being are most universal, if they were principles of genera, it would follow that genera would not be the principles of things. Hence the position which maintains that the most common genera are principles is an impossible one, because from it there follows the opposite of what was held, namely, that genera are not principles.

433. That being and unity cannot be genera he proves by this argument. Since a difference added to a genus constitutes a species, a species cannot be predicated of a difference without a genus, or a genus without a species. That it is impossible to predicate a species of a difference is clear for two reasons.

First, because a difference applies to more things than a species, as Porphyry says.

Second, since a difference is given in the definition of a species, a species can be predicated per se of a difference only if a difference is understood to be the subject of a species, as number is the subject of evenness, in whose definition it is given. This, however, is not the case; but a difference is rather a formal principle of a species. Therefore, a species cannot be predicated of a difference except, perhaps, in an incidental way.

Similarly too neither can a genus, taken in itself, be predicated of a difference by per se predication. For a genus is not given in the definition of a difference, because a difference does not share in a genus, as is stated in Topics 4. Nor again is a difference given in the definition of a genus. Therefore, a genus is not predicated per se of a difference in any way. Yet it is predicated of that which has a difference, namely, of a species, which actually contains a difference.

Hence he says that a species is not predicated of the proper differences of a genus, nor is a genus independently of its species, because a genus is predicated of its differences inasmuch as they inhere in a species. But no difference can be conceived of which unity and being are not predicated, because any difference of any genus is a one and a being, otherwise it could not constitute any one species of being. It is impossible, then, that unity and being should be genera.

434. Further, those things (998b28). Then he gives the second argument, which runs thus. If genera are called principles because they are common and predicated of many things, then for a like reason all those things that are principles because they are common and predicated of many will have to be genera. But all things that are intermediate between the first genera and individuals (namely, those which are considered together with some differences) are common predicates of many things. Hence they are both principles and genera. But this is evidently false. For some of them are genera, like subaltern species, whereas others are not, as the lowest species. It is not true, then, that the first or common genera are the principles of things.

435. Further, if the first genera are principles, because they are the principles by which we know species, then differences will be principles to a greater degree, because differences are the formal principles of species, and form or act is chiefly the principle of knowing. But it is unfitting that differences should be the principles of things, because in that case there would be an infinite number of principles, so to speak. For the differences of things are infinite, in a way—not infinite in reality but to us. That they are infinite in number is revealed in two ways: in one way if we consider the multitude of differences in themselves; in another way if we consider the first genus as a first principle, for evidently innumerable differences are contained under it. The first genera, then, are not the principles of things.

436. But, on the other hand (999a1). Then he shows that the lowest species are principles to a greater degree than genera. He gives three arguments, of which the first runs thus.

According to the Platonists it is the one which seems to have the species, or character, of a principle to the greatest degree. Indeed, unity has the character of indivisibility, because a one is merely an undivided being. But a thing is indivisible in two ways, namely, in quantity and in species. In quantity, as the point and unit, and this is a sort of indivisibility opposed to the division of quantity; in species, as what is not divided into many species. But of these two types of indivisibility the first and more important one is indivisibility in species, just as the species of a thing is prior to its quantity. Therefore, that which is indivisible in species is more of a principle because it is indivisible in quantity. And in the division of quantity the genus seems to be more indivisible, because there is one genus of many species, but in the division of species one species is more indivisible. Hence the last term which is predicated of many which is not a genus of many species (namely, the lowest species) is one to a greater degree in species than a genus—for example, man or any other lowest species is not the genus of particular men. Therefore, a species is a principle to a greater degree than a genus.

437. Further, in the case (999a6). Then he gives the second argument, which is based on a certain position of Plato.

At one time Plato held that there is some one thing which is predicated of many things without priority and posteriority, and that this is a separate unity, as man is separate from all men. At another time he held that there is some one thing which is predicated of many things according to priority and posteriority, and that this is not a separate unity.

This is what Aristotle means when he says in the case of those things to which prior and subsequent apply—in other words, when one of the things of which a common term is predicated is prior to another, it is impossible in such cases that there should be anything separate from the many things of which this common term is predicated.

For example, if numbers stand in such a sequence that two is the first species of number, no separate idea of number will be found to exist apart from all species of numbers. And on the same grounds no separate figure will be found to exist apart from all species of figures.

438. The reason for this can be that a common attribute is held to be separate so as to be some first entity in which all other things participate. If, then, this first entity is a one applicable to many in which all other things participate, it is not necessary to hold that there is some separate entity in which all things participate. But all genera seem to be things of this kind, because all types of genera are found to differ insofar as they are more or less perfect, and thus insofar as they are prior and subsequent in nature.

Hence, if in those cases in which one thing is prior to another, it is impossible to regard anything common as a separate entity on the supposition that there is a genus apart from species, then in the case of other things the teaching will differ—there will be another doctrine and rule concerning them, and the foregoing rule will not apply to them.

But considering the individuals of one species, it is evident that one of these is not prior and another subsequent in nature, but only in time. And thus according to Plato’s teaching a species is separate. Since, then, these common things are principles inasmuch as they are separate, it follows that a species is a principle to a greater degree than a genus.

439. Further, where one thing (999a13). Here he gives the third argument, which uses the notions “better or worse.” For in all those cases where one thing is better than another, that which is better is always prior in nature. But there cannot be held to be one common genus of those things that exist in this way. Hence there cannot be held to be one separate genus in the case of those things in which one is better and another worse. Thus the conclusion is the same as the above. For this argument is introduced to strengthen the preceding one, so to speak, with a view to showing that there is priority and posteriority among the species of any genus.

440. And from these three arguments he draws the conclusion in which he is chiefly interested: the lowest species, which are predicated immediately of individuals, seem to be the principles of things to a greater degree than genera. Here he use the genitive case in the place of the ablative, as is the Greek custom. Thus Boethius’ rendition is more clear, which expressly concludes that lowest species are more principles than genera.

441. But again it is not (999a16). Here he argues the opposite side of the question as follows. A principle and a cause are distinct from the things of which they are the principle and cause, and are capable of existing apart from them. And this is true, because nothing is its own cause. He is speaking here of extrinsic principles and causes, which are causes of a thing in its entirety. But the only thing that is held to exist apart from singular things is what is commonly and universally predicated of all things. Therefore, the more universal a thing is, the more separate it is, and the more it should be held to be a principle. But the first genera are most universal. Therefore, the first genera are the principles of things in the highest degree.

442. Now the solution to these questions is implied in this last argument. For, according to this argument, genera or species are held to be universal principles inasmuch as they are held to be separate. But the fact that they are not separate and self-subsistent is shown in book 7 [1592] of this work. Hence the Commentator also shows, in book 8, that the principles of things are matter and form, to which genus and species bear some likeness. For a genus is derived from matter and difference from form, as will be shown in the same book [720].

Hence, since form is more of a principle than matter, species will consequently be principles more than genera. But the objection which is raised against this, on the grounds that genera are the principles of knowing a species and its definitions, is answered in the same way as the objection raised about their separateness. For, since a genus is understood separately by the mind without understanding its species, it is a principle of knowing. And in the same way it would be a principle of being, supposing that it had a separate being.

Are there universals separate from singular things?

But there is a problem connected with these things, which is the most difficult of all and the most necessary to consider, with which our analysis is now concerned.

For if there is nothing apart from singular things, and singular things are infinite in number, how is it possible to acquire scientific knowledge of them?

For insofar as there is something that is one and the same, and insofar as there is something universal which relates to singular things, to that extent we acquire knowledge of them.

But if this is necessary, and there must be something apart from singular things, it will be necessary that genera exist apart from singular things, and they will be either the last or the first. But the impossibility of this has already appeared from our discussion.

Further, if there is something apart from the concrete whole (which is most disputable)—as when something is predicated of matter—if there is such a thing, the problem arises of whether it must exist apart from all concrete wholes, or apart from some and not from others, or apart from none.

If, then, there is nothing apart from singular things, nothing will be intelligible, but all things will be sensible, and there will be no science of anything, unless one might say that sensory perception is science.

Further, neither will anything be eternal or immobile; for all sensible things perish and are subject to motion.

But if there is nothing eternal, neither can there be generation, for there must be something which has come to be and something from which it comes to be; and the last of these must be ungenerated, since the process of generation must have a limit, and since it is impossible for anything to come to be from non-being.

Further, since generation and motion exist, there must be a terminus. For no motion is infinite, but every motion has a terminus. And that which is incapable of coming to be cannot be generated. But that which has come to be must exist as soon as it has come to be.

Further, if matter exists because it is ungenerated, it is much more reasonable that substance should exist, since that is what matter eventually comes to be. For if neither the one nor the other exists, nothing at all will exist. But if this is impossible, there must be something besides the synolon, and this is the form or species.

But again if anyone holds this to be true, the problem arises concerning in what cases one may hold this and in what not. For evidently this is not thought to be so in all cases. For we do not hold that there is a house apart from particular houses.

Is there anything separate from sensible things, which is their principle?

443. Having debated the question of whether universals are the principles of things, the Philosopher now raises a question about their separability, namely, whether there is anything separate from sensible things as their principle. In regard to this he considers two questions.

The first (999a24; [443]) of these is whether universals are separate from singular things.

