The matter and subject of physics

Since, indeed, to understand and to know happen in all sciences of which there are principles, causes, or elements, it is through acquaintance with these that knowledge is attained. For we do not think that we know a thing until we know its first causes and first principles and have carried our analysis as far as its elements. Plainly, therefore, in the science of nature, as in other branches of study, our first task will be to try to determine what relates to its principles.

The natural way of doing this is to start from the things that are more knowable and certain to us and proceed toward those that are clearer and more knowable by nature; for the same things are not “knowable relatively to us” and “knowable” without qualification.

So, in the present inquiry, we must follow this method and advance from what is more obscure by nature but clearer to us toward what is more clear and more knowable by nature.

Now, what is plain and obvious to us at first is confused masses, the elements and principles of which become known to us later by analysis. Thus we must advance from universals to singulars.

For it is a whole that is best known to sense perception, and a universal is a kind of whole, comprehending many things within it, like parts.

Much the same thing happens in the relation of the name to the formula. A name, such as “round,” means vaguely a sort of whole: its definition divides into particular elements.

Similarly, children begin by calling all men “father” and all women “mother,” but later on distinguish each of them.

1. Because this book upon which we intend to comment here, the Physics, is the first book of natural science, it is necessary in the beginning to decide what is the matter and the subject of natural science.

Since every science is in the intellect, it should be understood that something is rendered intelligible in act insofar as it is in some way abstracted from matter. And, inasmuch as things are differently related to matter, they pertain to different sciences.

Furthermore, since every science is established through demonstration, and since the definition is the middle term in a demonstration, it is necessary that sciences be distinguished according to the diverse modes of definition.

2. It must be understood, therefore, that there are some things whose existence depends upon matter and that cannot be defined without matter. Further, there are other things that, even though they cannot exist except in sensible matter, have no sensible matter in their definitions. And these differ from each other as the curved differs from the snub. For the snub exists in sensible matter and sensible matter must fall in its definition, for the snub is a curved nose. And the same is true of all natural things, such as man and stone. But sensible matter does not fall in the definition of the curved, even though the curved cannot exist except in sensible matter. And this is true of all the mathematical objects, such as numbers, magnitudes, and figures.

There are still other things that do not depend upon matter, either according to their existence or according to their definitions. And this is either because they never exist in matter, such as God and the other separated substances, or because they do not universally exist in matter, such as substance, potency and act, and being itself.

3. Now metaphysics deals with things of this latter sort, while mathematics deals with those things that depend upon sensible matter for their existence but not for their definition. And natural science, which is called “physics,” deals with those things that depend upon matter not only for their existence but also for their definition.

And because everything that has matter is mobile, it follows that mobile being is the subject of natural philosophy. For natural philosophy is about natural things, and natural things are those whose principle is nature. But nature is a principle of motion and rest in that in which it is. Therefore, natural science deals with those things that have in them a principle of motion.

4. Furthermore, those things that follow from something common must be treated first and by themselves. Otherwise, it becomes necessary to repeat such things many times while discussing each instance of that which is common.

Therefore, it was necessary that one book in natural science be set forth in which those things that are consequent upon mobile being in common are treated, just as first philosophy, in which those things that are common to being insofar as it is being are determined, is set forth for all the sciences.

This, then, is the book, the Physics, or On Physics or of the Natural to be Heard, because it was handed down to hearers by way of instruction. And its subject is mobile being simply.

I do not, however, say “mobile body,” because the fact that every mobile being is a body is proven in this book, and no science proves its own subject. Thus, in the very beginning of the De caelo, which follows this book, we begin with the notion of body.

Moreover, after the Physics, there are other books of natural science in which the species of motion are treated: in De caelo, we treat the mobile according to local motion, which is the first species of motion; in De generatione, we treat of motion’s relation to form and of the first mobile things, the elements, with respect to their changes in general; but we consider their particular changes in Meteororum, and in De mineralibus, we consider the mobile mixed bodies that are non-living. Living bodies are considered in De anima and the books that follow it.

5. To this book, then, the Philosopher writes a preface in which he shows the order in which natural science must proceed. In this preface, he does two things.

First, he shows that it is necessary to begin with a consideration of principles.

Second, at the natural way of doing this (184a16; [6]), he shows that, among principles, it is necessary to begin with the more universal principles.

Therefore, he first gives the following argument. In all sciences of which there are principles, causes, or elements (184a10), understanding and science proceed from a knowledge of the principles, causes, and elements. Now, the science that is about nature has principles, elements, and causes. Therefore, in that science it is necessary to begin with a determination of principles.

When he says, to understand, he refers to definitions, and when he says, to know, he refers to demonstrations. For as demonstrations are from causes, so also are definitions, since a complete definition is a demonstration differing only by position, as is said in Posterior Analytics 1.8.¹

When he speaks of principles or causes or elements, however, he does not intend to signify the same thing by each. For “cause” is wider in meaning than “element.” An element is a first component of a thing and is in the composed thing, as is said in Metaphysics 5.¹ Thus, letters are elements of speech, but syllables are not. But those things are called “causes” upon which things depend for their existence or their coming to be.

Thus, even that which is outside the thing or that which is in it—though the thing is not first composed of it—can be called a “cause,” though it cannot be called an “element.” But “principle” implies a certain order in any progression. Thus, something can be a principle that is not a cause, as that from which motion begins is a principle of motion but is not a cause, and a point is a principle of a line but not a cause.

Therefore, by principle he seems to mean moving causes and agents in which—more than in others—there is found an order of some progression. By causes he seems to mean formal and final causes upon which things most of all depend for their existence and their coming to be. By elements he means properly the first material causes.

Moreover, he uses these terms disjunctively and not conjunctively in order to point out that not every science demonstrates through all the causes. For mathematics demonstrates only through the formal cause. Metaphysics demonstrates principally through the formal and final causes, but also through the agent. Natural science, however, demonstrates through all the causes.

He then proves the first proposition of his argument from common opinion. This is also proven in Posterior Analytics 1.2.¹ For a man thinks that he knows something when he knows all its causes from the first to the last. The meanings here of causes, principles, and elements is exactly the same as we have explained above, even though the Commentator disagrees.

Furthermore, Aristotle says, as far as its elements, because matter is the last to be known. For matter is for the sake of form, and form is from the agent for the sake of the end, unless it itself is the end. For example, we say that a saw has teeth in order to cut, and these teeth ought to be made of iron so they will be apt for cutting.

6. Next, at the natural way of doing this (184a16), he shows that, among principles, it is necessary to treat the more universal ones first.

And first, he shows this by means of an argument;

second, by an example, at for it is a whole (184a23; [9]).

Therefore, he first gives the following argument. It is natural for us to proceed in knowing from those things that are better known to us to those that are better known by nature. But the things that are better known to us are confused, and such are the universals. Therefore, it is necessary for us to proceed from universals to singulars.

7. To clarify the first proposition, he makes the point that things that are better known to us and things that are better known according to nature are not the same. Rather, those things better known according to nature are less known to us. And, because the natural way or order of learning is that we should come to what is unknown to us from what is known to us, it is necessary for us to arrive at the better known by nature from the better known to us.

It must be noted, however, that “what is known by nature” and “what is known simply” are the same. Those things are better known simply that are in themselves better known. But those things are better known in themselves that have more being, because each thing is knowable insofar as it is a being. However, those beings are greater that are greater in act. Thus, these are the most knowable by nature.

For us, however, the converse is true, because we proceed in understanding from potency to act. Our knowledge begins from sensible things, which are material and intelligible in potency. Thus, these things are known by us before the separated substances, which are better known according to nature, as is clear in Metaphysics 2.¹

Therefore, he does not say knowable by nature as if nature knew these things, but because they are known better in themselves and according to their proper natures. And he says better known and more certain because, in the sciences, not just any kind of knowledge is sought, but certain knowledge.

Next, in order to understand the second proposition, it must be known that those things are here called confused that contain in themselves something potential and indistinct. And because knowing something indistinctly is a mean between pure potency and perfect act, therefore, while our intellect proceeds from potency to act, it knows the confused before it knows the distinct. But it has complete science in act when it arrives, through resolution, at a distinct knowledge of the principles and elements. And this is the reason why the confused is known by us before the distinct.

That universals are confused is clear. For universals contain in themselves their species in potency, and whoever knows something in the universal knows it indistinctly. The knowledge, however, becomes distinct when each of the things contained in potency in the universal is known in act. For he who knows “animal” does not know “rational” except in potency. But knowing something in potency is prior to knowing it in act. Therefore, according to this order of learning, in which we proceed from potency to act, we know “animal” before we know “man.”

8. It would seem, however, that this is contrary to what the Philosopher says in Posterior Analytics 1.2,¹ that singulars are better known to us, whereas universals are better known by nature or simply.

But it must be understood that, there, he takes as singulars the individual sensible things themselves, which are better known to us because the knowledge of sense, which is of singulars, does precede in us the knowledge of the intellect, which is of universals. But because intellectual knowledge is more perfect, and because universals are intelligible in act—whereas singulars are not (since they are material)—universals are better known simply and according to nature.

Here, however, by singulars, he means not the individuals themselves, but the species. And these are better known by nature, existing more perfectly, as it were, and being known with a distinct knowledge. But the genera are known by us first, being known, as it were, confusedly and in potency.

It should be known, however, that the Commentator explains this passage in another way. At the natural way of doing this (184a16), he says that the Philosopher wishes to explain the method of demonstration of this science:

this science demonstrates through the effect and what is posterior according to nature. Hence, what is said here is to be understood of the progression in demonstration, and not of the progression in determination.

Then, at now, what is plain and obvious (184a21), according to the Commentator, Aristotle intends to make clear what things are better known to us and what is better known by nature, namely, what is composed of simple things—understanding confused to mean composed.

Finally, then, he concludes, as if to a corollary, that we must proceed from the more universal to the less universal.

It is clear that the Commentator’s explanation is not suitable, because he does not join the whole passage to one intention. Moreover, the Philosopher does not intend to set forth the mode of demonstration of this science here, because he will do this in book 2, according to his order of treatment. Furthermore, the “confused” should not be taken to mean “composed,” but rather to mean “indistinct.” For nothing could be concluded from such universals, because genera are not composed of species.

9. Next, at for it is a whole (184a23), he clarifies his position with three examples.

The first of these is taken from the integral sensible whole. He says that, since the sensible whole is better known to the sense, the intelligible whole is also better known to the intellect. But the universal is a sort of intelligible whole, because it comprehends many as parts—namely, its inferiors. Therefore, the universal is known better to us intellectually.

But it would seem that this proof is not effective, because he uses whole, part, and comprehension equivocally.

However, it must be said that the integral whole and the universal agree in that each is confused and indistinct. For just as he who apprehends a genus does not apprehend the species distinctly, but in potency only, so also he who apprehends a house does not yet distinguish its parts. Hence it is that a whole is first known to us as confused. This applies to both of these wholes. However, to be composed is not common to each whole. Thus, it is clear that Aristotle significantly said confused above, and not composed.

10. Next, at much the same thing (184a26), he gives another example taken from the integral intelligible whole. For that which is defined is related to the things defining it as a kind of integral whole, insofar as the things defining it are in act in that which is defined.

But he who apprehends a name—for example, man or circle—does not at once distinguish the defining principles. Thus it is that the name is, as it were, a sort of whole and is indistinct, while the definition divides into particular elements, that is, distinctly sets forth the principles of that which is defined.

This, however, seems to be contrary to what he said above. For the things that define would seem to be more universal, and these, he said, were first known by us. Furthermore, if that which is defined were better known to us than the things that define, we would not grasp that which is defined through the definition, for we grasp nothing except through that which is better known to us.

But it must be said that the things that define are in themselves known to us before that which is defined, but we know the thing that is defined before we know that these are the things that define it. Thus we know animal and rational before we know man. But man is known confusedly before we know that animal and rational are the things that define man.

11. Next, at similarly, a child (184b12), he gives the third example taken from the more universal sensible. For as the more universal intelligible is first known to us intellectually—for example, animal is known before man—so the more common sensible is first known to us according to sense—for example, we know this is an animal before we know this is a man.

And I say “first according to sense” both with reference to place and with reference to time. This is true according to place, for when someone is seen at a distance, we perceive him to be a body before we perceive that he is an animal, and an animal before we perceive him to be a man, and finally we perceive that he is Socrates. And in the same way, with reference to time, a boy apprehends this individual as some man before he apprehends this man, Plato, who is his father. And this is what he says, children begin by calling all men “father” and all women “mother,” but later on distinguish; that is, they know each determinately.

From this, it is clearly shown that we know a thing confusedly before we know it distinctly.

The ancient philosophers’ opinions about the principles of nature and of beings

The principles in question must be either one or more than one. If there is one, it must be either motionless, as Parmenides and Melissus assert, or in motion, as the physicists hold—some declaring air to be the first principle, others water. If there are more than one, then either a finite or an infinite plurality. If they are finite (but more than one), then either two or three or four or some other number. If they are infinite, then either (as Democritus) believed one in kind but differing in shape or form, or different in kind and even contrary.

A similar inquiry is made by those who inquire into the number of existents. For they inquire whether the ultimate constituents of existing things are one or many, and if many, whether a finite or an infinite plurality. So they, too, are inquiring whether the principle or element is one or many.

Now, to investigate whether being is one and motionless does not belong to natural science. For just as the geometer has nothing more to say to one who denies the principles of his science—this being a question for a different science or common to all—so a man investigating principles cannot argue with one who denies their existence.

For if being is just one, and one in the way mentioned, there is no longer a principle, since a principle must be the principle of some thing or things.

To inquire, therefore, whether being is one in this sense would be like arguing against any other position maintained for the sake of argument, such as the Heraclitean thesis or such a thesis as that being is one man—

or like refuting a merely contentious argument. This applies to the arguments both of Melissus and of Parmenides: they have accepted what is false and they are not syllogizing. Or rather, the argument of Melissus is much worse and offers no difficulty at all: accept one ridiculous proposition, and the rest follow—a simple enough proceeding.

We physicists, on the other hand, must take for granted that the things that exist by nature are—either all or some of them—in motion. This is indeed made plain by induction.

Moreover, no one is bound to solve every kind of difficulty that may be raised, but only as many as are drawn falsely from the principles of the science. It is not our business to refute those that do not arise in this way; just as it is the duty of the geometer to refute the squaring of the circle by means of segments, but it is not his duty to refute Antiphon’s proof.

At the same time, the holders of the theory of which we are speaking do incidentally raise physical questions, though nature is not their subject, so it will perhaps be as well to spend a few words on them, especially as the inquiry is not without philosophical interest.

12. Having completed the preface, in which it was shown that natural science ought to begin with the more universal principles, he here begins, according to the order already stated, to pursue those matters that pertain to natural science.

This discussion is divided into two parts.

In the first part, he treats the universal principles of natural science.

In the second part, he treats mobile being in common, which is what he intends to treat in the Physics. This is taken up in book 3, at nature has been defined (200b12; [275]).

The first part is divided into two parts.

First, he treats the principles of the subject of this science, that is, the principles of mobile being as such;

second, he treats the principles of the doctrine. This he does in book 2, at of things that exist (192b8; [141]).

The first part is divided into two parts.

First, he considers the opinions others have had concerning the common principles of mobile being.

Second, he seeks the truth concerning them, at all thinkers, then, agree (188a19; [75]).

Concerning the first part, he makes three points.

First, he sets forth the different opinions of the ancient philosophers concerning the common principles of nature.

Second, at now, to investigate (184b25; [15]), he shows that it does not pertain to natural science to pursue some of these opinions.

Third, at the most pertinent question (185a20; [21]), he considers these opinions, showing their falsity.

Concerning the first part, he makes two points.

First, he sets forth the different opinions of the philosophers concerning the principles of nature.

Second, at a similar inquiry is made (184b21; [14]), he shows that this same diversity exists with reference to the opinions of the philosophers concerning beings.

13. He says, therefore, first of all (184b15), that it is necessary that there be either one principle of nature or many. And each position has claimed the opinions of the philosophers.

Some of them, indeed, held that there is one principle; others held that there are many. And, of those who held that there is one principle, some held that it was immobile, as did Parmenides and Melissus, whose opinions he will examine below. Some, however, held that it was mobile, as did the natural philosophers.

Of these, some held that air was the principle of all natural things, as did Diogenes, but others held that it was water, such as Thales, others that it was fire, such as Heraclitus, and still others some mean between air and water, such as vapor.

But none of those who held that there was only one principle said that it was earth, because of its density. For they held that principles of this sort were mobile, because they said that other things come to be through the rarefication and condensation of certain of these principles.

Of those who held the principles to be many, some held them to be finite, while others held them to be infinite.

Of those who held that they were finite (although more than one), some held that there were two—fire and earth—as he will say of Parmenides below.¹ Others held that there were three: fire, air, and water (for they thought earth to be composed in some way, because of its density). Others, however, held that there were four, as Empedocles did, or even some other number (for even Empedocles himself posited two other principles, friendship and strife, along with the four elements).

Those who held that there was an infinite plurality of principles had a diversity of opinions. Democritus held that indivisible bodies called “atoms” are the principles of all things, and he held that bodies of this sort were all of one genus according to nature, but that they differed according to figure and form, and that they not only differed but even had contrariety among themselves. For he held three contrarieties:

one according to figure, which is between the curved and the straight;

another according to order, which is the prior and the posterior;

and another according to position, namely, before and behind, above and below, or to the right and to the left.

And so he held that, from these bodies existing of one nature, different things come to be according to the diversity of the figure, position, and order of the atoms.

In this opinion, then, he gives us some basis for understanding the opposing opinion, that of Anaxagoras, who held that the principles were infinite but not of one genus according to nature. For he held that the principles of nature were the infinite, smallest parts of flesh, bone, and other such things, as will be made clear below.¹

It must be noted, however, that he did not divide these many principles into mobile and immobile. For none of those who held that the first principles were many held that they were immobile. For since all place contrariety in the principles, and since it is natural for contraries to change, immobility could not stand with a plurality of principles.

14. Second, at a similar inquiry is made (184b21), he shows that there is the same diversity of opinions concerning beings. He says that, in like manner, the physicists, when inquiring about those things that are—that is, about beings—wondered how many there are, namely, whether there is one or many, and if many, whether finite or infinite.

And the reason for this is that the ancient physicists did not know any cause but the material cause (although they touched lightly upon the other causes). Rather, they held that the natural forms were accidents, as the forms of artificial things are. Since, therefore, the whole substance of artificial things is their matter, so it followed, according to them, that the whole substance of natural things would be their matter.

Hence, those who held one principle only—for example, air—thought that other beings were air according to their substance. And the same is true of the other opinions. Hence Aristotle says that the physicists seek the ultimate constituents of existing things; that is, in inquiring about principles, they sought the material causes from which beings are said to be. Thus it is clear that, when they inquire whether beings are one or many, their inquiry concerns the material principles that are called elements.

15. Next, at now, to investigate (184b25), he shows that it does not pertain to natural science to disprove some of these opinions.

And concerning this, he makes two points.

First, he shows that it does not pertain to natural science to disprove the opinion of Parmenides and Melissus;

second, at at the same time, the holders of the theory (185a17; [19]), he gives a reason why it is useful to the present work to disprove this opinion.

Concerning the first part, he makes two points.

First, he shows that it does not pertain to natural science to disprove the opinion already given.

Second, at or like refuting (185a7; [17]), he shows that it does not pertain to natural science to resolve the arguments that are brought forth to prove this opinion.

He establishes his first point with two arguments, the second of which begins at to inquire, therefore (185a5; [16]).

He says, therefore, that it does not pertain to natural science to undertake a thorough consideration of the opinion whether being is one and immobile. For it has already been shown that, according to the intention of the ancient philosophers, there is no difference whether we hold one immobile principle or one immobile being. And that it should not pertain to natural science to disprove this opinion he shows as follows. It does not pertain to geometry to bring forth reasons against an argument that destroys its principles. Rather, either this pertains to some other particular science (if, indeed, geometry is inferior to some particular science as music is inferior to arithmetic, to which it pertains to dispute against any position denying the principles of music) or it pertains to a common science, such as logic or metaphysics.

But the position just given destroys the principles of nature. For if there is only one being, and one in the way mentioned, namely, immobile, such that others cannot come to be from it, then the very definition of a principle is taken away. For every principle is a principle either of some thing or of some things.

Therefore, if we posit a principle, multiplicity follows, because one is the principle and the other is that of which it is the principle. Therefore, whoever denies multiplicity also removes principles. Therefore, natural science ought not to argue against this position.

16. Next, at to inquire, therefore (185a5), he shows the same point with another argument. It is not required of any science that it bring forth arguments against manifestly false and untenable opinions. For it is stupid to worry about one who offers positions contrary to the opinions of the wise, as is said in Topics 1.11.¹

He says, therefore, that to undertake a thorough consideration of the question whether being is one (and hence immobile) is like arguing against any other untenable position. For example, it is like arguing against the position of Heraclitus, who said that all things are always moved and that nothing is true, or against the position of one who would say that the whole of being is one man—which position, indeed, would be altogether untenable. And indeed, whoever holds being to be only one immobile thing is forced to hold that the whole of being is some one thing. It is clear, therefore, that it does not belong to natural science to argue against this position.

17. Next, at or like refuting (185a7), he shows that it does not belong to natural science even to resolve the arguments of the previously mentioned philosophers.

And this is for two reasons, the second of which begins at we physicists (185a12; [18]).

First, he proves his position by pointing out that it is not incumbent upon any science to resolve sophistic arguments that have an obvious defect of form or matter. He says that to deal with untenable arguments is like refuting a merely contentious, that is, sophistic, argument. But each argument of both Melissus and Parmenides is sophistic, for they err in matter. Thus he says that they have accepted what is false; that is, they assume false propositions. They also err in form; thus he says that they are not syllogizing. But the position of Melissus is much worse, that is, more vain and foolish, and offers no difficulty, that is, does not give rise to any doubt. This will be shown below.¹ Moreover, it is not inconsistent that, given one inconsistency, another should follow. Therefore, it can be concluded that it is not required of the philosopher of nature that he resolve the arguments of this man.

18. He sets forth the second argument for this at we physicists (185a12). The argument is as follows. In natural science, it is supposed that natural things are moved, either all or some of them. He says this because there is doubt whether some things are moved and how they are moved—for example, about the soul and the center of the earth, and the pole of heaven, and about natural forms and other such things.

But the fact that natural things are moved can be made clear from induction, for it is apparent to the sense that natural things are moved. It is as necessary that motion be supposed in natural science as it is necessary that nature be supposed. For motion is placed in the definition of nature, since nature is a principle of motion, as will be said below.¹

Having established this point—that motion is supposed in natural science—he proceeds further to prove his position as follows. Not all arguments must be resolved in any science, but only those that conclude something false from the principles of that science. Any arguments that do not reach their conclusions from the principles of the science, but from the contraries of these principles, are not resolved in that science.

He proves this by an example taken from geometry, saying that it pertains to geometry to resolve the problem of squaring (that is, the squaring of a circle) by means of segments of the circumference, because this method supposes nothing contrary to the principles of the science of geometry. For a certain man wished to find a square equal to a circle by dividing the circumference of the circle into many parts and placing straight lines in each part. And so, by finding some rectilinear figure equal to some of the figures that were contained by the dissections of the circumference and either many or all of the chords, he thought he had found a rectilinear figure equal to the whole circle, to which it was easy to find an equal square through the principles of geometry. And thus he thought that he was able to find a square equal to a circle.

But he did not argue well enough, for although these dissections used up the whole circumference of the circle, the figures contained by the dissections of the circumference and the straight lines did not encompass the whole circular surface.

But to resolve the square of Antiphon does not pertain to geometry, because he used principles contrary to those of geometry. For he described in a circle a certain rectilinear figure, such as a square, and divided in half the arcs by which the sides of the square were subtended. From the points of dissection, he led straight lines to all the angles of the square. Then there resulted in the circle a figure of eight angles that more closely approached equality with the circle than the square. Then he again divided in half the arcs by which the sides of the octagon were subtended, and thus, by leading straight lines from the points of dissection to the angles of this figure, there resulted a figure of sixteen angles that still further approached equality with the circle. Therefore, by always dividing the arcs and leading straight lines to the angles of the figure already existing, there will arise a figure very near to equality with the circle. He said, then, that it was impossible to proceed to infinity in the dissection of arcs. Therefore, it was necessary to arrive at some rectilinear figure equal to the circle to which some square could be equal. But, because he supposed that an arc is not always divisible in half, which is contrary to the principles of geometry, it does not pertain to geometry to resolve an argument of this sort.

Therefore, because the arguments of Parmenides and Melissus suppose being to be immobile, as will be shown below,¹ and since this is contrary to the principles supposed in natural science, it follows that it does not pertain to the natural philosopher to resolve arguments of this sort.

19. Next, at at the same time (185a17), he states why he will argue against the aforementioned position. He says that, because the philosophers mentioned above did speak of natural things, even though they did not create questions (that is, in the sphere of natural science), it is useful for his present purpose to argue against opinions of this sort. For even though it does not pertain to natural science to argue against such positions, it does pertain to first philosophy.

Refutation of Parmenides and Melissus

The most pertinent question with which to begin will be this: in what sense is it asserted that all things are one? For that which “is” is used in many senses. Do they mean that all things “are” substance or quantities or qualities? And, further, are all things one substance (one man, one horse, or one soul) or one particular quality (white or hot or some other such thing)?

These are all very different doctrines and all impossible to maintain. For if both substance and quantity and quality are, then being will be many whether these exist independently of each other or not. If, on the other hand, it is asserted that all things are quality or quantity, then, whether substance exists or not, an absurdity results—if the impossible can properly be called absurd. For none of these except substance can exist independently, for everything is predicated of substance as subject.