The second (999a32; [447]) is whether there is any formal principle separate from things that are composed of matter and form, at further, if there is something.

In regard to the first he does three things.

First, he describes the problem.

Second (999a26; [444]), he argues one side of the question, at for if there is nothing.

Third (999a29; [445]), he argues the other side of the question, at but if this is.

Accordingly, this problem arises with regard to a point mentioned in the last argument of the preceding question, namely, whether a universal is separate from singular things, as the aforesaid argument supposed. He describes this problem as the one with which our analysis is now concerned (999a24), that is, the one which immediately preceded the foregoing argument. And he speaks of it in this way:

first, that it is connected with (or is a consequence of) the foregoing one, because the consideration of the preceding question depends on this, as has already been stated. For if universals are not separate, they are not principles; if they are separate, they are principles.

Second, he speaks of this problem as the most difficult of all the problems in this science. This is shown by the fact that the most eminent philosophers have held different opinions about it. For the Platonists held that universals are separate, whereas the other philosophers held the contrary.

Third, he says that this problem is one which it is most necessary to consider, because the entire knowledge of substances, both sensible and immaterial, depends on it.

444. For if there is nothing (999a26). Here he advances an argument to show that universals are separate from singular things. For singular things are infinite in number, and what is infinite cannot be known. Hence all singular things can be known only insofar as they are reduced to some kind of unity which is universal. Therefore, there is science of singular things only inasmuch as universals are known. But science is only about things that are true and which exist. Therefore, universals are things that exist of themselves apart from singular things.

445. But if this is (999a29). Then he argues the other side of the question in this way. If it is necessary that universals be something apart from singular things, it is necessary that genera exist apart from singular things, either the first genera or also the last, which are immediately prior to singular things. But this is impossible, as is clear from the preceding discussion. Therefore, universals are not separate from singular things.

446. The Philosopher solves this problem in book 7 (1039a24; [1592]) of this work, where he shows in many ways that universals are not substances which subsist of themselves. Nor is it necessary, as has often been said, that a thing should have the same mode of being in reality that it has when understood by the intellect of a knower. For the intellect knows material things immaterially, and in a similar way it knows universally the natures of things that exist as singulars in reality, without considering the principles and accidents of individuals.

447. Further, if there is something (999a32). Here he raises another question, namely, whether anything is separate from things composed of matter and form; in regard to this he does two things.

First, he raises the question.

Second (999b1; [448]), he proceeds to deal with it, at if, then, there is.

In regard to the first, it should be observed that he first raises the question of whether a universal is separate from singular things.

Now it happens to be the case that some singular things are composed of matter and form. But not all singular things are so composed, either according to the real state of affairs, since separate substances are particular because existing and operating of themselves, or even according to the opinion of the Platonists, who held that even among separate mathematical entities there are particulars inasmuch as they held that there are many of them in a single species. And while it is open to dispute whether there is anything separate in the case of those things that are not composed of matter and form, as the universal is separate from the particular, the problem is chiefly whether there is anything separate in the case of things that are composed of matter and form.

Hence he says that the point which causes most difficulty is whether there is something apart from the concrete whole, that is, apart from the thing composed of matter and form. The reason why a composite thing is called a concrete whole he explains by adding as when something is predicated of matter. For Plato held that sensible matter participates in separate universals, and that for this reason universals are predicated of singular things. These participations in universal forms by material sensible things constitute a concrete whole inasmuch as a universal form is predicated of matter through some kind of participation.

Now in regard to these things he raises a question which has three parts, namely, whether there is anything that exists apart from all things of this kind, or apart from some and not from others, or apart from none.

448. If, then, there is (999b1). Here he proceeds to deal with this problem; and concerning it he does two things.

First, he argues against the position that nothing can be held to be separate from things composed of matter and form.

Second (999b16; [454]), he argues the other side of the question, at but again if anyone holds this.

In regard to the first (999b1), he advances two arguments.

First, he argues from the principle that those things that are composed of matter and form are sensible things; therefore, he proposes that those things that are composed of matter and form are singulars. However, singular things are not intelligible, but sensible. Therefore, if there is nothing, apart from singular things that are composed of matter and form, nothing will be intelligible, but all beings will be sensible.

But there is science only of things that are intelligible. Therefore, it follows that there will be no science of anything, unless one were to say that sensory perception and science are the same, as the ancient philosophers of nature held, as is stated in On the Soul 1.

But both of these conclusions are untenable, namely, that there is no science and that science is sensory perception. Therefore, the first position is also untenable, namely, that nothing exists except singular things that are composed of matter and form.

449. Further, neither will anything (999b3). Second, he argues on the grounds that things composed of matter and form are mobile. He gives the following argument. All sensible things composed of matter and form perish and are subject to motion. Therefore, if there is nothing apart from beings of this kind, it will follow that nothing is eternal or immobile.

450. But if there is (999b5). Here he shows that this conclusion is untenable, namely, that nothing is eternal and immobile.

He does this first with respect to matter;

second (999b8; [451]) with respect to form, at further, since generation.

Accordingly, he says first (999b5) that if nothing is eternal, it is impossible for anything to be generated. He proves this as follows. In every process of generation there must be something which comes to be and something from which it comes to be. Therefore, if that from which a thing comes to be is itself generated, it must be generated from something.

Hence either there must be an infinite regress in material principles or the process must stop with some first thing which is a first material principle that is ungenerated, unless it might be said, perhaps, that it is generated from non-being; but this is impossible. Now if the process were to go on to infinity, generation could never be completed, because what is infinite cannot be traversed.

Therefore, it is necessary to hold either that there is some material principle which is ungenerated or that it is impossible for any generation to take place.

451. Further, since generation (999b8). Here he proves the same thing with respect to the formal cause, and he gives two arguments, the first of which is as follows.

Every process of generation and motion must have some terminus. He proves this on the grounds that no motion is infinite, but that each motion has some terminus. This is clear in the case of other motions which are completed in their termini. But it seems that a contrary instance is had in the case of circular motion, which can be perpetual and infinite, as is proved in Physics 8. And even though motion is assumed to be eternal, so that the entire continuity of circular motion is infinite insofar as one circular motion follows another, still each circular motion is both complete in its species and finite. That one circular motion should follow another is accidental so far as the specific nature of circular motion is concerned.

452. The things that he said about motion in general he proves specially in regard to generation; for no process of generation can be infinite, because that thing cannot be generated whose process of generation cannot come to an end, since the end of generation is to have been made. That its being made is the terminus of generation is clear from the fact that what has been generated must exist as soon as it has come to be, that is, as soon as its generation is first terminated.

Therefore, since the form whereby something is, is the terminus of generation, it must be impossible to have an infinite regress in the case of forms, and there must be some last form of which there is no generation. For the end of every generation is a form, as we have said. Thus it seems that, just as the matter from which a thing is generated must itself be ungenerated because it is impossible to have an infinite regress, in a similar way there must be some form which is ungenerated because it is impossible to have an infinite regress in the case of forms.

453. Further, if matter exists (999b12). He gives the second argument, which runs thus.

If there is some first matter which is ungenerated, it is much more reasonable that there should be some substance, that is, some form, which is ungenerated, since a thing has being through its form, whereas matter is rather the subject of generation and transmutation. But if neither of these is ungenerated, then absolutely nothing will be ungenerated, since everything which exists has the character of matter or form or is composed of both. But it is impossible that nothing should be ungenerated, as has been proved (999b8; [452]). Therefore, it follows that there must be something else besides the synolon, or concrete whole—that is, besides the singular thing which is composed of matter and form.

And by something else I mean the form or species. For matter in itself cannot be separated from singular things, because it has being only by reason of something else. But this seems to be true rather of form, by which things have being.

454. But again if anyone (999b16). Here he argues the other side of the question. For if one holds that there is some form separate from singular things that are composed of matter and form, the problem arises as to in which cases this must be admitted and in which not. For obviously this must not be held to be true in the case of all things, especially in that of those made by art. For it is impossible that there should be a house apart from this sensible house, which is composed of matter and form.

455. Now Aristotle solves this problem partly in book 12 [2488] of this work, where he shows that there are certain substances separate from sensible things and intelligible in themselves, and partly in book 7 [1503], where he shows that the forms or species of sensible things are not separate from matter.

However, it does not follow that no science of sensible things can be had or that science is sensory perception. For it is not necessary that things have in themselves the same mode of being which they have in the intellect of one who knows them. For those things that are material in themselves are known in an immaterial way by the intellect, as has also been stated above [446]. And even though a form is not separate from matter, it is not therefore necessary that it should be generated, for it is not forms that are generated, but composites, as will be shown in book 7 [1417] of this work.

It is clear, then, in what cases it is necessary to posit separate forms and in what not. For the forms of all things that are sensible by nature are not separate from matter, whereas the forms of things that are intelligible by nature are separate from matter. For the separate substances do not have the nature of sensible things, but are of a higher nature and belong to another order of existing things.

Do all things have a single substance?

Again, there is the problem of whether all things (for example, all men) have a single substance.

But this is absurd; for not all things whose substance is one are themselves one, but are many and different. But this too is untenable.

And at the same time there is the problem of how matter becomes each of the many things and a concrete whole.