Now, Melissus says that being is infinite. It is, then, a quantity, since the infinite is in the category of quantity, whereas substance or quality or passion cannot be infinite except accidentally—that is, if at the same time they are also quantities. For to define the infinite, you must use quantity in your formula, but not substance or quality. If, then, being is both substance and quantity, it is two, not one; but if only substance, it is not infinite and has no magnitude, for to have that, it will have to be a quantity.

Again, “one” itself, no less than “being,” is used in many senses, so we must consider in what sense the word is used when it is said that the all is one. Now, we say either that the continuous is one or that the indivisible is one, or that things are said to be one when their essence is one and the same, as “vintage” and “wine.” If they are one in the sense of continuous, then it is many, for the continuous is infinitely divisible.

There is, indeed, a difficulty about part and whole, perhaps not relevant to the present argument, yet deserving consideration on its own account,

namely, whether the part and the whole are one or more than one, and how they can be one or many, and if they are more than one, in what sense they are more than one.

(It is similar with the parts of wholes that are not continuous.)

Further, if each of the two parts is indivisibly one with the whole, the difficulty arises that they will be indivisibly one with each other also.

But to proceed: if their one is one as indivisible, nothing will have quantity or quality, and so the one will not be infinite, as Melissus says—nor, indeed, limited, as Parmenides says, for though the limit is indivisible, the limited is not.

But, if all things are one in the sense of having the same definition, like “raiment” and “dress,” then it turns out that they are maintaining the Heraclitean doctrine, for it will be the same thing “to be good” and “to be bad,” and “to be good” and “to be not good,” and so the same thing will be “good” and “not good,” and “man” and “horse.”

In fact, their view will be not that all things are one, but that they are nothing, and that “to be of such-and-such a quality” is the same as “to be of such-and-such a size.”

20. After he has set forth the opinions of the philosophers concerning principles, here Aristotle argues against them.

First, he argues against those who spoke unnaturally about nature.

Second, at the physicists, on the other hand (187a12; [53]), he argues against those who spoke of nature in a natural way.

Concerning the first part, he makes two points.

First, he argues against the position of Melissus and Parmenides;

second, against their arguments, at further, the arguments they use (186a5; [29]).

Concerning the first part, he makes two points.

First, he argues against the position that “being is one” by using an argument dealing with the “being” that is the subject in this proposition.

Second, at again, “one” itself (185b5; [22]), he uses an argument dealing with the “one” that is the predicate.

21. He says first (185a20) that that which should be taken primarily as a principle in arguing against the position just given is the fact that that which “is”—namely, being—is said in many ways. For we must ask of those who say that being is one how they are using “being”: whether they take it for substance, or for quality, or for one of the other genera. And because substance is divided into the universal and the particular—that is, into first and second substance—and further into many species, we must ask the following questions. Do they say that being is one as one man, or as one horse, or as one soul, or as one quality, such as white or hot or some other such thing? For it makes a great difference which of these is said.

Hence, if being is one, either it must be substance and accident together or it must be accident alone or substance alone.

If, however, it is substance and accident together, then being will not be one only, but two. Nor does it differ with reference to this whether substance and accident are together in one thing as one or as different. For even though they are together in one thing, they are not one simply, but one in subject. And so, by positing substance with accident, it follows that they are not one simply, but many.

If, however, it is said that being is accident only and not substance, this is altogether impossible, since accident can in no way be without substance. For every accident is said of substance as of its subject, and the very definition of accident involves this.

If, however, it is said that being is substance only, without accident, then it follows that it would not be a quantity, for quantity is an accident. And this is contrary to the position of Melissus, who held that being was infinite, from which it follows that it is quantity, because the infinite, properly speaking, does not exist except in quantity. And substance and quality and the like are not said to be infinite except accidentally, insofar as they are, for instance, together with quantity. Since, then, Melissus held being to be infinite, he cannot hold that it is substance without quantity.

If, therefore, being is substance and quantity together, it follows that being is not one only, but two. If, however, it is substance alone, it is not infinite, because it will not have magnitude or quantity. Hence what Melissus says—namely, that being is one—can in no way be true.

22. Then, at again, “one” itself (185b5), he sets forth his second argument that deals with the one.

Concerning this, he makes two points.

First, he gives the argument.

Second, at even the more recent (185b25; [25]), he shows how some have erred in the solution of this question.

He says first that, just as “being” is said in many ways, so also is “one.” And so, we must consider in what way they say that all things are one. For “one” is used in three ways: as the continuous is one, such as a line or a body; as the indivisible is one, such as a point; or as those things are said to be one whose account or definition is one, as “vintage” and “wine” are said to be one.

First, therefore, he shows that we cannot say that all are one by continuity, because a continuum is in a certain respect many. For every continuum is divisible to infinity, and so contains many in itself as parts. Hence, whoever holds that being is a continuum must hold that it is in a certain respect many.

And this is true not only because of the number of the parts but also because of the difference that seems to exist between the whole and the parts. For there is a question whether the whole and the parts are one or many. And, although perhaps this question does not pertain to the matter at hand, it is nevertheless worthy of consideration for its own sake.

And here we consider not only the continuous whole but also the contiguous whole whose parts are not continuous, such as the parts of a house, which are one by contact and composition. It is clear that that which is a whole accidentally is the same as its parts. But this is not true of that which is a whole simply.

For if that which is a whole simply is the same as one of the parts, then it would for the same reason be the same as another of the parts. But things that are identical with the same thing are identical with each other. And thus it would follow that both parts, if they are held simply to be the same as the whole, would be identical with each other. Hence it would follow that the whole would be indivisible, with no diversity of parts.

23. Next, at but to proceed (185b16), he shows that it is impossible for all to be one as the indivisible is one. For that which is indivisible cannot be a quantity, since every quantity is divisible. As a result of this, it cannot be a quality, if it is understood that we are speaking of a quality that is founded upon quantity. And, if it is not a quantity, it cannot be finite (as Parmenides has said), nor can it be infinite (as Melissus has said). For an indivisible terminus, such as a point, is an end and not ended, for the finite and the infinite are found in quantity.

24. Next, at but if all things (185b19), he shows how it cannot be said that all things are one in definition. For if this were true, three absurdities would follow.

The first is that contraries would be one according to definition, such that the definitions of good and evil would be the same, just as Heraclitus held the definitions of contraries to be the same (as is made clear in Metaphysics 4¹).

The second absurdity is that the definitions of the good and the non-good would be the same, because non-good follows upon evil. And thus it would follow that the definitions of being and non-being would be the same. And it would also follow not only that all beings would be one being, as they hold, but also that they would be non-being or nothing. For things that are one in definition are so related that they may be used interchangeably as predicates. Thus, if being and nothing are one according to definition, then it follows that, if all are one being, all are nothing.

The third absurdity is that the different genera, such as quantity and quality, would be the same according to definition. He sets forth this absurdity where he says, “to be of such-and-such a quality” is the same as “to be of such-and-such a size.”

However, we must note that, as the Philosopher says in Metaphysics 4,¹ against those who deny principles there can be no unqualified demonstration that proceeds from what is more known simply. But we may use a “demonstration to contradiction,” which proceeds from those things that are supposed by our adversary—which things are, for the time being, simply less known. And so, in this argument, the Philosopher uses many things that are less known than the fact that beings are many and not only one—the point about which he argues.

Error of more recent philosophers about the one and the many

Even the more recent of the ancient thinkers were alarmed lest the same thing should turn out to be both one and many. So some, like Lycophron, were led to omit “is,” and others to change the mode of expression and say “man whitened” instead of “is white” and “walks” instead of “is walking,” for fear that, if they added the word “is,” they should be making the one to be many—as if “one” and “being” were always used in one way.

What “is” may be many either in definition (for example “to be white” is one thing and “to be musical” another, yet the same thing may be both, so the one is many) or by division, as the whole and its parts.

On this point, indeed, they were already getting into difficulties and admitted that the one was many—as if there was any difficulty about the same thing being both one and many.

For these are not opposites, since “one” may mean either “one in potency” or “one in act.” If, then, we approach the thesis in this way, it seems impossible for all things to be one.

25. Having disproven the opinion of Parmenides and Melissus that being is one, the Philosopher here shows that certain later philosophers fell into the difficulty on the same basis.

Parmenides and Melissus erred because they did not know how to distinguish the uses of the term “one.” Thus, they said that what is one in a certain respect is one simply. But the later philosophers, also not knowing how to distinguish the uses of the term “one,” thought it absurd that the same thing should be in some way one and many. Yet, being convinced by the arguments, they were forced to believe it. And so Aristotle says that the later philosophers were alarmed (that is, fell into a difficulty similar to that of the ancients, Parmenides and Melissus) lest they be forced to say that one and the same thing is one and many. Now, this seemed absurd to both groups of philosophers. So, the earlier philosophers, holding that all is one, rejected all multiplicity. The later philosophers, on the other hand, tried to remove multiplicity from anything they held to be one.

26. Thus some, such as Lycophron, removed the verb is from propositions. They said that we must not say man is white, but rather white man. For they thought that man and white were in some way one; otherwise, white would not be predicated of man. And it seemed to them that the word is, since it is a verbal copula, must serve as a copula between two. And so, wishing to remove all multiplicity from that which is one, they said the verb is must not be used.

But because such speech seemed to be imperfect, and because an imperfect understanding was produced in the soul of the listener if names were spoken without the addition of any verb, some changed the mode of speech, wishing to correct this. They did not say white man, because of the imperfection of this mode of speech. Nor did they say man is white, lest they give the impression that there is multiplicity.

Rather, they said man whitened, because, by this expression whitened, a thing is not understood (as it seemed to them), but rather a certain change in the subject. And in like manner, they said that we must not say, man is walking, but man walks, lest by the addition of the verbal copula is, they make that which they thought to be one (namely, white man) to be many, as if one and being were used singularly, that is, in only one way and not in many.

27. But this is false, for that which is one in one respect can be many in some other respect, as what is one in subject can be many in concept. Thus, the white thing and the musical thing are the same in subject but many in concept; for the concept of music is one thing, and the concept of white is another. Hence it can be concluded that the one may be many.

This may happen also in another way. That which is actually one as a whole may be many according to a division of parts. Thus, the whole is one in its totality but it has multiplicity of parts. And, although those who wished to remove the verb is or alter it, as was said above, found some solution to the objection that things could be one in subject and many in definition, nevertheless on this point, namely, on the whole and parts, they, in their ignorance, failed to respond to the objection altogether, believing that it was something of a problem that the one should be many.

But it is not problematic if the one and the many are not taken as opposites. For the one in act and the many in act are opposed, but the one in act and the many in potency are not opposed. And, because of this, he adds that “one” is said in many ways—namely, one in potency and one in act. And so, nothing prohibits the same thing from being one in act and many in potency, as is clear with regard to the whole and the parts.

28. Finally, he draws the conclusion that he primarily intended, namely, that it is clear from the foregoing arguments that it is impossible for all beings to be one.

The argument of Melissus is answered

Further, the arguments they use to prove their position are not difficult to expose. For both Melissus and Parmenides syllogized sophistically. Their premises are false, and their conclusions do not follow.

Or rather, the argument of Melissus is more gross and offers no difficulty at all. If you admit one ridiculous proposition, the rest follows—a simple enough proceeding.

The fallacy of Melissus is obvious. He supposes that if what is made always has a beginning, then what is not made has no beginning.

Then this also is absurd, that in every case there should be a beginning of a thing—not of the time and not only in the case of generation in the full sense but also in the case of coming to have a quality—as if change never took place suddenly.

Again, does it follow that being, if one, is motionless?

Why should not the whole of it move within itself, as parts of it do that are unities, such as this water? Again, why is qualitative change impossible?

Further, being cannot be one in form, though it may be in what it is made of. (Even some of the physicists hold it to be one in the latter way, though not in the former.) Man obviously differs from horse in form, and contraries from each other.

29. Having disproved the position of Parmenides and Melissus, here the Philosopher begins to answer their arguments.

Concerning this, he makes three points.

First, he shows how their arguments are to be answered;

second, at the fallacy of Melissus (186a10; [31]), he answers the argument of Melissus;

third, at the same kind of argument (186a22; [36]), he answers the argument of Parmenides.

30. He says that it is not difficult to answer the arguments with which Parmenides and Melissus reasoned. For each syllogized sophistically both in that they assumed false propositions and in that they did not observe the proper form of the syllogism. But the argument of Melissus is the more gross—that is, more vain and foolish—and offers no difficulty at all, that is, does not give rise to any doubt. For he assumed what is contrary to natural principles and what is manifestly false, namely, that being is not generated. And it is not a serious matter, granting one absurdity, if another should follow.

31. Next, at the fallacy of Melissus (186a10), he answers the argument of Melissus. The argument is as follows. What is made has a beginning. Therefore, what is not made has no beginning. But being is not made. Therefore, it has no beginning, and consequently has no end. But what has neither beginning nor end is infinite. Therefore, being is infinite. But what is infinite is immobile, for it would not have outside itself that by which it would be moved.

Furthermore, what is infinite is one, for if there were many, there must necessarily be something outside the infinite. Therefore, being is one and infinite and immobile.

Furthermore, in order to show that being is not generated, Melissus used a certain argument that some natural philosophers also used. Aristotle gives this argument below, near the end of book 1.¹

32. Aristotle disproves this argument of Melissus on four counts. He first argues against the statement of Melissus that if what is made always has a beginning, then what is not made has no beginning. This does not follow. Rather, it is a fallacy of the consequent.

For he argues from the denial of the antecedent to the denial of the consequent, when the correct form of argumentation would be the converse.

Hence, it does not follow that, if a thing that is made has a beginning, then that which is not made does not have a beginning. The correct conclusion would be that, if a thing does not have a beginning, then it is not made.

33. Second, at then this also is absurd (186a13), he disproves the argument under discussion with reference to the inference that, if something has no beginning, then it is infinite. For “beginning” may be taken in two ways.

In one way, we speak of a beginning of time and of generation. And this meaning of “beginning” is taken when it is said that what is made has a beginning or what is not made has no beginning.

In another sense, “beginning” is the beginning of a thing or a magnitude. And, in this sense, it would follow that, if a thing has no beginning, then it is infinite.

From this, it is clear that Melissus uses the term “beginning” as if it had one meaning only. Hence, Aristotle says that it is absurd to say that every case of beginning is the beginning of a thing, that is, of a magnitude, such that the beginning of time and of generation is not another meaning of the term. Nevertheless, a simple and instantaneous generation (which is the induction of a form in matter) does not have a beginning, for simple generation does not admit of a beginning. But there is a beginning for a whole alteration whose terminus is a generation, since this would not be an instantaneous change. And because of this terminus, this is sometimes called a “generation.”

34. Third, at again, does it follow (186a15), he disproves the above position with reference to its third inference: because being is infinite, it is immobile. He shows in two ways that this does not follow.

First, it does not follow in regard to local motion. For a part of water could be moved in water such that it is not moved to any extrinsic place. In this case, it would be moved by a joining and separation of the parts. And likewise, if the whole infinite body were water, it would be possible for the parts of it to be moved within the whole and not proceed outside the place of the whole.

Again, he disproves this with reference to the motion of alteration. For nothing prevents the infinite from being altered either as a whole or in its parts, for it would not be necessary to posit something outside the infinite to account for this.

35. Fourth, at further, being cannot (186a19), he disproves the given argument with reference to its fourth inference, by which it is concluded that, if being is infinite, it is one. For it does not follow that it is one according to species, but rather that it is one according to matter, just as some of the philosophers of nature have held that all things are one according to matter but not according to species. For it is obvious that man and horse differ in species, and in like manner, contraries differ from each other in species.

The argument of Parmenides is answered

The same kind of argument holds good against Parmenides also, besides any that may apply specially to his view. The answer to him is that “this is false” and “that does not follow.”

His assumption that “what is” is used only simply is false, because it is used in several ways.

His conclusion does not follow because, if we take only white things, and if “white” has a single meaning, nevertheless what is white will be many and not one. For white will not necessarily be one by continuity nor in definition. “Whiteness” will be different from “what has whiteness.”

Nor does this mean that there is anything that can exist separately.

For “whiteness” and “that which is white” differ in definition, but not in the sense that they are things that can exist apart from each other.

But Parmenides did not see this distinction.

It is necessary for him, then, to assume not only that “being” has the same meaning whenever it is predicated, but further that it means what truly is and what is truly one. It must be so, for an accident is predicated of some subject, such that the subject to which “being” is attributed will not be, as it is something different from “being.” Something which is not will therefore be.

Hence “substance” will not be a predicate of anything else. For the subject cannot be a being, unless “being” means several things, in such a way that each is something. But it was supposed that “being” means only one thing.

If, then, “substance” is not attributed to anything, but other things are attributed to it, how does “substance” mean what truly is rather than what is not? Suppose that “substance” is also “white.” Since the definition of the latter is different (for being cannot even be attributed to white, as nothing is that is not “substance”), it follows that “white” is non-being—and that not in the sense of a particular non-being, but in the sense that it is not at all.

Hence, “substance” is not, for it is true to say that it is white, which we found to mean non-being. If, to avoid this, we say that even “white” means substance, it follows that “being” has more than one meaning.

In particular, then, being will not have magnitude, if it is substance. For each of the two parts must be in a different sense.

Substance is plainly divisible into other substances if we consider the mere nature of a definition. For instance, if “man” is what truly is, “animal” and “biped” must also be what truly is. For if not substances, they must be accidents—and if accidents, accidents either of man or of some other subject. But neither is possible.

An accident is either that which may or may not belong to the subject or that in whose definition the subject of which it is an accident is involved. Thus, “sitting” is an example of a separable accident, while “snubness” contains the definition of “nose,” to which we attribute snubness.

Further, the definition of the whole is not contained in the definitions of the contents or elements of the definitory formula—for instance, that of “man” in “two-footed” or that of “white man” in “white.”

If, then, this is so, and if “two-footed” is supposed to be an accident of man, either it must be separable, such that man might possibly not be “two-footed,” or the definition of “man” must come into the definition of “two-footed”—which is impossible, since the converse is the case.

If, on the other hand, we suppose that “two-footed” and “animal” are accidents not of man but of something else, and are not each of them a substance, then “man” will also be an accident of something else.

But what truly is, is not the accident of anything, and that of which both “two-footed” and “animal” are separately predicated is also the subject of “two-footed animal.” Are we then to say that the whole is composed of indivisibles?

36. Having disproved the argument of Melissus, here the Philosopher disproves the argument of Parmenides.

First, he disproves the argument.

Second, at some thinkers did (187a1; [47]), he rejects what has been said by some who have argued badly against Parmenides.

Concerning the first part, he makes two points.

First, he sets forth the ways in which the argument of Parmenides is to be refuted.

Second, at his assumption (186a24; [39]), he resolves the argument in these ways.

37. Concerning the first part, it must be known that, as is clear from Metaphysics 1,¹ the argument of Parmenides was as follows: whatever is other than being is non-being; but what is non-being is nothing; therefore, whatever is other than being is nothing. But being is one; therefore, whatever is other than one is nothing; therefore, there is only one being.

And he concluded from this that it would be immobile, because it would not have anything by which it would be moved, nor would there be anything outside of it by which it would be moved.

Moreover, it is clear from their very arguments that, while Parmenides considered being under the account of being, and so held it to be one and finite, Melissus considered being from the point of view of matter. For Melissus considered being insofar as it is made or not made. And so he held being to be one and infinite.

38. Aristotle says, therefore (186a22), that the same approach must be used against the argument of Parmenides that was used against the argument of Melissus.

For as the argument of Melissus was answered on the basis that he assumed false propositions and did not draw his conclusions according to the correct form of the syllogism, so also the argument of Parmenides is answered partly because he assumed false propositions and partly because he did not draw his conclusions correctly.

He says, however, that there are also other appropriate ways of arguing against Parmenides. For it is possible to argue against Parmenides from the propositions that he assumed and that are in a certain respect true and probable.

But Melissus proceeded from what was false and improbable—for example, that being is not generated. Because of this, Aristotle did not argue against Melissus from the propositions that he assumed.

39. Next, at his assumption (186a24), he follows the procedures just mentioned.

First, according to the first way;

second, according to the second way, at his conclusion does not follow (186a25; [40]).

He first says, therefore, that Parmenides assumed false propositions, because he held that what is—namely, being—is used simply, that is, in one way. In fact, it is used in many ways. For “being” is used in one way for substance and in another way for accident; the latter is used in many ways according to the different genera. “Being” can also be used commonly for substance and accident. Hence, it is clear that the propositions assumed by Parmenides are true in one sense and false in another.

For when it is said that whatever is other than being is non-being, this is true if “being” is taken commonly, as it were, for substance and accident. If, however, “being” is taken for accident alone or for substance alone, this is false, as will be shown below. Likewise, when he says that being is one, this is true if “being” is taken for some one substance or for some one accident. But this will not be true in the sense that whatever is other than that being is non-being.

40. Next, at his conclusion does not follow (186a25), he follows the second method of answering the argument, namely, that the argument of Parmenides does not draw its conclusion according to proper form.

He shows this first in an example;

second, at it is necessary for him (186a32; [41]), he adapts this example to the problem at hand.

He says, therefore, first that it can be seen that the argument of Parmenides does not draw its conclusion properly, because the form of argumentation used is not efficacious in every matter. And this could not be true if a proper form of argumentation were used.

For if we take white in the place of being, and if we say that “white” signifies one thing only and is not used equivocally, and if we say that whatever is other than white is non-white, and whatever is non-white is nothing, then it will not follow that white would be one only. For it will not be necessary that all white things are one continuum.

Or, to put it differently, white will not necessarily be one by continuity; that is, from the fact that white is a continuum, it will not be one simply. For a continuum is many in a certain respect, as was said above.¹ And in like manner, “white” will not be one in definition, for the white and that which is receptive of the white are different in definition.

Nevertheless, there will not be something other than white separated from it, as it were. The reason that the white is not other than that which is receptive of it is not because the white is separable from that which is receptive of it, but because the definitions of the white and of that which is receptive of it are different.

But it was not yet known at the time of Parmenides that something could be one in subject and many in definition, and thus he believed that, if there is nothing outside a certain subject, then it follows that it is one. But this is false on account of the multiplicity of parts, as well as on account of the different definitions of subject and accident.

41. Next, at it is necessary for him (186a32), he adapts this example to the matter at hand in order to show how what he has said of the white also applies to being.

Concerning this, he makes two points.

First, he shows that it does not follow that being is one simply. For subject and accident are different according to definition.

Second, at in particular, then (186b12; [44]), he shows that this does not follow, because of the multiplicity of parts.

Concerning the first part, he makes two points.

First, he shows that, when it is said that whatever is other than being is non-being, this being cannot be taken to mean accident alone.

Second, at if, then, “substance” (186b4; [43]), he shows that this “being” cannot be taken to mean substance alone.

42. He says, therefore, first that, when it is said that whatever is other than being is non-being, if being is said to signify one thing, then it will be necessary that it not signify any one being or what is predicated of any one thing. Rather, it will signify what truly is—namely, substance—and it will signify what is truly one, namely, the indivisible. For if being were to signify accident, then, since accident would be predicated of a subject, the subject could not be that to which the accident, which is called being, occurs.

For if whatever is other than being is non-being (that is, other than accident), and if the subject is other than the accident, which is here said to be being, then it follows that the subject is non-being. And so, when accident, which is being, is predicated of the subject, which is non-being, it follows that being is predicated of non-being.

Hence, Aristotle concludes, something that is not will therefore be; that is, it will follow that non-being is being. This, however, is impossible. For what is first of all assumed in the sciences is that contradictories are not to be predicated of each other, as is said in Metaphysics 4.¹ Thus, he concludes that, if anything is truly being, as is supposed in the proposition whatever is other than being is non-being, it follows that it is not an accident inhering in something else. For in this case, its subject would not be a being. That is, this subject would not have the account of being unless being should signify “many,” such that each of the many would be a being. But it was assumed by Parmenides that being signifies one only.

43. Next, at if, then, “substance” (186b4), after he has concluded that being cannot refer to accident when it is said that whatever is other than being is non-being, he shows further that being cannot refer to substance either. Thus, he says that, if what truly is does not happen to something, but other things happen to it, then, in the proposition whatever is other than being is non-being, it is necessary that what truly is, substance, be signified by “being” rather than by “non-being.” But this cannot stand. For let it be held that that which truly is, namely, substance, is white. But white is not that which truly is. For it has already been said that that which truly is cannot happen to something. And this is so because what is not truly—namely, what is not substance—is not at all, namely, is not being. But what is other than being—namely, other than substance—is non-being.

Hence it follows that white is non-being, not only in the sense that it is not this being, as a man is not this being, which is an ass, but also in the sense that it is not in any way. For he says that whatever is other than being is non-being, and what is non-being is nothing. From this, therefore, it follows that non-being would be predicated of that which truly is, because white is predicated of substance, which truly is. And white does not signify being, as was said. Thus it follows that being is non-being. And this indeed is impossible, because one contradictory is not predicated of another. If, then, in order to avoid this inconsistency, we say that “true being” signifies not only the subject but also the white itself, it follows that “being” will signify many. And thus there will not be only one being, for subject and accident are several according to definition.

44. Next, at in particular, then (186b12), he shows, because of the multiplicity of parts, that it does not follow from the argument of Parmenides that there is only one being.

He shows this first with reference to quantitative parts;

second, with reference to the parts of definition, at substance is plainly divisible (186b14; [45]).

Therefore, he first says that, if “being” signifies only one thing, not only will it not be accident with subject, but neither will it be a magnitude. For every magnitude is divisible into parts. But the account of each of the parts is not the same, but different. Hence it follows that this one being is not a corporeal substance.

45. Second, at substance is plainly divisible (186b14), he shows that this being cannot be a definable substance. For in a definition, it is clear that what truly is, the substance, is divided into many, each one of which is what truly is—namely, substance—and each one of which has a different account.

Let us suppose that man is one thing that truly exists. Since man is a two-footed animal, it is necessary that “animal” be and that “two-footed” be. And each of these will be what truly is, namely, substance. And, if they are not substances, they are accidents, either of man or of some other thing. But it is impossible that they be accidents of man.