And again one might also raise this problem about principles. For if they are specifically one, there will be nothing that is numerically one. Nor again will unity itself and being be one. And how will there be science unless there is some unity in all things?

But, on the other hand, if they are numerically one, each of the principles will also be one, and not, as in the case of sensible things, different for different things; for example, if the syllable BA is taken as a species, its principles in every case are specifically the same, for they are numerically different.

However, if this is not so, but the things that are the principles of beings are numerically one, there will be nothing else besides the elements. For it makes no difference whether we say “numerically one” or “singular,” because it is in this way that we say each thing is numerically one.

But the universal is what exists in these. For example, if the elements of a word were limited in number, there would have to be as many letters as there are elements. Indeed, no two of them would be the same, nor would more than two.

Are there one or many forms and principles of things?

456. Having asked what the principles are, and whether some are separate from matter, the Philosopher now asks what the principles are like.

First (999b20; [456]), he asks whether the principles are one or many;

second (1002b32; [519]), whether they exist potentially or actually, at and connected with these problems;

third (1003a6; [523]), whether they are universals or singular things, at and there is also the problem.

In regard to the first, he does two things.

First (999b20; [456]), he inquires how the principles stand with respect to unity;

second (1001a4; [488]), what relationship unity has to the notion of principle, at but the most difficult.

In regard to the first he does three things.

First, he inquires specially about the formal principle, asking whether all things that are specifically the same have a single form.

Second (999b24; [460]), he asks the same question of all principles in general, at and again one might.

Third (1000a5; [466]), he asks whether corruptible and incorruptible things have the same principles or different ones, at again, there is a problem.

In regard to the first he does two things.

First, he introduces the problem.

Second (999b21; [457]), he debates it, at but this is absurd.

The problem (999b20), then, is whether all things that belong to the same species (for example, all men) have a single substance or form.

457. But this is absurd (999b21). Then he advances arguments on one side of the question to show that all things belonging to one species do not have a single form. He does this by means of two arguments,

the first of which runs thus. Things that belong to one species are many and different. Therefore, if all things that belong to one species have a single substance, it follows that those which have a single substance are many and different. But this is unreasonable.

458. And at the same time (999b23). Then he gives the second argument, which runs thus. That which is one and undivided in itself is not combined with something divided in order to constitute many things. But it is evident that matter is divided into different singular things. Hence, if substance in the sense of form is one and the same for all things, it will be impossible to explain how each of these singular things is a matter having a substance of the kind that is one and undivided, so that as a singular thing it is a concrete whole having two parts: a matter and a substantial form which is one and undivided.

459. Now he does not argue the other side of the question, because the very same arguments which were advanced above regarding the separateness of universals are applicable in the inquiry which follows it against the arguments just given. For if a separate universal exists, it must be held that things having the same species have a single substance numerically, because a universal is the substance of singular things. Now the truth of this question will be established in book 7 (1031a15; [1356]) of this work, where it is shown that the whatness or essence of a thing is not other than the thing itself, except in an accidental way, as will be explained in that place.

460. And again one might (999b24). Here he raises a difficulty concerning the unity of principles in general: whether the principles of things are numerically the same, or only specifically the same and numerically distinct. And in regard to this he does two things.

First, he advances arguments to show that they are numerically the same.

Second (999b27; [464]), he argues on the other side of the question, at but, on the other hand.

In regard to the first (999b24) he gives three arguments. He introduces the problem by saying that the same question which was raised about substance can be raised about principles in general (that is, whether the principles of things are numerically the same).

461. He introduces the first argument to show that they are numerically the same. For things composed of principles merely contain what they receive from these principles. Therefore, if principles are not found to be one numerically but only specifically, the things composed of these principles will not be one numerically but only specifically.

462. The second argument runs thus. Unity itself or being itself must be numerically one. And by “unity itself” or “being itself,” he means unity or being in the abstract. Hence, if the principles of things are not one numerically but only specifically, it will follow that neither unity itself nor being itself will subsist of itself.

463. The third argument is this. Science is had of things because there is found to be a one-in-many, as man in common is found in all men, for there is no science of singular things but of the unity found in them. Moreover, all science or cognition of things that are composed of principles depends on a knowledge of these principles. If, then, principles are not one numerically, but only specifically, it will follow that there is no science of beings.

464. But, on the other hand (999b27). Here he argues the opposite side of the question in the following fashion.

If principles are numerically one so that each of the principles considered in itself is one, it will be impossible to say that the principles of beings exist in the same way as the principles of sensible things. For we see that the principles of different sensible things are numerically different but specifically the same, just as the things of which they are the principles are numerically different but specifically the same.

We see, for example, that syllables which are numerically distinct but agree in species have letters as their principles, which are the same specifically but not numerically. And if anyone were to say that this is not true of the principles of beings, but that the principles of all beings are the same numerically, it would follow that nothing exists in the world except the elements, because what is numerically one is a singular thing. For what is numerically one we call singular, just as we call universal what is in many. But what is singular is incapable of being multiplied, and is encountered only as a singular.

Therefore, if it is held that, numerically, the same letters are the principles of all syllables, it will follow that those letters could never be multiplied so that there could be two of them or more than two. Thus A could not be found in these two different syllables, BA or DA. And the argument is the same in the case of other letters.

Therefore, by the same reasoning, if the principles of all beings are numerically the same, it will follow that there is nothing besides these principles. But this seems to be untenable, because when a principle of anything exists it will not be a principle unless there is something else besides itself.

465. Now this question will be solved in book 12 [2464], for it will be shown there that the principles which things have (namely, matter, or privation, or form) are not numerically the same for all things, but analogically or proportionally the same. But those principles which are separate—namely, the intellectual substances, of which the highest is God—are each numerically one in themselves. Now that which is one in itself and being is God, and from him is derived the numerical unity found in all things.

And there is science of these, not because they are numerically one in all, but because in our conception there is a one in many. Moreover, the argument which is proposed in support of the opposite side of the question is true in the case of essential principles but not in that of separate ones, which is the genus to which the agent and final cause belong. For many things can be produced by one agent or efficient cause, and can be directed to one end.

Do corruptible and incorruptible things have the same principles?

Again, there is a problem which has been neglected no less by the moderns than by their predecessors: whether the principles of corruptible and incorruptible things are the same or different.

For if they are the same, how is it that some things are incorruptible and others corruptible? And what is the cause?

The followers of Hesiod and all those who were called theologians paid attention only to what was plausible to themselves and have neglected us. For making the principles of things to be gods or generated from the gods, they say that whatever has not tasted nectar and ambrosia became mortal.

And it is clear that they are using these terms in a way known to themselves, but what they have said about the application of these causes is beyond our understanding.

For if it is for the sake of pleasure that the gods partake of these things, nectar and ambrosia are not the cause of their being. But if they partake of them to preserve their being, how will the gods be eternal in requiring food?

But with regard to those who have philosophized by using fables, it is not worth our while to pay any serious attention to them.

However, from those who make assertions by demonstration it is necessary to find out, by questioning them, why some things derived from the same principles are eternal in nature and others are corrupted. But since they mention no cause, and it is unreasonable that things should be as they say, it is clear that the principles and causes of these things will not be the same.

For the explanation which one will consider to say something most to the point is that of Empedocles, who has been subject to the same error. For he posits a certain principle, hate, which is the cause of corruption.

Yet even hate would seem to generate everything except the one. For all things except God are derived from this. Hence he says: From which have blossomed forth all that was and is—trees, and men and women, and beasts and flying things, and water-nourished fish, and the long-lived gods. And apart from these things it is evident that, if hate did not exist in the world, all things would be one, as he says: For when they have come together, then hate will stand last of all.

For this reason too it turns out that God, who is most happy, is less wise than other beings. For he does not know all the elements, because hate he does not have, and knowledge is of like by like. For one knows earth by earth, water by water, and affection by affection, and hate by mournful hate.

But it is also clear (and this is where our discussion began) that hate no more turns out to be the cause of corruption than of being.

Nor, similarly, is love the cause of existence, for in blending things together into a unity it corrupts other things.

Moreover, he does not speak of the cause of change itself, except to say that it was naturally disposed to be so.

But thus mighty hate was nourished among the members and rose to a position of honor when the time was fulfilled, which, being changeable, dissolved the bond. Hence change is a necessity, but he gives no reason for its necessity.

Yet he alone speaks expressly to this extent. For he does not make some beings corruptible and others incorruptible, but makes all things corruptible except the elements.

But the problem that has been stated is why some things are corruptible and others are not, if they come from the same principles. To this extent, then, it has been said that the principles of things will not be the same.

But if the principles are different, one problem is whether they will be incorruptible or corruptible. For if they are corruptible, it is evident that they must come from something, since all corrupted things are dissolved into the elements from which they come.

Hence it follows that there are other principles prior to these principles. But this is also unreasonable, whether the process stops or goes on to infinity. Further, how will corruptible things exist if their principles are destroyed?

But if they are incorruptible, why will corruptible things come from incorruptible principles, and incorruptible things from others? For this is unreasonable, and is either impossible or requires a great deal of reasoning.

Further, no one has attempted to say that these things have different principles, but all thinkers say that all things have the same principles. But they admit the first problem, considering it a trifling matter.

466. Having investigated in a general way whether all principles belonging to one species are numerically the same, the Philosopher inquires here whether the principles of corruptible and incorruptible things are numerically the same. In regard to this he does three things.

First (1000a5; [466]), he raises the question.

Second (1000a7; [467]), he introduces an argument to show that the principles of corruptible things and those of incorruptible things are not the same, at for if they are the same.

Third (1000b23; [483]), he introduces arguments to show that they are not different, at but if the principles.

He says first (1000a5), then, that there is a problem which has been neglected no less by the modern philosophers, who followed Plato, than by the ancient philosophers of nature, who also were puzzled about whether the principles of corruptible and incorruptible things are the same or different.

467. For if they are the same (1000a7). Here he advances an argument to show that the principles of corruptible things and of incorruptible things are not the same. In regard to this he does three things.

First (1000a7; [467]), he gives the argument.

Second (1000a9; [468]), he criticizes the solution of the proposed argument which the theological poets gave, at the followers of Hesiod.

Third (1000a19; [472]), he criticizes the solution which some philosophers of nature gave, at however, from those who.

He says first (1000a7), then, that if the principles of corruptible and of incorruptible things are held to be the same, since from the same principles there follow the same effects, it seems that either all things are corruptible or all are incorruptible. Therefore, the question arises of how some things are corruptible and others incorruptible, and what the reason is.

468. The followers of Hesiod (1000a9). He criticizes the solution given by the theological poets.

First (1000a9; [468]), he gives their solution.

Second (1000a13; [470]), he argues against it, at and it is clear that.

Third (1000a18; [471]), he gives the reason why he does not criticize this position with more care, at but with regard to those.

Concerning the first (1000a9), it must be noted that there were among the Greeks, or philosophers of nature, certain students of wisdom (such as Orpheus, Hesiod, and certain others) who were concerned with the gods and hid the truth about the gods under a cloak of fables, just as Plato hid philosophical truth under mathematics (as Simplicius says in his Commentary on the Categories). Therefore, he says that the followers of Hesiod, and all those who were called theologians, paid attention to what was convincing to themselves and have neglected us, because the truth which they understood was treated by them in such a way that it could be known only to themselves. For if the truth is obscured by fables, then the truth which underlies these fables can be known only to the one who devised them. Therefore, the followers of Hesiod called the first principles of things gods, and said that those among the gods who have not tasted a certain delectable food called nectar or manna became mortal, whereas those who had tasted it became immortal.

469. But some part of the truth could lie hidden under this fable, provided that by nectar or manna is understood the supreme goodness itself of the first principle. For all the sweetness of love and affection is referred to goodness. But every good is derived from a first good. Therefore, the meaning of these words could be that some things are incorruptible by reason of an intimate participation in the highest good, as those which participate perfectly in the divine being. But certain things, because of their remoteness from the first principle, which is the meaning of “not tasting manna and nectar,” cannot remain perpetually the same in number, but only in species, as the Philosopher says in On Generation and Corruption 2. But whether they intended to treat this obscurely, or something else, cannot be perceived any more fully from this statement.

470. And it is clear (1000a13). He argues against the aforesaid position. He says that the meaning which these followers of Hesiod wished to convey by the terms “nectar” or “manna” was known to them but not to us. Therefore, their explanation of the way in which these causes are meant to solve this question and preserve things from corruption is beyond our understanding. For if these terms are understood in their literal sense, they appear to be inadequate, because the gods who tasted nectar or manna did so either for the sake of pleasure or because these things were necessary for their existence, since these are the reasons why men partake of food.

Now if they partook of them for the sake of pleasure, nectar and manna could not be the cause of their existence so as to make them incorruptible, because pleasure is something that follows on being. But if they partook of the aforesaid nourishment because they needed it to exist, they would not be eternal, having repeated need of food. Therefore, it seems that gods who are first corruptible, as it were, standing as they do in need of food, are made incorruptible by means of food. This also seems to be unreasonable, because food does not nourish a thing according to its species unless it is corrupted and passes over into the species of the one nourished. But nothing that is corruptible can be responsible for the incorruptibility of something else.

471. But with regard to those (1000a18). Here he gives his reason for not investigating this opinion with more care. He says that it is not worth our while to pay any attention to those who have philosophized by using fables, that is, by hiding philosophical truth under fables. For if anyone argues against their statements insofar as they are taken in a literal sense, these statements are ridiculous. But if one wishes to inquire into the truth hidden by these fables, it is not evident. Hence it is understood that Aristotle, in arguing against Plato and other thinkers of this kind who have treated their own doctrines by hiding them under something else, does not argue about the truth which is hidden, but about those things that are outwardly expressed.

472. However, from those who make assertions (1000a19). Then he argues against the answer given by some of the philosophers of nature, and in regard to this he does three things.

First (1000a19; [472]), he gives the argument.

Second (1000a24; [473]), he gives the answer, at for the explanation.

Third (1000a28; [474]), he criticizes it, at yet even hate.

Accordingly, he says, first (1000a19), that, having dismissed those who treated the truth by using fables, it is necessary to seek information about the aforesaid question from those who have treated the truth in a demonstrative way, by asking them why it is that, if all beings are derived from the same principles, some beings are eternal by nature and others are corrupted. And since these men give no reason why this is so, and since it is unreasonable that things should be as they say (namely, that, in the case of beings having the same principles, some should be corruptible and others eternal), it seems clearly to follow that corruptible and eternal things do not have the same principles or the same causes.

473. For the explanation (1000a24). Then he gives one solution. He says that the explanation given to the aforesaid question which seems to fit it best is the one which Empedocles gave, although he was subject to the same error as the others, because the explanation which he gave is no more adequate than theirs, as is about to be shown. For he maintained that corruptible and incorruptible things have certain common principles, but that a special principle, hate, causes the corruption of the elements in such a way that the coming together of this cause and another principle produces corruption in the world.

474. Yet even hate (1000a28). Here he criticizes Empedocles’ argument, and he does this in three ways.

First (1000a28; [474]), he does this by showing that the argument which Empedocles gave is not in keeping with his position;

second (1000b12; [478]), by showing that it is not adequate, at moreover, he does not;

third (1000b17; [481]), by showing that it is not to the point, at yet he alone speaks.

In regard to the first, he does three things.

First, he shows that Empedocles’ argument does not agree with his other views about hate;

second (1000b3; [476]), that it does not agree with his view about God himself, at for this reason;

and third (1000b11; [477]), that it does not agree with his view about love, at nor, similarly.

Accordingly, he says, first (1000a28), that Empedocles’ position that hate is the cause of corruption is untenable, because according to his position hate also seems to be the cause of the generation of all things except one. For he held that everything else is composed essentially of hate along with the other principles, with the exception of God alone, whom he claimed to be composed of the other principles without hate. Moreover, he called the heavens God, as was stated above in book 1 (984b23; [101]), because Xenophanes, after reflecting upon the whole heavens, said that the one itself is God.

And Empedocles, considering the indestructibleness of the heavens, held that the heavens are composed of the four elements and love, but not of strife or hatred. But in the case of other things, he said that all those which are or were or will be come from hate, such as sprouting trees, and men and women, and beasts (which are terrestrial animals), and vultures (which are flying and long-lived animals), and fish (which are nourished in the water), and the long-lived gods.

And by the gods he seems to mean either the stars, which he held are sometimes corrupted (although after a long period of time), or the demons, which the Platonists held to be ethereal animals. Or by the gods he also means those beings whom the Epicureans held to be of human form, as was stated above (997b5; [408]). Therefore, from the fact that all living things except one are generated from hate, it can be said that hate is the cause of generation.

475. And in addition to this there is another reason, for, according to Empedocles’ position, it is evident that, if hate did not exist in the world, all things would be one, since hate is the reason why things are distinct. Hence he quotes Empedocles’ words to the effect that, when all things come together into a unity (for example, when chaos comes into being), hate will stand last of all, separating and dissolving things. Hence the text of Boethius says: when it comes together, then chaos knows the ultimate discord. Thus it is clear that, since the being of the world consists in the distinction of things, hate is the cause of the world’s generation.

476. For this reason (1000b3). Here he gives a second argument, which pertains to the deity. He says that, since Empedocles would hold that hate is not a constituent of the divine composition, it follows, according to his arguments, that God, who is said by all men to be most happy, and consequently most knowing, is less prudent than all other beings who have knowledge. For, according to Empedodes’ position, it follows that God does not know the elements because he does not contain hate. Hence he does not know himself. And like knows like according to the opinion of Empedodes, who said that by earth we know earth, by water, water, and by affection, which is love or concord, we know affection, or love or concord. And in a similar way we know hate by mournful hate, which is sadness, whether unpleasant or evil, according to the text of Boethius, who says that by evil discord we know discord. It is evident, then, that Aristotle thought this untenable and contrary to the position that God is most happy, because he himself would not know some of the things that we know. And since this argument seemed to be beside the point, therefore, returning to his principal theme, he says (1000b8) that, in returning to the point from which the first argument began, it is evident, so far as Empedocles is concerned, that hate is no more a cause of corruption than of being.