And, to make this clear, he assumes two things.

First, he assumes that “accident” is used in two ways.

One type of accident is separable and, as such, can be in something or not in it, for example, to sit.

Another type of accident is inseparable and per se. And this latter is the accident in whose definition is placed the subject in which it is. For example, the snub is a per se accident of nose, because nose is placed in the definition of the “snub.” For the “snub” is a curved nose.

The second thing he assumes is that, if certain things are placed in the definition of that which is defined, or in the definition of the things on which the definition depends, then it is impossible that the whole definition of that which is defined be placed in the definition of these certain things. Thus, “two-footed” is placed in the definition of “man” and certain other things are placed in the definition of “two-footed” or “animal,” from which man is defined.

Hence it is impossible that “man” be placed in the definition of “two-footed” or in the definition of any of the things that fall in the definition of “two-footed” or of “animal.” Otherwise, we would have a circular definition and one and the same thing would be both prior and posterior, better-known and less-known. For every definition is from the prior and the better known, as is said in Topics 6.4.

And for the same reason, when “white” is placed in the definition of “white man,” it is impossible for “white man” to be placed in the definition of “white.” These things having been assumed, the argument is as follows.

If two-footed is an accident of man, it must be either a separable accident (and thus it could happen that man is not two-footed, which is impossible) or an inseparable accident (and thus it will be necessary that man be placed in the definition of “two-footed”). But this also is impossible, because “two-footed” is placed in the definition of “man.” It is impossible, therefore, that two-footed be an accident of man. For the same reason, “animal” cannot be an accident.

But if it is said that both are accidents of something else, it would follow that man also would be an accident of something else. But this is impossible, for it has already been said above that that which truly is, is an accident of nothing. But man was assumed to be that which truly is, as is clear from what was said above.

He shows in the following way that it would follow that man would be an accident of another if animal and two-footed were accidents of some other thing. What is said of both animal and two-footed taken separately may be said of them taken together, namely, two-footed animal. And what is said of two-footed animal may be said of that which is from them—namely, man—because man is nothing other than a two-footed animal.

Therefore, it is clear that, if being is held to be one only, we cannot hold that there are quantitative parts, or parts of a magnitude, or parts of a definition. Therefore, it follows that every being is numerically indivisible. Otherwise, while holding being to be one, we would be forced to posit a multiplicity because of the parts.

46. The Commentator, however, says that, beginning at but what truly is (186b33), Aristotle sets forth the second argument of Parmenides to show that being is one. And this argument is as follows. A being that is one is substance and not accident (and by “substance” he means body). If, however, that body is divided into two halves, it will follow that being is predicated of each half and of the union of the two. And either this proceeds to infinity, which is impossible in itself, or the being is divided into points. But this also is impossible. Hence it follows that being is an indivisible one. But this exposition is fabricated and contrary to the intention of Aristotle, as is sufficiently clear from an examination of the letter of the text according to the first explanation.

Refutation of those who say non-being is something

Some thinkers did, in point of fact, give way to both arguments. To the argument that all things are one if “being” means one thing, they conceded that non-being is; to that from bisection, they yielded by positing indivisibles by division.

But obviously it is not true that, if being means one thing and cannot at the same time mean the contradictory of this, then there will be nothing that is not, for even if what is not cannot be without qualification, there is no reason why it should not be a particular non-being.

To say that all things will be one, if there is nothing besides being itself, is absurd. For who understands “being itself” to be anything but a particular substance? But, if this is so, there is nothing to prevent there being many beings, as has been said. It is, then, clearly impossible for being to be one in this sense.

47. After the Philosopher has disproved the argument of Parmenides by bringing forth certain inconsistencies found in it, he here disproves the position of those who have conceded these absurdities.

Concerning this, he makes two points.

First, he sets forth their position.

Second, he disproves it, at but obviously it is not (187a3; [50]).

48. It must be noted first that the Philosopher used two arguments above against the argument of Parmenides.¹

He used one to show that, because of the diversity of subject and accident, it does not follow from the argument of Parmenides that all is one. This argument led to the absurdity that non-being is being, as is clear from what was said above.

The other argument proceeded to show that the conclusion that all is one does not follow, because, if it were a magnitude, it would follow that magnitude is indivisible. For if it were divisible, there would be some sort of multiplicity.

49. The Platonists, however, gave in to each argument, conceding the impossibilities to which they led. They accepted the first argument, which led to the conclusion that non-being would be being. Suppose that someone were to say that being signifies one thing, either substance alone or accident alone, and because of this, he might also wish to say that all things are one.

In regard to this argument, I say, they accepted the conclusion that non-being would be being. For Plato said that accident is non-being. And, because of this, it is said in Metaphysics 6¹ that Plato held that sophistry dealt with non-being, because it treated most of all those things that are predicated per accidens.

Therefore Plato, understanding being to be substance, conceded the first proposition of Parmenides, who said that whatever is other than being is non-being. For Plato held that accident, which is other than substance, was non-being. He did not, however, concede the second proposition, namely, that whatever is non-being is nothing. For although he would say that accident is non-being, he did not say that accident is nothing, but rather that it is something. And, because of this, according to Plato, it does not follow that being is one only.

But Plato, when he made magnitudes to be indivisible by dissection—that is, when he said that a magnitude is terminated in indivisibles by division—did assent to the other argument, which led to the conclusion that a magnitude would be indivisible. For he held that bodies are resolved into surfaces, and surfaces into lines, and lines into indivisibles, as is clear in De caelo et mundo 3.1.¹

50. Next, at but obviously (187a3), he disproves the above position in regard to the point that Plato conceded, namely, that non-being is something. In regard to the other point, namely, that Plato held that there are indivisible magnitudes, this is disproved in its proper place in the following books of natural science.¹

He disproves the first point in two ways.

First, he shows that it does not follow from the argument of Plato that non-being is something.

Second, at to say that all things (187a6; [52]), he disproves Plato’s remark that, unless we hold this (namely, if the non-being that is an accident is not something), it will follow that all is one.

51. He says, therefore, first (187a3) that the argument by which Plato concluded that being means one thing clearly does not follow. For he held that being is a genus and is predicated univocally of all things by participation in the first being. And further, he held that contradictories cannot be true at the same time. From these two points, he thought that it followed that non-being is not nothing, but something.

For if being signifies one thing, which is substance, it will be necessary that whatever is not substance is non-being. For if it were being, then, since being does not signify anything but substance, it would follow that it would be substance.

And so, it would at once be substance and non-substance, in which case, contradictories would be true at the same time.

If, therefore, it is impossible for contradictories to be true at the same time, and if being signifies one thing, which is substance, it would follow that whatever is not substance is non-being. But there is something that is not substance, namely, accident. Therefore, something is non-being. And so it is not true that non-being is nothing.

But Aristotle shows that this does not follow. For if being signifies principally the one, which is substance, there is nothing to prevent one from saying that accident, which is not substance, is not being simply. But, because of this, it is not necessary to say that that which is not something—that is, not substance—is absolute non-being. Hence, although accident is not being simply, it cannot, indeed, be called absolute non-being.

52. Next, at to say that all things (187a6), he shows further that, if the non-being that is accident is not something, it does not follow that all is one. For if “being” can mean only substance, which truly is, then he says that it is absurd to hold that it would follow that all things are one unless there is something outside of being. For if there is substance, there is nothing to prevent there being a multiplicity of substances, as has already been said,¹ even if magnitude and accident are removed. For the definition of “substance” is divided into the many things that are in the genus of substance, as “man” is divided into “animal” and “two-footed.” And further, it follows that, according to the diverse differentiae of a genus, there are many substances in act. And finally, he draws the conclusion that he principally intended, that all things are not one, as Parmenides and Melissus said.

The opinions of the physicists who spoke of the principles as natural philosophers

The physicists, on the other hand, have two modes of explanation. The first set make the underlying body one—either one of the three or something else that is denser than fire and rarer than air—and then generate everything else from this and obtain multiplicity by condensation and rarefaction.

Now, these are contraries, which may be taken universally as “excess” and “defect.” (Compare Plato’s “great” and “small”—except that he make these his matter, the one his form, while the others treat the one which underlies as matter and the contraries as differentiae, that is, forms.)

The second set assert that the contrarieties are contained in the one and emerge from it by separation; such are Anaximander and all those who assert that “what is” is one and many, like Empedocles and Anaxagoras. For they too produce other things from their mixture by separation.

But these differ from each other, in that the former imagines a cycle of such changes, but the latter a single series. Anaxagoras again made both his “homogeneous” substances and his contraries infinite in multitude, whereas Empedocles posits only the so-called elements.

53. After the Philosopher has disproved the opinion concerning principles of those who did not speak of nature as natural philosophers, he here pursues the opinions of those who, not disregarding motion, spoke of the principles of nature as natural philosophers. And he calls these men physicists, that is, natural philosophers.

Concerning this, he makes two points.

First, he sets forth the diversity of their opinions.

Second, he examines one of these opinions at the theory of Anaxagoras (187a26; [58]).

54. He says first that, according to the opinion of the natural philosophers, there are two ways in which things are generated from principles.

One of the opinions was advanced by the natural philosophers who held that there is only one material principle. This principle would be either one of three elements—fire, air, or water, since no one made earth alone the principle, as was said above¹—or else some intermediate between them, such as that which would be more dense than fire and more subtle than air. They then said that all other things were generated from this one principle by rarity and density. For example, those who made air to be the principle said that fire was generated from air by rarefaction, and water by condensation. However, the dense and the rare are contraries and are reduced to excess and defect as to something more universal. For the dense is what has much matter, whereas the rare has little.

55. And thus they agreed in a certain respect with Plato, who held that the great and the small are principles that also pertain to excess and defect. But they differed from Plato as follows. Plato held that the great and the small are on the side of matter, because he posited one formal principle that is a certain idea participated in by different things according to a diversity of matter.

The ancient natural philosophers, on the other hand, maintained a contrariety on the part of form, because they held that the first principle is one matter from which many things were constituted in being according to different forms.

56. Other natural philosophers, however, held that things come to be from principles in such a way that contrary and differing things themselves are drawn forth from one thing in which they already existed, as it were, mixed and confused. But they differed as follows.

Anaximander held the one confused state, but not the many things commixed in it, to be the principle. Thus he held one principle only. But Empedocles and Anaxagoras held rather that the principles are the very things that are mixed together in that one confused state, and so they held many principles, although they also held that this one confused state is in some way a principle.

57. But Anaxagoras and Empedocles differed on two points.

First, Empedocles held that there is a certain cycle of mixing and separating. For he held that the world has been made and corrupted many times; that is to say, when the world has been corrupted by friendship gathering all into one, the world is then generated again by strife separating and distinguishing. And thus, the distinction of things follows upon their being confused, and vice versa.

But Anaxagoras held that the world was made only once, such that, from the beginning, all things were mixed into one. But mind, which began to draw out and to distinguish, will never cease to do this, such that everything will never be mixed into one.

They also differed in another way. Anaxagoras held that the principles are infinitely many parts that are alike and contrary. Thus, there are infinite parts of flesh that are like each other and infinite parts of bone and other things that have similar parts, yet each has a contrariety to the others. Thus, the contrariety of the parts of bone to the parts of blood is that of the dry to the moist. But Empedocles held as principles only those four things that are commonly called elements: fire, air, water, and earth.

Refutation of Anaxagoras’ opinion about an infinite number of principles

The theory of Anaxagoras that the principles are infinite in multitude was probably due to his acceptance of the common opinion of the physicists that nothing comes into being from non-being.

For this is the reason why they use the phrase “all things were together,” and the coming into being of such and such a kind of thing is reduced to change of quality, while some spoke of combination and separation.

Moreover, the fact that the contraries proceed from each other led them to the conclusion.

The one, they reasoned, must have already existed in the other, for since everything that comes into being must arise either from what is or from what is not, and it is impossible for it to arise from what is not (on this point all the physicists agree),

they thought that the truth of the alternative necessarily followed, namely, that things come into being out of existent things—that is, out of things already present but imperceptible to our senses because of the smallness of their bulk.

So they assert that everything has been mixed in everything, because they saw everything arising out of everything.

But things, as they say, appear different from one another and receive different names according to the nature of the particles that are numerically predominant among the innumerable constituents of the mixture.

For nothing, they say, is purely and entirely white or black or sweet, bone or flesh, but the nature of a thing is held to be that of which it contains the most.

Now the infinite as infinite is unknowable, such that what is infinite in multitude or size is unknowable in quantity and what is infinite in variety of kind is unknowable in quality. But the principles in question are infinite both in multitude and in kind. Therefore it is impossible to know things that are composed of them, for it is when we know from what and from how many it is composed that we suppose we know a complex.

Further, if the parts of a whole may be of any size in the direction either of greatness or of smallness (by “parts,” I mean components that are actually present and into which a whole can be divided), it is necessary that the whole thing itself may be of any size. Clearly, therefore, since it is impossible for an animal or plant to be indefinitely big or small, neither can its parts be such, or the whole will be the same. But flesh, bone, and the like are the parts of animals, and the fruits are the parts of plants. Hence it is obvious that neither flesh, bone, nor any such thing can be of indefinite size in the direction either of the greater or of the less.