477. Nor, similarly, is love (1000b11). Here he gives the third argument, which pertains to love. He says that in like manner love is not the cause of generation or being, as Empedocles claimed, if another position of his is considered. For he said that, when all the elements are combined into a unity, the corruption of the world will then take place. Thus love corrupts all things. Therefore, with respect to the world in general, love is the cause of corruption, whereas hate is the cause of generation. But with respect to singular things, hate is the cause of corruption and love of generation.

478. Moreover, he does (1000b12). Here he shows that Empedocles’ argument is not adequate. For Empedodes said that there exists in the world a certain alternation of hate and friendship, in such a way that at one time love unites all things and afterward hate separates them. But as to the reason why this alternation takes place, so that at one time hate predominates and at another time love, he said nothing more than that it was naturally disposed to be so.

479. And next he gives Empedocles’ words, which, because they are written in Greek verse, are difficult and differ from the common way of speaking. These words are: but thus mighty hate was nourished among the members and rose to a position of honor when the time was fulfilled, which, being changeable, dissolved the bond (1000b14). But the text of Boethius runs thus: but when mighty discord in the members was promoted to a place of honor, because it marched forward in a completed year, which, when these things have been changed, returns to a full bond. Now in order to understand this it must be noted that he speaks poetically of the whole world as though it were a single living thing in whose members and parts there is found at first the greatest harmony, which he calls love or concord, and afterward there begins to exist little by little a certain dissonance, which he calls discord. And, similarly, in the parts of the universe at first there was maximum concord, and afterward hate was nourished little by little until it acquired a position of honor, that is, it acquired dominion over the elements. This comes about when a completed time is reached or a year is completed, as Empedocles held, which (hate or discord, or the year), being changeable, dissolves the bond, that is, the former union of the elements. Or the year or hate returns to a full bond because by a certain ability and hidden power it returns to predominate over things.

480. After these words of Empedodes, Aristotle, in giving the meaning of the word changeable which he used, explains it as though change were necessary. For he says that Empedocles made the foregoing statements as though it were necessary that there should be an alternation of hate and love, but he gives no reason for this necessity. For, in the case of this one living thing, it is evident that what causes the alternation of hate and love is the motion of the heavens which causes generation and corruption in the world. But no such cause can be assigned for why the whole should be changed in this way by love and hate. Hence it is clear that his argument was inadequate.

481. Yet he alone (1000b17). Here he shows that this argument of Empedocles is not to the point. He says that Empedocles seems to say expressly, or clearly, only that he does not hold that some of the things derived from these principles are corruptible and others incorruptible, but he holds that all things are corruptible with the exception of the elements alone. Thus he seems to avoid the foregoing problem inasmuch as the question remains why some things are corruptible and some not, if they come from the same principles. Hence it is also clear that his argument is not to the point, because he neglects the very point that requires explanation.

482. But it can be asked how he can say here that Empedocles held all things to be corruptible except the elements, since Empedocles has said above that the one is God, that is, what is composed of the other principles except hate.

It must be noted, however, that Empedocles posited two processes of corruption in the world, as is clear from what was said above. He posited one with respect to the blending of the whole universe, which was brought about by love. From this process he did not make even God immune, because in God he placed love, which caused other things to be mixed with God. And he posited another process of corruption for singular things, and the principle of this process is hate. But he excluded this kind of corruption from God, seeing that he did not posit hate in God. In summing up, then, Aristotle concludes that this much has been said for the purpose of showing that corruptible and incorruptible things do not have the same principles.

483. But if the principles (1000b23). Here he argues the other side of the question, with two arguments.

The first is this. If the principles of corruptible and incorruptible things are not the same, the question arises of whether the principles of corruptible things are corruptible or incorruptible. If one says that they are corruptible, he proves that this is false by two arguments.

The first runs thus. Every corruptible thing is dissolved into the principles of which it is composed. If, then, the principles of corruptible things are corruptible, it will be necessary to hold also that there are other principles from which they are derived. But this is untenable, unless an infinite regress is posited.

Now it was shown in book 2 (994a1; [299]) that it is impossible to have an infinite regress in principles in any genus of cause. And it would be just as untenable for someone to say that this condition applies in the case of corruptible principles, since corruption seems to come about as a result of something being dissolved into prior principles.

484. The second argument runs thus. If the principles of corruptible things are corruptible, they must be corrupted, because every corruptible thing will be corrupted. But after they have been corrupted they cannot be principles, for what is corrupted or has been corrupted cannot cause anything. Therefore, since corruptible things are always caused in succession, the principles of corruptible things cannot be said to be corruptible.

485. Again, if it is said that the principles of corruptible things are incorruptible, evidently the principles of incorruptible things are incorruptible. Therefore, the question remains of why it is that, from certain incorruptible principles, corruptible effects are produced, and from certain others, incorruptible effects are produced. For this seems to be unreasonable and either is impossible or requires considerable explanation.

486. Further, no one (1000b32). Then, relative to his main thesis, he gives his second argument, which is drawn from the common opinions of all men. For no one has attempted to say that corruptible and incorruptible things have different principles, but all say that all things have the same principles. Yet, all pass lightly over the first argument, given in favor of the first part of the question, as though it were of little importance; but this is to acknowledge its truth. Hence the text of Boethius says: but they swallow the first argument as though they considered it a minor matter.

Are the principles of corruptible and incorruptible things the same?

487. Now the solution to this problem is given in book 12 [2553], where the Philosopher shows that the first active or motive principles of all things are the same, but in a certain sequence. For the first principles of things are unqualifiedly incorruptible and immobile, whereas the second are incorruptible and mobile, that is, the celestial bodies, which cause generation and corruption in the world as a result of their motion. Now the intrinsic principles of corruptible things and of incorruptible things are the same, not numerically but analogically. Still the intrinsic principles of corruptible things, which are matter and form, are not corruptible in themselves, but only accidentally. For it is in this way that the matter and form of corruptible things are corrupted, as is stated in Physics 1.

Are unity and being the substance and principle of all things?

But the most difficult problem which has to be considered, and the one which is most necessary for a knowledge of the truth, is whether unity and being are the substance of existing things, and whether each of them is nothing else than unity and being. Or whether it is necessary to investigate what being and unity themselves are, as though there were some other nature which underlies them.

For some think that reality is of the former sort, and some of the latter.

For Plato and the Pythagoreans thought that being and unity were nothing else than themselves, and that this is their nature, their substance being simply unity and being. But among the other philosophers there are different opinions about the nature of unity.

Empedocles, for example, as though reducing it to something better known, says that unity is being; for he would seem to say that this is love, since this is the cause of why unity belongs to all things.

Others say that this unity and being of which existing things consist and have been made is fire, and others say it is air. And those who hold that there are many elements say the same thing; for they must also speak of unity and being in as many ways as they say there are principles.

But if anyone holds that unity and being are not substances, it will follow that no other universals are such, for these are the most universal of all. But if there is no one-in-itself or being-in-itself, there will hardly be any other things that exist apart from what are called singular things. Further, if unity is not a substance, evidently number will not exist as another reality separate from existing things, for number is of units, and a unit is truly something one. But if there is a one-in-itself and being-in-itself, the substance of these must be unity itself and being itself. For nothing else is predicated universally of all things but these two.

But, on the other hand, if there is to be a one-in-itself and being-in-itself, there is great difficulty in seeing how there will be anything else besides these. I mean, how will there be more beings than one? For that which differs from being does not exist, Hence according to Parmenides’ argument it must follow that all beings are one, and that this is being.

But there is a difficulty in either case; for whether unity itself is not a substance, or whether there is a unity itself, it is impossible for number to be a substance.

Now it has already been stated why this follows if unity is not a substance; but if it is, the same difficulty will arise with regard to being. For from something outside of being something else will be one; for it must be not one. But all beings are either one or many, each of which is a one.

Further, if unity itself is indivisible, according to Zeno’s axiom it will be nothing.

For that which when added does not make a thing greater or when subtracted does not make it smaller, this, he says, does not belong to the realm of existing things, as though it were evident that whatever has being is a continuous quantity.

And if it is a continuous quantity, it is bodily; for this in every respect is a being.

But other quantities (for example, a surface and a line) will make a thing greater when added in one way, but in another way they will not. A point and a unit will do so in no way.

But this philosopher speculates clumsily, and it is possible for a thing to be indivisible in such a way that some answer may be made against him; for when something of this kind is added it will not make a thing greater, but more.

Yet how will continuous quantity come from such a unity or from many of them? For this would be like saying that a line is made up of points.

But even if someone were to think that number has come, as some say, from unity itself and from something else that is not one, nonetheless it would be necessary to inquire as to why and how the thing which has come to be would sometimes be a number and sometimes a continuous quantity, if that not-one were inequality and the same nature in either case. For it is not clear how continuous quantities would be produced from unity and this principle, or from some number and this principle.

Are “one” and “being” substances or principles of things?

488. Having asked whether the principles of things are the same or different, the Philosopher now asks how unity itself could have the nature of a principle, and in regard to this he does three things.

First, he asks whether unity itself is a principle;

second (1001b26; [502]), he asks whether numbers, which arise or follow from unity, are the principles of things, at and connected with these;

third (1002b12; [515]), whether the forms, which are certain separate unities, are the principles of things, at but in general one will wonder.

In regard to the first he does three things.