Again, according to the theory, all such things are already present in one another and do not come into being, but are constituents that are separated out, and a thing receives its designation from that which abounds in it. Further, anything may come out of anything—water by separation from flesh and flesh from water.

Hence, since every finite body is exhausted by the repeated abstraction of a finite body, it seems obviously to follow that everything cannot subsist in everything else.

For let flesh be extracted from water, and again, let more flesh be produced from the remainder by repeating the process of separation; then, even though the quantity separated out will continually decrease, still it will not fall below a certain magnitude.

If, therefore, the process comes to an end, everything will not be in everything else (for there will be no flesh in the remaining water); if, on the other hand, it does not, and further extraction is always possible, there will be an infinite multitude of finite equal particles in a finite quantity—which is impossible.

Another proof may be added: since every body must diminish in size when something is taken from it, and flesh is quantitatively definite in respect both of greatness and smallness, it is clear that no body can be separated out from the minimum quantity of flesh, for the flesh left would be less than the minimum of flesh.

Finally, in each of these infinite bodies, there would be already present infinite flesh and blood and brain—having a distinct existence, however, from one another, and no less real than the infinite bodies, and each infinite. This is contrary to reason.

The statement that complete separation never will take place is correct enough, for passions are indeed inseparable. If, then, colors and states had entered into the mixture, and if separation took place, there would be a “white” or a “healthy” that was nothing but white or healthy, that is, was not the predicate of a subject.

So, the intellect which seeks these impossibilities is absurd, if he truly wishes to separate such things and it is impossible to do so, both in respect of quantity and of quality—of quantity, because there is no minimum magnitude; and of quality, because passions are inseparable.

Nor is Anaxagoras right about the generation of things of the same species. It is true there is a sense in which clay is divided into pieces of clay, but there is another in which it is not. Water and air are and are generated from each other, but not in the way in which bricks come “from” a house and again a house “from” bricks.

And it is better to assume a smaller and finite number of principles, as Empedocles does.

58. Having set forth the opinions of the natural philosophers concerning the principles, he here pursues one of these opinions, namely, that of Anaxagoras. For this opinion seemed to assign a common cause for all the species of motion.

The discussion is divided into two parts.

In the first part, he sets forth Anaxagoras’ argument;

in the second part, he raises objections against it, at now the infinite (187b7; [64]).

Concerning the first part, he makes three points.

First, he sets forth those things that Anaxagoras supposed and from which he argued.

Second, at the one, they reasoned (186a32; [62]), he sets forth the order of his argument.

Third, at but things, as they say (187b2; [63]), he sets forth Anaxagoras’ response to a certain tacit objection.

59. Anaxagoras assumed two things from which he argued. The first of these is a point that is assumed by all of the natural philosophers, namely, that nothing comes to be from nothing. And Aristotle says that, because of this, Anaxagoras seemed to have held the opinion that the principles are infinite. For he accepted as true the common opinion of all philosophers of nature, namely, that what simply is not in no way comes to be. For they assumed this as a principle and then developed their different opinions.

60. Lest they should be forced to hold that something new comes to be that previously was in no way at all, some held that all things from the beginning existed together, either in some one confused state, as Anaxagoras and Empedocles held, or in some material principle, such as water, fire, and air, or some intermediate between these.

And, in accordance with this, they posited two modes of production.

Those who held that all things preexisted together as in one material principle said that coming to be is nothing other than being altered. For they said that all things come to be from that one material principle through its condensation and rarefaction.

Others, however, who held that all things preexisted together in some one confused state and mixture of many, said that the coming to be of things is only a joining together and a separation.

All of these philosophers were deceived because they did not know how to distinguish between potency and act. For being in potency is, as it were, a mean between pure non-being and being in act. Therefore, those things that come to be naturally do not come to be from non-being simply, but from being in potency, and not, indeed, from being in act, as they thought. Hence things that come to be did not necessarily preexist in act, as they said, but only in potency.

61. Next, at moreover, the fact that (187a31), he mentions the second thing that Anaxagoras assumed. Anaxagoras said that contraries come to be from each other. For we see the cold come to be from the hot, and vice versa. And from this he concluded that, since nothing comes to be from nothing, one of the contraries preexists in the other. And this is true, of course, in respect to potency. For the cold is in the hot in potency, but not in act, as Anaxagoras thought. For he was not aware of being in potency, which is a mean between pure non-being and being in act.

62. Next, where he says, the one, they reasoned (187a32), he sets forth the deductive order of the argument. Anaxagoras proceeded as follows. If something comes into being, it is necessary that it should come to be either from being or from non-being.

But he excluded one of these alternatives—namely, that something should come to be from non-being. He did this because of the common opinion of the philosophers mentioned above.

From this, he concluded that the remaining alternative was correct, namely, that a thing comes to be from being. For example, if air comes to be from water, then air preexisted. For it cannot be said that air comes to be from water unless air preexisted in water.

Hence he wished to say that everything that comes to be from something preexisted in that from which it comes to be.

But, because this seemed to be contrary to what appears to the senses (for it is not apparent to the senses that that which is generated from something preexists in it), he forestalled this objection by holding that that which comes to be from something preexists in it as certain most minute parts that are not sensible to us because of their smallness. For example, if air comes to be from water, certain minute parts of air are in the water, but not in that quantity in which it is generated. And so he said that, by the gathering together of these parts of air by themselves, and by their separation from the parts of water, air comes to be.

Having accepted, therefore, that everything that comes to be from something preexists in it, he further assumed that everything comes to be from everything. Hence he concluded that everything would be mixed in everything else as minute, non-sensible parts. And, because an infinite variety of things can come to be from another, he said that there are infinite, minute parts in each thing.

63. Next, at but things, as they say (187b2), he heads off a certain unspoken objection. It is possible for someone to object as follows. If infinite parts of everything are in everything, it would follow that things neither differ from each other nor appear to differ from each other. Therefore, as if he were answering this objection, Anaxagoras says that things appear to differ from each other and are diversely named because of that which is dominant in them, even though there is an infinite number of minute parts contained in any mixture. And so nothing is purely and totally white or black or bone. Rather, that which abounds in each thing seems to be the nature of that thing.

64. Next, at now the infinite (187b7), Aristotle refutes the above mentioned position.

Concerning this, he makes two points.

First, he disproves the position absolutely.

Second, at and it is better (188a17; [74]), he compares it to the opinion of Empedocles.

Concerning the first part, he makes two points.

First, he sets forth arguments to disprove the opinion of Anaxagoras.

Second, at the statement that (188a5; [72]), he disagrees with Anaxagoras’ way of understanding his own position.

Concerning the first part, he gives five arguments.

The first of these is as follows. Every infinite thing is unknown insofar as it is infinite. He explains why he says as infinite. If it is infinite in respect to multitude or magnitude, it will be unknown with respect to quantity. If, however, it is infinite with respect to species (for example, if it is composed of an infinite variety of species), then it will be unknown according to quality. And the reason for this is that what is known by the intellect is grasped by the intellect with respect to all that belongs to that thing. But this cannot happen with regard to something infinite. If, therefore, the principles of a thing are infinite, they must be unknown either with respect to quantity or with respect to species. But, if the principles are unknown, those things that are from the principles must be unknown. He proves this as follows. We think that we know any composite when we know from what and from how many it is composed, that is, when we know both the species and the quantity of the principles. It follows, therefore, from first to last that, if the principles of natural things are infinite, then natural things are unknown either with respect to quantity or with respect to species.

65. At further, if the parts (187b13), he gives the second argument, which is as follows. If the parts of a whole do not have a determinate quantity, either great or small, but can be any size, either great or small, it is necessary that the whole not have a determinate greatness or smallness. Rather, the whole could have any size. This is so because the quantity of the whole comes from the parts. (But this must be understood of the parts existing in act in the whole, as flesh and nerve and bone exist in an animal. Hence he says, by “parts,” I mean components that are actually present and into which a whole can be divided. And by this, he excludes the parts of a continuous whole that are in the whole in potency.)

But it is impossible that an animal or a plant or some such thing be related indeterminately to any size, whether great or small. For there is some quantity so large that no animal exceeds it in size. So also there is some quantity so small that no animal is found to be smaller. And the same must be said of plants. Therefore, by denying the consequent, it follows that the parts are not of indeterminate quantity. For what is true of the whole is true of the parts. But flesh and bone and things of this sort are parts of an animal, and fruits are parts of plants. Therefore, it is impossible that flesh and bone and such things should have an indeterminate quantity, either greater or smaller. Therefore, it is not possible that there should be certain parts of flesh or bone that are non-sensible because of smallness.

66. It seems, however, that what is said here is contrary to the statement that a continuum is divisible to infinity. For if the continuous is divisible to infinity, and flesh is, indeed, a kind of continuum, it seems that flesh is divisible to infinity. Therefore, some part of flesh, according to a division to infinity, goes beyond every determinate smallness. But it must be pointed out that, although a body is divisible to infinity when considered mathematically, the natural body is not divisible to infinity. For in a mathematical body, nothing but quantity is considered. And in this there is nothing repugnant to division to infinity. But, in a natural body, the form also is considered, which form requires a determinate quantity, and also other accidents. Hence it is not possible for quantity to be found in the species of flesh except as determined within some termini.

67. He gives the third argument at again, according to the theory (187b21).

Concerning this, he makes two points.

First, he sets forth certain things that are the basis of the argument.

Second, at for let flesh (187b27; [68]), he sets forth the deductive order of the argument.

Concerning the first part, he proposes three things.

The first is that, according to the position of Anaxagoras, as was said above, all things are together. And, from this, Aristotle wishes to reduce Anaxagoras’ argument to absurdity. For Anaxagoras said, as was pointed out, that all such things—that is, all things that are of like parts, such as flesh and bone and the like—are in each other and do not come to be from nothing, but are separated from that in which they preexist. And each thing is named from that which abounds in it, that is, from the largest number of parts existing in the thing.

The second point is that everything comes to be from everything, as water comes to be by separation from flesh and flesh likewise comes to be from water.

The third point is that every finite body is exhausted by a finite body. If, from some finite body, however large, a finite body, however small, is taken away, the smaller can be taken away from the larger until eventually the greater whole is consumed by the smaller through division.

And, from these three points, Aristotle concludes what he primarily intended, namely, that each thing is not in each thing. And this is contrary to the first of these three points. For this is how the reductio ad absurdam works: the conclusion contradicts some premise.

68. Next, at for let flesh (187b27), he develops his argument and assumes what was concluded in the preceding argument. He says that, if flesh is removed from water (since flesh is generated from water), and if again another separation of flesh is made from the remaining water, then, although there will always remain a smaller quantity of flesh in the water, still the size of that flesh will not fall below a certain magnitude; that is, there happens to be a certain small measure of flesh than which there will not be any smaller flesh, as is clear from the argument given above.

Therefore, having established that there is some smallest particle of flesh than which there is no smaller, he proceeds as follows. If flesh is separated from water, and again other flesh, either the process of separation will stop or it will not. If it stops, then there is no flesh in the remaining water, and everything will not be in everything. If it does not stop, then some part of flesh will always remain in the water.

Thus, in the second separation, the remaining flesh is smaller than in the first, and in the third, it is smaller than in the second. And, since we cannot proceed to infinity in smallness of parts, as was said, then the smallest parts of flesh are equal and infinite in number in some finite body of water. Otherwise, separation could not proceed to infinity.

It follows, therefore, that, if the separation does not stop, but flesh is always removed from water to infinity, then, in some finite magnitude—namely, water—there are certain things that are finite in respect to quantity and equal to each other, but infinite in respect to number—namely, the infinite, smallest parts of flesh. But this is impossible and contrary to what was said above, namely, that every finite body is reduced by some finite body. Therefore, the first point—namely, that everything is in everything, as Anaxagoras held—is also impossible.

69. We must note that it is not without reason that the Philosopher used the term equal in stating the last absurdity to which this position leads. For if the definition of quantity is considered, it is not absurd that an infinity of unequal parts be in a finite body. For if a continuum is divided according to the same proportion, it will be possible to proceed to infinity, such as if we take a third of a whole, and then a third of the third, and so on. In this case, however, the parts were not taken as equal in quantity. But, if the division is made according to equal parts, we will not be able to proceed to infinity even if we consider only the account of quantity that is found in a mathematical body.

70. He gives his fourth argument at another proof may be added (187b35). The argument is as follows. Every body becomes a smaller one when something is taken from it, because every whole is greater than its parts. Since, then, the quantity of flesh is determinately great or small, as is clear from what was said above, there must be some smallest bit of flesh.

Therefore, nothing can be separated from this, because the remaining flesh would be smaller than this smallest piece of flesh. Therefore, it is impossible that everything comes to be from everything by separation.