First, he raises the question.

Second (1001a8; [489]), he gives the opinions on both sides, at for some think.

Third (1001a19; [490]), he advances arguments on both sides, at but if anyone.

He says first (1001a4) that, of all the different questions which have been raised, one is more difficult to consider because of the weight of the arguments on both sides, and that this question is also one about which it is necessary to know the truth, because our decision about the substances of things depends on it.

Now this question is whether unity and being are the substances of things not in such a way that either of them must be attributed to some other nature which would be informed, as it were, by unity and being, but rather such that the unity and being of a thing are its substance. Or, in an opposite way, whether it is necessary to ask what that thing is to which unity and being properly belong, as though there were some other nature which is their subject.

489. For some think (1001a8). Here he gives the opinions on each side of the question. He says that some philosophers thought that reality was of one kind, and some of another. For Plato and the Pythagoreans did not hold that unity and being are the attributes of some nature, but that they constitute the nature of things, as though being itself and unity itself were the substance of things. But some philosophers, in speaking about the natural world, attributed unity and being to certain other natures, as Empedocles reduced the one to something better known, which he said is unity and being. (And this seems to be love, which is the cause of unity in the world.)

But other philosophers of nature attributed these to certain elementary causes, whether they posited one first principle, as fire or air, or more than one. Since they would hold that the material principles of things are the substances of things, it was necessary that each of these should constitute the unity and being of things. Thus whichever one of these anyone might hold to be a principle, he would logically think that through it being and unity would be attributed to all things, whether he posited one principle or more than one.

490. But if anyone (1001a19). Here he gives arguments on both sides of the question.

First, he gives arguments in support of the view of Plato and Pythagoras.

Second (1001a29; [493]), he gives arguments on the other side of the question, in support of the view of the philosophers of nature, at but, on the other hand.

In regard to the first (1001a19), he makes use of division as follows. It is necessary to hold either that unity and being, separate and existing apart, are a substance, or not. Now if it is said that unity and being are not a substance, two untenable consequences will follow.

The first of these is that unity and being are said to be the most universal of all; therefore, if unity and being are not separate in such a way that unity itself or being itself is a certain substance, it will then follow that no universal is separate. Thus it will follow that there is nothing in the world except singular things, which seems to be inappropriate, as has been stated in earlier questions [443].

491. The other untenable consequence is this. Number is nothing else than units, because number is composed of units (for a unit is nothing else than unity itself). Therefore, if unity itself is not separate as a substance existing of itself, it will follow that number will not be a reality separate from those things that are found in matter. This can be shown to be inappropriate in view of what has already been stated above. Hence it cannot be said that unity and being are not a substance which exists by itself.

492. Therefore, if the other part of the division is conceded, that there is something which is unity itself and being itself, and that this exists separately, it must be the substance of all those things of which unity and being are predicated. For everything that is separate and is predicated of many things is the substance of those things of which it is predicated. But nothing else is predicated of all things in as universal a way as unity and being. Therefore, unity and being will be the substance of all things.

493. But, on the other hand (1001a29). Then he argues the other side of the question, and he gives two arguments.

The second (1001b7; [496]) of these begins where he says, further, if unity itself.

In regard to the first he does two things.

First, he gives the argument.

Second (1001b1; [494]), he shows how the question is made difficult as a result of the argument given, at but there is a difficulty in either case.

The first (1001a29) argument, then, is as follows. If there is something which is itself being and unity as something existing separately, it will be necessary to say that unity is the very same thing as being. But that which differs from being is non-being. Therefore, it follows, according to the argument of Parmenides, that besides the one there is only non-being. Thus all things will have to be one, because it could not be held that that which differs from the one, which is per se separate, is a being.

494. But there is a difficulty (1001b1). Here he shows how this argument creates a difficulty in the case of the position of Plato, who held that number is the substance of things. He says that Plato faces a difficulty in either case, whether it is said that this separate one is a substance or not. For whichever view is held, it seems impossible that number should be the substance of things. For if it is held that unity is not a substance, it has already been stated (1001a29; [493]) why number cannot be held to be a substance.

495. But if unity itself is a substance, the same problem will arise with respect to both unity and being. For either there is some other unity besides this unity which exists separately of itself or there is not. And if there is no other, a multitude of things will not exist now, as Parmenides said. But if there is another unity, then that other unity, since it is not unity itself, must have as a material element something that is other than unity itself, and is consequently other than being. And that material element from which this second unity comes to be will have not to be a being. Thus a multitude of beings cannot be constituted from this unity which exists apart from unity itself, because all beings are either one or many, each of which is a one. But this one has as its material element something that is neither unity nor being.

496. Further, if unity (1001b7). Here he gives the second argument; and in regard to this he does three things.

First (1001b7; [496]), he gives the argument.

Second (1001b13; [498]), he criticizes it, at but this philosopher.

Third (1001b17; [499]), he shows that the difficulty remains, at yet how will continuous quantity.

He says first (1001b7), then, that if this separate unity is indivisible, there follows from this the other position that nothing exists, which Zeno assumed. For Zeno supposed that that which when added does not make a thing greater and when taken away does not make it smaller is nothing in the real order.

But he makes this assumption on the grounds that continuous quantity is the same as being. For it is evident that this is not a continuous quantity—I mean that which, when added, does not make a thing greater and, when subtracted, does not make it smaller.

Therefore, if every being were a continuous quantity, it would follow that that which when added does not make a thing greater and when subtracted does not make it smaller is non-being.

497. And better still, if any particular thing were to bear this out, every being would have to be a bodily continuous quantity. For anything added to or subtracted from a body in any one of its dimensions makes the body greater or less. But other continuous quantities, such as lines and surfaces, become greater insofar as one dimension is added, whereas others do not. For line added to line in length causes increase in length but not in width, and surface added to surface causes increase in width and in length but not in depth. But a point and a unit do not become greater or less in any way. Hence according to Zeno’s axiom it would follow that a point and a unit are non-beings in an absolute sense, whereas a body is a being in every respect, and surfaces and lines are beings in one respect and non-beings in another respect.

498. But this philosopher (1001b13). Here he criticizes the argument which has been given. He says that Zeno, by proposing such an axiom, speculated clumsily, or in an unskilled and rude manner, such that according to him there cannot be anything indivisible. And for this reason some answer must be given to the foregoing argument; and if not to the point at issue, at least to the man.

Now we say that, even though a unity when added to something else does not make it larger, it does cause it to be more. And this suffices for the notion of being, that it makes continuous things larger, and discreet things more.

499. Yet how will (1001b17). Then he states the difficulty which still faces the Platonists after the above solution. And he advances two difficulties.

The first of these is that the Platonists held that the one which is indivisible is the cause not only of number, which is a plurality, but also of continuous quantity. Therefore, if it is granted that when a one is added it makes a thing more, as would seem to suffice for the one which is the cause of number, how will it be possible for continuous quantity to come from an indivisible one of this kind, or from many such ones, as the Platonists held? For this would seem to be the same thing as to hold that a line is composed of points. For unity is indivisible just as a point is.

500. But even if someone (1001b19). Here he gives the second difficulty. He says that if anyone were to think that the situation is such that number is the result of the indivisible one and of something else which is not one, but participates in the one as a kind of material nature (as some say), the question would still remain as to why and how that which comes from the one as form and from another material nature, which is called the not-one, is sometimes a number and sometimes a continuous quantity.

The difficulty would be most acute if that material not-one were inequality, as is implied in the continuously extended, and were to be the same reality. For it is not clear how numbers come from this inequality as matter and from the one as form. Nor again is it clear how continuous quantities come from some number as form and from this inequality as matter. For the Platonists held that number comes from a primary one and a primary two, and that, from this number and material inequality, continuous quantity is produced.

501. The solution of this problem is treated by Aristotle in the following books. For the fact that there is something separate, which is itself one and being, he will prove below in book 12 [2553], when he establishes the oneness of the first principle which is separate in an absolute sense, although it is not the substance of all things that are one, as the Platonists thought, but is the cause and principle of the unity of all things.

And insofar as unity is predicated of other things it is used in two ways.

In one way it is interchangeable with being, and in this way each thing is one by its very essence, as is proved below in book 4 [548]. Unity in this sense adds nothing to being except merely the notion of undividedness.

Unity is used in another way insofar as it has the character of a first measure, either in an absolute sense or with respect to some genus.

And this unity, if it is both a minimum in the absolute sense and indivisible, is the one which is the principle and measure of number. But if it is not both a minimum in an absolute sense and indivisible, it will not be a unit and measure in an absolute sense, as a pound in the case of weights and a half-tone in the case of melodies and a foot in the case of lengths. And nothing prevents continuous quantities from being composed of this kind of unity. He will establish this in book 10 [1940] of this work.

But because the Platonists thought that the one which is the principle of number and the one which is interchangeable with being are the same, they therefore held that the one which is the principle of number is the substance of each thing, and consequently that number, inasmuch as it is composed of many substantial principles, makes up or comprises the substance of composite things. But he will treat this question at greater length in books 13 and 14 of this work.

Is quantity the substance and principle of sensible things?

And connected with these is the question of whether numbers and bodies and surfaces and points are substances, or not.