71. At finally, in each (188a2), he gives his fifth argument, which is as follows. If infinite parts of each thing are in each thing and everything is in everything, it follows that infinite parts of flesh and infinite parts of blood and brain are in an infinite number of bodies. And, regardless of how much is separated, the same amount would always remain. Therefore, it would follow that the infinite is in the infinite infinitely. But this is unthinkable.

72. Next, at the statement that (188a5), he disproves the position of Anaxagoras according to Anaxagoras’ own understanding of it.

He does this in two ways.

First, he shows that Anaxagoras did not understand his own position.

Second, at nor is Anaxagoras (188a13; [73]), he shows that Anaxagoras did not have sufficient evidence for holding this position.

Therefore, he says first that, although Anaxagoras has in a certain respect spoken the truth, he himself did not understand what he said when he held that the process of separation would never end. For accidents can never be separated from substance, yet he held that there was a mixture not only of bodies, but also of accidents. When something becomes white, he said that this happened by an abstraction of white from the previously existing mixture.

If, then, colors and other accidents of this sort are mixed together, as he said, and if someone says, on this supposition, that all things that are mixed can be separated, it would follow that there would be white and healthy but no subject of which these are predicated and in which they are. But this is impossible. Therefore, the truth is that, if accidents are in the mixture, it is impossible that all mixed things can be separated.

Another problem results from this. Anaxagoras held that all things were mixed from the very beginning, but intellect began to separate them. Now, any intellect that attempts to do what cannot be done is not worthy of the name “intellect.”

Hence, that intellect will be inconsistent, intending the impossible, if he truly wishes, that is, wishes to separate things completely. For this is impossible both from the point of view of quantity—because there is no smallest magnitude, as Anaxagoras said, since something can be subtracted from any small quantity—and from the point of view of quality, because accidents are not separable from their subjects.

73. Next, at nor is Anaxagoras (188a13), he disproves this position by reason of the fact that Anaxagoras did not have sufficient evidence. Since Anaxagoras saw that a thing is made large by the coming together of many small parts that are similar, as a stream is made from many brooks, he believed this to be the case for all things.

And thus Aristotle says that Anaxagoras did not correctly understand the generation of things of the same species; that is, he did not understand that a thing is always generated by things that are similar in respect to species.

For some things are both generated from and are resolved into things like unto themselves, as clay is divided into pieces of clay, but in other instances, this is not so. For some things are generated from that which is dissimilar.

And, in these instances, there is not merely one mode of production. For some things are made by alteration from that which is unlike, as the sides of a house are made from clay and not from sides; but other things are made by composition, as the house is not made of houses, but of sides.

It is in this way that air and water come to be from each other, that is, as from the unlike.

Another reading here is as the sides are from the house. And thus he sets forth a twofold way in which things come to be from the unlike: through composition, as the house is made of sides, and by resolution, as the sides come to be from the house.

74. Next, at and it is better (188a17), he disproves the position of Anaxagoras by comparing it with the opinion of Empedocles. He says that it is better to make the principles smaller in number and finite, as Empedocles does, than to make them many and infinite, as does Anaxagoras.

All thinkers, then, agree in making the contraries principles, both those who describe the all as one and unmoved (for even Parmenides treats hot and cold as principles under the names of fire and earth) and those too who use the rare and the dense. The same is true of Democritus also, with the substantial and the void, both of which exist, he says, the one as being and the other as non-being.

Again, he speaks of differences in position, shape, and order, and these are genera of which the species are contraries: of position, as above and below or before and behind; and of shape, as angular and angle-less or straight and round.

It is plain, then, that they all in one way or another identify the contraries with the principles.

And with good reason. For first principles must be derived neither from one another nor from anything else, while everything has to be derived from them.

But these conditions are fulfilled by the primary contraries, which are not derived from anything else, since they are primary, nor from each other, since they are contraries.

But we must see how this can be arrived at as a reasoned result as well as in the way just indicated. Our first presupposition must be that, in nature, no contingent thing acts on, or is acted on, by any other contingent thing, nor may anything come from anything else unless we mean that it does so accidentally.

For how could “white” come from “musical” unless “musical” happened to be an accident of the not-white or of the black?

No; “white” comes from “not-white”—and not from just any “not-white,” but from black or some intermediate color.

Similarly, “musical” comes to be from “not-musical,” and not from just any thing other than musical, but from “unmusical” or any intermediate state there may be.

Nor again do things pass into the first contingent thing;

“white” does not pass into “musical” (except maybe accidentally), but into “not-white”—and not into any contingent thing that is not white, but into black or an intermediate color.

“Musical” passes into “not-musical”—and not into any contingent thing other than musical, but into “unmusical” or any intermediate state there may be.

The same holds of other things also: even things that are not simple, but complex, follow the same principle, but the opposite state has not received a name, so we fail to notice the fact. What is harmonious must come from what is inharmonious, and vice versa; harmony passes into inharmony—and not into just any inharmony, but into the corresponding opposite. It does not matter whether we take attunement, order, or composition for our illustration; the principle is obviously the same in all, and in fact applies equally to the production of a house, a statue, or any other complex. A house comes from certain things in a certain state of separation instead of conjunction, a statue (or any other thing that has been shaped) from shapelessness—each of these objects being partly order and partly composition.

If, then, this is true, everything that comes to be or passes away comes from or passes into its contrary or an intermediate state. But the intermediates are derived from the contraries—colors, for instance, from black and white. Therefore, everything that comes to be by a natural process is either a contrary or a product of contraries.

Up to this point, we have practically had most of the other writers on the subject with us, as I have said already, for all of them identify their elements and what they call their principles with the contraries, giving no reason indeed for the theory, but constrained, as it were, by the truth itself.

They differ from one another, however, in that some assume contraries that are more primary, others contraries that are less so; some assume those more knowable in the order of explanation, others those more familiar to sense. For some make hot and cold, or again moist and dry, the causes of generation, while others make odd and even, or again love and strife. These differ from each other in the way mentioned.

Hence, their principles are the same in one sense, but different in another; different certainly, as indeed most people think, but the same according to analogy. For all are taken from the same columns, some of the pairs being wider, others narrower in extent.

In this way, then, their theories are both the same and different, some better, some worse. Some, as I have said, take as their contraries what is more knowable in the order of explanation, others what is more familiar to sense. (The universal is more knowable in the order of explanation, the particular in the order of sense, for explanation has to do with the universal, but sense with the particular.) The great and the small, for example, belong to the former class, but the dense and the rare to the latter. It is clear, then, that our principles must be contraries.

75. Having set forth the opinions of the ancient philosophers concerning the principles of nature, Aristotle here begins to seek the truth.

He seeks it first by way of disputation, proceeding from probable opinions.

Second, at we will now give (189b30; [98]), he determines the truth demonstratively.

Concerning the first part, he makes two points.

First, he investigates the contrariety of the principles;

second, at the next question is (189a11; [82]), he inquires about their number.

Concerning the first part, he makes three points.

First, he sets forth the opinion of the ancients about the contrariety of the principles.

Second, at and with good reason (188a27; [77]), he gives an argument in favor of this position.

Third, at up to this point (188b26; [79]), he shows how the philosophers are related to each other in saying that the principles are contraries.

76. He says, therefore, first (188a19) that all of the ancient philosophers posited contrariety in the principles. And he makes this clear by citing three opinions of the philosophers. For some philosophers have said that the whole universe is one immobile being. Of these, Parmenides said that all things are one according to reason but many according to sense. And, to the extent that there are many, he posited in them contrary principles, namely, the hot and the cold. He attributed the hot to fire and the cold to earth.

Second, there was the opinion of the natural philosophers who posited one material and mobile principle. They said that other things come to be from this principle according to rarity and density. Thus, they held that the rare and the dense are principles.

A third opinion was advanced by those who posited many principles. Among them, Democritus held that all things come to be from indivisible bodies that are joined together. And, in this contact with each other, they left a sort of void. Such voids he called pores, as is clear in De generatione 1.8.¹

Therefore, he held that all bodies are composed of the substantial and the void, that is, the full and the empty. Hence he said that the full and the empty are principles of nature. But he associated the full with being and the empty with non-being. And, although all of these indivisible bodies are one in nature, he said that different things are composed of them according to a diversity of figure, position, and order. Thus, he held that the principles are contraries in the genus of position (such as above and below or before and behind), and also contraries in the genus of figure (such as the straight, the angular, and the circular). The principles also are contraries in the genus of order—namely, prior and posterior—which are not mentioned in the text because they are obvious.

And thus Aristotle concludes, by a sort of induction, that all of the philosophers held that the principles are contraries in some way. He makes no mention of the opinion of Anaxagoras and Empedocles because he has already explained their position at length above.¹ However, they also placed a certain contrariety in the principles when they said that all things come to be through joining and separating, which agree in genus with the rare and the dense.

77. Next, at and with good reason (188a27), he gives a probable argument to show that the first principles are contraries. The argument is as follows.

Three things seem to belong to the very definition of principles.

First, they are not from other things.

Second, they are not from each other.

Third, all other things are from them.

But these three things are found in the primary contraries. Therefore, the primary contraries are principles.

Now, in order to understand what he means when he speaks of primary contraries, we must realize that some contraries are caused by other contraries; for instance, the sweet and the bitter are caused by the wet and the dry and the hot and the cold.

Since, however, it is impossible to proceed to infinity, but one must come to certain contraries that are not caused by other contraries, he calls these last contraries the primary contraries.

Now, the three conditions proper to principles mentioned above are found in these primary contraries. For things that are first are manifestly not from others. Moreover, things that are contraries are manifestly not from each other. For even though the cold comes to be from the hot, insofar as that which was previously hot is later cold, nevertheless coldness itself never comes to be from heat, as will be pointed out later.¹

The third point—precisely how all things come to be from the contraries—we must investigate more carefully.

78. Now, in order to clarify this latter point, he states first that neither action nor passion can occur between things that are contingent in the sense of merely happening to be together, or between things that are contingent in the sense of being indeterminate. Nor does everything come to be from everything, as Anaxagoras said, except perhaps accidentally.

This is first of all seen clearly in simple things. For white does not come to be from musical except accidentally, insofar as white or black happen to be in the musical. But white comes to be per se from the non-white, and not from just any non-white, but from that non-white that is black or some intermediate color.

And in like manner, the musical comes to be from the non-musical, and again not from just any non-musical, but from its opposite, which is called the unmusical—namely, from that which is disposed to be musical but is not—or from some mean between these two. And for the same reason, a thing is not corrupted primarily and per se into just any contingent thing (for instance, the white into the musical) except accidentally. Rather, white is corrupted per se into the non-white, and not into just any non-white, but into black or some intermediate color. And he says the same of the corruption of the musical and of other similar things.

The reason for this is as follows. Whatever comes to be or is corrupted does not exist before it comes to be and does not exist after it is corrupted. Hence it is necessary that what a thing comes to be per se and that into which a thing is corrupted per se be such that it includes in its account the non-being of that which comes to be or is corrupted.

And he shows that the same is true of composite things. He says that the situation is the same with composite things as it is with simple things, but it is more hidden in composite things because the opposites of composite things have no names, as do the opposites of simple things. For the opposite of house has no name, although we give a name to the opposite of white. Hence, if the composite is reduced to something with a name, it will be clear.

For every composite consists of a certain harmony. Now, the harmonious comes to be from the inharmonious, and the inharmonious from the harmonious. And, in like manner, the harmonious is corrupted into the inharmonious (not just any inharmonious, but the opposite).

However, we can speak of the harmonious according to order alone or according to composition. For some wholes consist of a harmony of order, such as an army, while other wholes consist of a harmony of composition, such as a house. And the account of each of these is the same.

It is also clear that all composites come to be from the non-composed; for example, a house comes to be from non-composed things, and the figured from the non-figured. And, in all such things, nothing is involved except order and composition.

Thus, it is clear by induction, as it were, that all things that either come to be or are corrupted come to be from contraries (or from some intermediate between them) or are corrupted into them.

Moreover, intermediates between contraries come to be from the contraries, as the intermediate colors come to be from black and white.

Hence, he concludes that whatever comes to be according to nature either is a contrary, such as white and black, or comes to be from the contraries, such as the intermediates between the contraries.

This, then, is the principal conclusion that he intended to draw, namely, that all things come to be from contraries, which was the third characteristic of principles.

79. Next, at up to this point (188b26), Aristotle shows how the philosophers are related in holding that the principles are contraries.

First, he shows how they are related with reference to what drove them to this position.

Second, at they differ from one another (188b30; [80]), he shows how they are related in respect to the position itself.

He says, therefore (188b26), as was pointed out above, that many of the philosophers followed the truth to the point where they held that the principles are contraries. Although they indeed held this position, they did not hold it as though moved by some argument, but rather as forced to it by the truth itself. For truth is the good of the intellect, a good toward which the intellect is naturally ordered. Hence, as things that lack knowledge are moved to their ends without reason, so, at times, the intellect of man tends toward the truth by a sort of natural inclination, though it does not perceive the reason for the truth.

80. Next, at they differ from one another (188b30), he shows how the previously mentioned philosophers are related in respect to the position itself.

Concerning this, he makes two points.

First, he shows how they differ in holding that the principles are contraries.

Second, at hence, their principles (188b35; [81]), he shows how they both differ and agree.