For if they are not, we are in a quandary as to what being is, and what the substances of things are. For passions and motions and relations and dispositions and their complex conceptions do not seem to signify substance, because all are predicated of some subject, and no one of them is a particular thing. And those things that seem to signify substance most of all, as fire, water, and earth, of which composite bodies are constituted (their heat and cold and similar passions), are not substances. And it is only the body which undergoes these that remains as a being and is a substance.

Yet a body is a substance to a lesser degree than a surface, and this than a line, and this in turn than a unit and a point. For a body is defined by means of these, and these seem to be capable of existing without a body, but that a body should exist without these is impossible.

For this reason many of the natural philosophers, including the first, thought that substance and being are bodies, and that other things are attributes of this kind of thing, and hence too that the principles of bodies are the principles of beings. But the later philosophers, who were wiser than these, thought that the principles of things are numbers. Therefore, as we have said, if these are not substance, there is no substance or being at all, for the accidents of these things are not worthy to be called beings.

But if it is admitted that lengths and points are substances to a greater degree than bodies, and we do not see to what sort of bodies these belong (because it is impossible for them to exist in sensible bodies), there will then be no substance at all.

Further, all of these seem to be dimensions of bodies, one according to width, another according to depth, and another according to length.

Similarly, any figure whatever already exists in a solid. Hence if neither Mercury is in the stone, nor one half of a cube in a cube as something segregated, neither will surface exist in a solid. For if this were true of anything whatever, it would also be true of that which divides a thing in half. And the same argument would apply in the case of a line, a point, and a unit.

If, then, a body is substance in the highest degree, and these things are such to a greater degree than it is, and these do not exist and are not substances, it escapes our understanding as to what being itself is and what the substance of beings is.

For along with what has been said there happen to be certain unreasonable views about generation and corruption. For if substance, not existing before, exists now, or does not exist afterwards when existing before, it seems to suffer these changes through generation and corruption.

But it is impossible for points and lines and surfaces either to come to be or to be destroyed, even though they sometimes exist and sometimes do not.

For when bodies are joined or divided, whenever they are joined the two at once become one, and whenever they are divided, two are produced, because the one thing is no longer composed but has perished, and when they are divided, what did not exist before exists.

For the indivisible point is not divided into two, and if things are generated and corrupted, they are generated from something.

And it is similar with regard to the now in time, for this cannot be generated and corrupted. Yet it seems always to exist, although it is not a substance. It is also clear that this is true of points, lines, and surfaces, because the argument is the same. For they are all similarly either limits or divisions.

Are numbers and continuous quantities the substances or principles of sensible things?

502. Having inquired whether unity and being are the substances of sensible things, the Philosopher now asks whether numbers and continuous quantities are the substances of sensible things; and in regard to this he does three things.

First (1001b26; [502]), he presents the question.

Second (1001b28; [503]), he argues in support of one side of the question, at for if they are not.

Third (1002a15; [507]), he argues on the other side, at but if it is admitted.

Accordingly he says, first, that connected with these, that is, following from the foregoing problem, there is the question of whether numbers and continuous quantities—bodies, surfaces, and their extremities, such as points—either are substances that are separate from sensible things or are the substances of sensible things themselves, or not. He says that this problem is a result of the foregoing one, because in the foregoing problem it was asked whether unity is the substance of things. Now unity is the principle of number. But number seems to be the substance of continuous quantity inasmuch as a point, which is a principle of continuous quantity, seems to be merely the number one having position, and a line to be the number two having position, and the primary kind of surface to be the number three having position, and a body to be the number four having position.

503. For if they are not (1001b28). Then he advances an argument to show that these are the substances of sensible things; and in regard to this he does two things.

First (1001b28; [503]), he introduces an argument to show that these are the substances of sensible things.

Second (1001b28; [506]), he shows how the early philosophers followed out the first arguments, at for this reason.

In regard to the first he does two things.

First, he advances an argument to show that body is the substance of things;

second (1002a4; [504]), to show that many other things are substances to an even greater degree, at yet a body.

He says first (1001b28) that, if these things are not substances, we are in a quandary as to what being is per se and what the substances of beings are. For it is evident that passions, motions, relations, dispositions (or arrangements), and their complex conceptions according as they are put into words do not seem to signify the substance of anything. For all things of this kind seem to be predicated of a subject as something belonging to the genus of quantity, and no one of them seems to signify a particular thing, that is, something that is complete and subsists of itself. This is especially evident in regard to the foregoing things, which are not said to be complete things but things whose nature consists in a kind of relation. But of all things those which especially seem to signify substance are fire, earth, and water, of which many bodies are composed. But he omits air, because it is less perceptible, and this is the reason why some thought air to be nothing. But in these bodies there are found certain dispositions—namely, hot and cold and other passions and passible qualities of this kind—which are not substances according to what has been said. It follows, then, that body alone is substance.

504. Yet a body (1002a4). Here he proceeds to examine those things that appear to be substance to an even greater degree than a body. He says that a body seems to be a substance to a lesser degree than a surface, and a surface than a line, and a line than a point or a unit. He proves this in two ways, of which the first is as follows. That by which a thing is defined seems to be its substance, for a definition signifies substance. But a body is defined by a surface, a surface by a line, a line by a point, and a point by a unit, because they say that a point is a unit having position. Therefore, surface is the substance of body, and so on for the others.

505. The second argument runs as follows. Since substance is the primary kind of being, whatever is prior seems to be substance to a greater degree. But a surface is naturally prior to a body, because a surface can exist without a body but not a body without a surface. Therefore, a surface is substance to a greater degree than a body. The same reasoning can be applied to all the others in turn.

506. For this reason (1002a8). Then he shows how the earlier philosophers followed out the foregoing arguments. He says that it was because of the foregoing arguments that many of the ancient philosophers, especially the first, thought that body alone was being and substance, and that all other things were accidents of bodies. Hence when they wanted to study the principles of beings, they studied the principles of bodies, as was stated above in book 1 (983b6; [74]) with regard to the positions of the ancient natural philosophers. But the other philosophers, who came later and were reputed to be wiser than the aforesaid philosophers inasmuch as they dealt more profoundly with the principles of things (namely, the Pythagoreans and Platonists), were of the opinion that numbers are the substances of sensible things inasmuch as numbers are composed of units. And the unit seems to be one substance of things.

Hence, according to the foregoing arguments and opinions of the philosophers, it seems that, if these things—numbers, lines, surfaces, and bodies—are not the substances of things, there will be no being at all. For if these are not beings, it is unfitting that their accidents should be called beings.

507. But if it is (1002a15). Then he argues in support of the other side of the question; and he gives four arguments,

the first of which is as follows. If anyone were to admit that lengths and points are substances to a greater degree than bodies, then supposing that things of this sort are not substances, it also follows that bodies are not substances. Consequently, no substance will exist, because the accidents of bodies are not substances, as has been stated above [503]. But points, lines, and surfaces are not substances. For these must be the limits of some bodies, because a point is the limit of a line, a line the limit of a surface, and a surface the limit of a body. But it is not evident to what sort of bodies these surfaces, lines, and points which are substances belong. For it is evident that the lines and surfaces of sensible bodies are not substances, because they are altered in the same way as the other accidents in reference to the same subject. Therefore, it follows that there will be no substance whatever.

508. Further, all of these (1002a18). Here he gives the second argument, which is as follows. All of the above-mentioned things seem to be certain dimensions of bodies, either according to width, as a surface, or according to depth, as a solid, or according to length, as a line. But the dimensions of a body are not substances. Therefore, things of this kind are not substances.

509. Similarly, any figure (1002a20). Here he gives a third argument, which is as follows. Any figure which can be educed from a solid body according to some dimension is present in that body in the same way, that is, potentially.

But in the case of a large piece of stone which has not yet been cut, it is evident that Mercury, that is, the figure of Mercury, is not present in it actually, but only potentially. Therefore, in like manner, in a cube (in a body having six square surfaces) one half of the cube, which is another figure, is not present actually; but it becomes actual in this way when a cube has already been divided into two halves.

And since every reduction of a new figure in a solid which has been cut is made according to some surface which limits a figure, it is also evident that such a surface will not be present in a body actually, but only potentially. For if each surface besides the external one were actually present in a solid body, then for the same reason the surface which limits one half of the figure would also be actually present in it.

But what has been said of a surface must also be understood of a line, a point, and a unit. For these are actually present in the continuum only insofar as they limit the continuum, and it is evident that these are not the substance of a body. But the other surfaces and lines cannot be the substance of a body, because they are not actually present in it, for a substance is actually present in the thing whose substance it is.

Hence he concludes that, of all of these, body especially seems to be substance, and that surfaces and lines seem to be substance to a greater degree than bodies. Now if these are not actual beings or substances, it seems to escape our comprehension as to what being is and what the substances of things are.

510. For along with what has been said (1002a28). Here he gives the fourth argument.

First, he states it,

and second (1002b8; [513]), he clarifies it by using a similar case, at and it is similar.

Accordingly, he says, first (1002a28), that along with the other untenable consequences mentioned there also happen to be certain unreasonable views about generation and corruption on the part of those who hold that lines and surfaces are the substances of sensible things.

For every substance which at first did not exist and later does exist, or which first was and afterwards is not, seems to suffer this change by way of generation and corruption. This is most evident in the case of all those things that are caused by way of motion. But points and lines and surfaces sometimes are and sometimes are not. Yet they are not generated or corrupted. Neither, then, are they substances.

511. He then proves each assumption. The first of these is that they sometimes are and sometimes are not. For it happens that bodies which were at first distinct are afterwards united, and that those which were at first united are afterwards divided. For when bodies which were initially separated are united, one surface is produced for the two of them, because the parts of a continuous body are united in having one common boundary, which is one surface.

But when one body is divided into two, two surfaces are produced, because it cannot be said that when two bodies are brought together their surfaces remain intact, but that both are corrupted, or cease to be. In like manner, when bodies are divided, there begin to exist for the first time two surfaces which previously did not exist.

For it cannot be said that a surface, which is indivisible according to depth, is divided into two surfaces according to depth; or that a line, which is indivisible according to width, is divided according to width; or that a point, which is indivisible in every respect, is divided in any respect whatsoever.

Thus it is clear that two things cannot be produced from one thing by way of division, and that one thing cannot be produced from two of these things by way of combination. Hence it follows that points, lines, and surfaces sometimes begin to be and sometimes cease to be.

512. After having proved this, he proves the second assumption, namely, that these things are neither generated nor corrupted. For everything that is generated is generated from something, and everything that is corrupted is dissolved into something as its matter. But it is impossible to assign any matter whatever from which these things are generated and into which they are dissolved, because they are simple. Therefore, they are neither generated nor corrupted.

513. And it is similar (1002b8). Then he makes the foregoing argument clear by using a similar case. For the now in time stands in relation to time as a point to a line. But the now in time does not seem to be generated or corrupted, because if it were, its generation or corruption would have to be measured by some particular time or instant. Thus the measure of this now either would be another now, and so on to infinity, or would be time itself. But this is impossible.

And even though the now is not generated or corrupted, still each now always seems to differ, not substantially but existentially, because the substance of the now corresponds to the mobile subject. But the difference of the now in terms of existence corresponds to the variation in motion, as is shown in Physics 4. Therefore, the same thing seems to be true of a point in relation to a line, and of a line in relation to a surface, and of a surface in relation to a body, namely, that they are neither corrupted nor generated, although some variation is observable in things of this kind.

For the same holds true of all of these, because all things of this kind are, in like manner, limits if regarded as at the extremities, or divisions if they are found in between. Hence, just as the now varies existentially as motion flows by, although it remains substantially the same because the mobile subject remains the same, so also does the point vary. And it does not become different because of the division of a line, even though it is not corrupted or generated in an absolute sense. The same holds true of the others.

514. But the Philosopher will treat this question in books 13 and 14. And the truth of the matter is that mathematical entities of this kind are not the substances of things, but are accidents which accrue to substances. But this mistake about continuous quantities is due to the fact that no distinction is made between the sort of body which belongs to the genus of substance and the sort which belongs to the genus of quantity. For body belongs to the genus of substance according as it is composed of matter and form, and dimensions are a natural consequence of these in bodily matter. But dimensions themselves belong to the genus of quantity, and are not substances, but accidents whose subject is a body composed of matter and form. The same thing too was said above [500] about those who held that numbers are the substances of things, for their mistake came from not distinguishing between the one which is the principle of number and that which is interchangeable with being.

Are there separate forms which are the essences of sensible things?

But in general one will wonder why, in addition to sensible things and those which are intermediate, it is necessary to look for certain other things that we posit as the specific essences (or forms) of sensible things.

For if it is because the objects of mathematics differ in one respect from the things that are at hand, they do not differ in being from many things that are specifically the same. Hence the principles of sensible things will not be limited in number but only in species; unless one were to consider the principles of this particular syllable or word, for these are limited in number. And this is likewise true of the intermediate entities, for in their case too there are an infinite number of things that are specifically the same.

Hence, if in addition to sensible substances and the objects of mathematics there are not certain other things, such as some call the forms, there will be no substance which is one both numerically and specifically. Nor will the principles of beings be limited in number, but only in species. Therefore, if this is necessary, it will also be necessary on this account that there should be forms. And even if those who speak of the forms do not express themselves clearly, although this is what they wanted to say, they must affirm that each of the forms is a substance, and that nothing accidental pertains to them.

But if we hold that the forms exist, and that principles are one numerically but not specifically, we have stated the untenable conclusions that follow from this view.

Are forms substances or principles of things?

515. Having inquired whether the objects of mathematics are the principles of sensible substances, the Philosopher now inquires whether in addition to the objects of mathematics there are certain other principles, such as those which we call forms, which are the substances and principles of sensible things. In regard to this, he does three things.

First, he presents the question.

Second (1002b14; [516]), he argues one side of the question, at for if it is because.

Third (1002b30; [518]), he argues the other side, at but if we hold.

Accordingly, he first says that, if one assumes that the objects of mathematics are not the principles of sensible things and their substances, one will next have the problem of why, in addition to both sensible things and the objects of mathematics (which are an intermediate genus between sensible things and the forms), it is necessary to posit a third genus of entities, namely, the specific essences, that is, the ideas or separate forms.

516. For if it is because (1002b14). Here he argues one side of the question. The reason why it is necessary to posit separate forms over and above sensible substances and the objects of mathematics seems to be that the objects of mathematics differ in one respect from the things that are at hand, that is, from sensible things, which exist in the universe. For the objects of mathematics abstract from sensible matter.

Yet in another respect they do not differ, but rather agree. For just as we find many sensible things that are specifically the same but numerically different, as many men or many horses, in a similar way we find many objects of mathematics which are specifically the same but numerically different, such as many equilateral triangles and many equal lines. And if this is true, it follows that, just as the principles of sensible things are not limited in number, but in species, the same thing is true of the intermediate entities—the objects of mathematics.

For, since in the case of sensible things there are many individuals of one sensible species, it is evident that the principles of sensible things are not limited in number, but in species—unless, of course, we can consider the proper principles of a particular individual thing, which are also limited in number and are individual.

He gives words as an example, for in the case of a word expressed in letters it is clear that the letters are its principles, yet there are not a limited number of individual letters taken numerically, but only a limited number taken specifically, some of which are vowels and some consonants. But this limitation is according to species and not according to number. For A is not only one, but many, and the same applies to other letters. But if we take those letters which are the principles of a particular syllable, whether written or spoken, then they are limited in number.

And for the same reason, since there are many objects of mathematics which are numerically different in one species, the mathematical principles of mathematical science could not be limited in number, but only in species. We might say, for example, that the principles of triangles are three sides and three angles, but this limitation is according to species, for any of them can be multiplied to infinity.

Therefore, if there were nothing besides sensible things and the objects of mathematics, it would follow that the substance of a form would be numerically one, and that the principles of beings would not be limited in number, but only in species. Therefore, if it is necessary that they be limited in number (otherwise it would happen that the principles of things are infinite in number), it follows that there must be forms in addition to the objects of mathematics and sensible things.

517. This is what the Platonists wanted to say, because it necessarily follows from the things that they held that, in the case of the substance of sensible things, there is a single form to which nothing accidental belongs. For something accidental, such as whiteness or blackness, pertains to an individual man; but to this separate man, who is a form according to the Platonists, there pertains nothing accidental, but only what belongs to the definition of the species. And although they wanted to say this, they did not express themselves clearly; that is, they did not clearly distinguish things.

518. But if we hold that (1002b30). Then he counters with an argument for the other side of the question. He says that, if we hold that there are separate forms and that the principles of things are limited not only in species but also in number, certain impossible consequences will follow, which are touched on above in one of the questions [464]. But the Philosopher will deal with this problem in book 12 [2450] and book 14 of this work. And the truth of the matter is that, just as the objects of mathematics do not exist apart from sensible things, neither do forms exist apart from the objects of mathematics and from sensible substances. And while the efficient and moving principles of things are limited in number, the formal principles of things (of which there are many individuals in one species) are not limited in number, but only in species.

Do first principles exist actually or potentially, and are they universal or singular?

And connected with these problems there is the question of whether the elements of things exist potentially or in some other way.

If they exist in some other way, then there will be something else prior to first principles. For potency is prior to that cause, but the potential need not exist in that way.

But if the elements exist potentially, it is possible for nothing to exist, for even that which does not yet exist is capable of existing, because that which does not exist may come to be. But nothing that is incapable of existing may come to be. It is necessary, then, to investigate these problems.

And there is also the problem of whether principles are universals or singular things, as we maintain.

For if they are universals, they will not be substances, because a common term signifies not a particular thing, but what sort of thing, and a substance is a particular thing.

But if it is a particular thing, and is held to be the common whatness which is predicated of things, Socrates himself will be many animals: himself and man and animal. (That is, if each of these signifies a particular thing and a one.) If, then, the first principles of things are universals, these consequences will follow.

However, if they are not universals but have the nature of singular things, they will not be knowable, for all scientific knowledge is universal. Hence, if there is to be any scientific knowledge of first principles, there will have to be different principles which are predicated universally and are prior to first principles.

Are principles of substances actual or potential?

519. Having inquired what the principles are, the Philosopher now asks how they exist.

First, he asks whether they exist potentially or actually;