Therefore, he says first that the philosophers who held that the principles are contraries differed in two ways.

First, those who argued reasonably held that the principles are the primary contraries. Others, however, considering the matter less well, held that the principles are posterior contraries. And, of those who appealed to the primary contraries, some considered those contraries that were better known to reason, while others considered those that were better known to sense.

Or it could be said that this second difference explains the first. For those things that are better known to reason are prior simply, whereas those things that are better known to sense are posterior simply but are prior relative to us. However, it is clear that the principles must be prior. Thus, those who judged “prior” according to what is better known to reason held that the principles are those contraries that are prior simply. On the other hand, those who judged “prior” according to what is better known to sense held that the principles are those contraries that are posterior simply.

Hence some held that the hot and the cold are first principles; others, the wet and the dry. And both of these are better known to sense. However, the hot and the cold, which are active qualities, are prior to the wet and the dry, which are passive qualities, because the active is naturally prior to the passive.

But others held principles that are better known to reason. Among these, some held that the equal and the unequal are the principles. For example, the Pythagoreans, thinking that the substance of all things is numbers, held that all things are composed of the equal and the unequal as of form and matter. For they attributed infinity and otherness to the equal, because of its divisibility, but to the unequal they attributed finiteness and identity, because of its indivisibility.

Others, however, held that the cause of generation and corruption is strife and friendship—that is, the cycles of Empedocles—which are also better known to reason. Hence it is clear that the diversity mentioned above appears in these positions.

81. Next, at hence, their principles (188b35), he shows how there is also a certain agreement within the differences of the aforementioned positions. He concludes from what he has said above that the ancient philosophers in a way called the same things principles and in a way called different things principles.

For they differed insofar as different philosophers assumed different contraries, as was said above, yet they are the same insofar as their principles were alike according to analogy, that is, proportion. For the principles taken by all of them have the same proportion.

And this is true in three respects.

First, all the principles that they assumed are related as contraries. And thus Aristotle says that they all took their principles from the same columns, that is, columns of contraries. For they all took contraries as their principles, even though the contraries differed. Nor is it remarkable that they took different principles from the columns of contraries. For among the contraries, some contain, as the prior and more common, and others are contained, as the posterior and less common. Hence, one way in which they spoke alike is that all of them took their principles from the order of contraries.

Another way in which they agree according to analogy is as follows. No matter what principles they accepted, one of these principles is better and the other is worse. For example, friendship, the full, and the hot are better, but strife, the void, and the cold are worse. And the same thing is true of the other pairs of contraries. This is so because one of the contraries always has privation joined to it. For the source of contrariety is the opposition of privation and having, as is said in Metaphysics 10.¹

Third, they agree according to analogy by reason of the fact that they all took principles that are better known. But some took principles that are better known to reason, while others took those better known to sense. Since reason treats the universal and sense treats the particular, universals (such as the great and the small) are better known to reason, while singulars (such as the rare and the dense, which are less universal) are better known to sense.

Then, as a final summary, he concludes with that which he had uppermost in mind, namely, that the principles are contraries.

There are only three principles of natural things

The next question is whether the principles are two or three or more in number.

One they cannot be, for there cannot be one contrary.

Nor can they be innumerable, for if so, being will not be knowable;

and, in any one genus, there is only one contrariety, and substance is one genus.

Also, a finite number is sufficient, and a finite number, such as the principles of Empedocles, is better than an infinite multitude. For Empedocles professes to obtain from his principles all that Anaxagoras obtains from his innumerable principles.

Finally, some contraries are more primary than others, and some arise from others—for example, sweet and bitter, white and black—but the principles must always remain principles. This will suffice to show that the principles are neither one nor innumerable.

Granted, then, that they are a limited number, it is plausible to suppose them more than two. For it is difficult to see how either density should be of such a nature as to act in any way on rarity, or rarity on density. The same is true of any other pair of contraries, for love does not gather strife together and make things out of it, nor does strife make anything out of love, but both act on a third thing different from both. Some indeed assume more than one such thing from which they construct the world of nature.

But someone would have still more difficulties if he did not assume some other nature besides the contraries. For we do not find that the contraries constitute the substance of any thing.

But what is a first principle ought not to be the predicate of any subject. If it were, there would be a principle of the supposed principle: for the subject is a principle, and prior presumably to what is predicated of it.

Again we hold that a substance is not contrary to another substance. How, then, can substance be derived from what are not substances? Or how can non-substances be prior to substance?

If, then, we accept both the former argument and this one, we must, to preserve both, assume a third somewhat as the substratum of the contraries, such as is spoken of by those who describe the all as one nature—water or fire or what is intermediate between them. What is intermediate seems preferable; for fire, earth, air, and water are already involved with pairs of contraries. There is, therefore, much to be said for those who make the underlying substance different from these four; of the rest, the next best choice is air, as presenting sensible differences in a less degree than the others; and after air, water.

All agree in this, however, that they differentiate their one by means of the contraries, such as density and rarity and more and less, which may of course be taken universally as excess and defect, as has already been said.

Indeed, this doctrine too (that the one and excess and defect are the principles of things) would appear to be of old standing, though in different forms, for the early thinkers made the two the active and the one the passive principle, whereas some of the more recent maintain the reverse. Thus, to suppose that the elements are three in number would seem, from these and similar considerations, a plausible view, as I said before.

On the other hand, the view that they are more than three in number would seem to be untenable. For the one substratum is sufficient to be acted on; but if we have four contraries, there will be two contrarieties, and we shall have to suppose an intermediate nature for each pair separately.

If, on the other hand, the contrarieties, being two, can generate from each other, the second contrariety will be superfluous.

Moreover, it is impossible that there should be more than one primary contrariety. For substance is a single genus of being, such that the principles can differ only as prior and posterior, not in genus; in a single genus, there is always a single contrariety, all the other contrarieties in it being held to be reducible to one. It is clear, then, that the number of elements is neither one nor more than two or three; but whether two or three is, as I said, a question of considerable difficulty.

82. After the Philosopher has investigated the contrariety of the principles, he here begins to inquire about their number.

Concerning this, he makes three points.

First, he raises the question.

Second, at one they cannot be (189a12; [83]), he excludes certain things that are not pertinent to this question.

Third, he takes up the question at granted, then, that (189a20; [89]).

Therefore, he first says that, after an investigation into the contrariety of the principles, an inquiry about their number should follow, namely, whether they are two, or three, or more.

83. Next, at one they cannot be (189a12), he excludes those things that are not pertinent to this question.

He shows first that there is not just one principle,

and second, at nor can they be (189a12; [84]), he shows that the principles are not infinite.

He says first that it is impossible for there to be only one principle. For it has been shown (188a19; [75]) that the principles are contraries. But contraries are not just one, for nothing is the contrary of itself; therefore, there is not just one principle.

84. Next, at nor can they be (189a12), he gives four arguments to show that the principles are not infinite.

The first of these is as follows. The infinite as such is unknown. If, therefore, the principles are infinite, they must be unknown. But, if the principles are unknown, then those things that are from the principles are unknown. It follows, therefore, that nothing in the world could be known.

85. He gives the second argument at and in any one genus (189a13). The argument is as follows. The principles must be primary contraries, as was shown above.¹ But the primary contraries belong to the primary genus, which is substance. But substance, since it is one genus, has one primary contrariety. For the first contrariety of any genus is that of the primary differentiae by which the genus is divided. Therefore, the principles are not infinite.

86. He gives the third argument at also, a finite number (189a14). The argument is as follows. It is better to say that what can be brought about by finite principles comes from finite principles rather than from infinite principles.

But all things that come to be according to nature are explained by Empedocles through finite principles, just as they are explained by Anaxagoras through infinite principles. Hence, an infinite number of principles should not be posited.

87. He gives the fourth argument at finally, some contraries (189a17). The argument is as follows. Principles are contraries. If, therefore, the principles are infinite, it is necessary that all the contraries be principles. But not all of the contraries are principles. This is clear for two reasons. First, the principles must be primary contraries, but not all contraries are primary, since some are prior to others. Second, the principles ought not to be from each other, as was said above.¹ But some contraries are from each other, as the sweet and the bitter, and the white and the black. Therefore, the principles are not infinite. Thus he finally concludes that the principles are neither one nor infinite.

88. However, we must note that the Philosopher proceeds here by way of disputation from probable arguments. Hence he assumes certain things that are seen in many instances and that cannot be false all the time, but are true in particular instances. Therefore, it is true that, in a certain respect, contraries do come to be from each other, as was said above,¹ if the subject is taken along with the contraries.

For that which is white later becomes black. However, whiteness itself is never changed into blackness. But some of the ancients, without including the subject, held that the primary contraries come to be from each other. Hence, Empedocles denied that the elements come to be from each other.

And thus Aristotle significantly does not say in this place that the hot comes to be from the cold, but the sweet from the bitter and the white from the black.

89. Next, at granted, then (189a20), he takes up the question under discussion, namely, the number of the principles.

Concerning this, he makes two points.

First, he shows that there are not just two principles, but three.

Second, at on the other hand (189b16; [95]), he shows that there are no more than three principles.

Concerning the first part, he makes two points.

First, he shows through arguments that there are not just two principles, but that a third must be added.

Second, at if, then, we accept (189a34; [93]), he shows that even the ancient philosophers agreed on this point.

90. Concerning the first part (189a20), he gives three arguments.

He says first that, since it was shown that the principles are contraries, and so could not be just one, but are at least two, and further since the principles are not infinite, then it remains for us to consider whether there are only two principles or more than two.

Since it was shown above that the principles are contraries,¹ it seems that there are only two principles, because contrariety exists between two extremes. But it is difficult to see how this is, that is, one might question this. For it is necessary that other things come to be from the principles, as was said above.²

If, however, there are only two contrary principles, it is not apparent how all things can come to be from these two. For it cannot be said that one of them makes something from the other one. For density is not by nature such that it can convert rarity into something, nor can rarity convert density into something.

And the same is true of any other contrariety. For peace does not move strife and make something out of it, nor does the converse happen.

Rather, each of the contraries changes some third thing that is the subject of both of the contraries. For heat does not make coldness itself to be hot, but makes the subject of coldness to be hot. And conversely, coldness does not make heat itself to be cold, but makes the subject of heat to be cold.

Therefore, in order that other things can come to be from the contraries, it seems that it is necessary to posit some third thing that will be the subject of the contraries. It does not matter for the present whether that subject is one or many. For some have posited many material principles from which they prepare the nature of beings. For they said that the nature of things is matter, as will be said later in book 2.¹

91. He gives the second argument at but someone would have still more difficulties (189a27). He says that, unless there is something other than the contraries that are given as principles, then there arises an even greater difficulty. For a first principle cannot be an accident that is predicated of a subject. For since a subject is a principle of the accident that is predicated of it and is naturally prior to the accident, then, if the first principle were an accident predicated of a subject, it would follow that there would be a principle of the principle, and there would be something prior to the first. But, if we hold that only the contraries are principles, it is necessary that the principles be an accident predicated of a subject. For no substance is the contrary of another. Rather, contrariety is found only between accidents. It follows, therefore, that the contraries cannot be the only principles. Moreover, it must be noted that, in this argument he uses predicate for accident, since a predicate designates a form of the subject. The ancients, however, believed that all forms are accidents. Hence he proceeds here by way of disputation from probable propositions that were well known among the ancients.

92. He gives the third argument at again we hold (189a32). The argument is as follows. Everything that is not a principle must be from principles. Therefore, if only the contraries are principles, then, since substance is not the contrary of substance, it follows that substance would be from non-substance. And, thus, what is not substance is prior to substance, because what is from something is posterior to it. But this is impossible. For substance, which is being per se, is the first genus of being. Therefore, it cannot be that only the contraries are principles; rather, it is necessary to posit some other third thing.

93. Next, at if, then, we accept (189a34), he shows how the position of the philosophers also agrees with this.

Concerning this, he makes two points.

First, he shows how they posited one material principle.

Second, at all agree in this, however (189b8; [94]), he shows how they posited two contrary principles besides this one material principle.

However, we must first note that the Philosopher seemed in the preceding arguments to be opposed, in the manner of those who dispute, to both sides of the question.

For he first proved that the principles are contraries, and now he brings forth arguments to prove that the contraries are not sufficient for the generation of things. And, since disputatious arguments do come to a partially true conclusion, though it is not the whole truth, he concludes one truth from each argument.

He says that, if someone thinks that the first argument (which proves that the principles are contraries) is true, and that the argument just given (which proves that contrary principles are not sufficient) is also true, then to maintain both conclusions he must say that some third thing lies beneath the contraries, as was said by those who held that the whole universe is some one nature—understanding nature to mean matter, such as water, or fire, or air, or some intermediate state between these, such as vapor, or some other thing of this sort.

This seems especially true in regard to an intermediate. For this third thing is taken as the subject of the contraries and as distinct from them in some way.

Hence, that which has less of the nature of a contrary about it is more conveniently posited as the third principle beyond the contraries. For fire and earth and air and water have contrariety attached to them, such as the hot and the cold and the wet and the dry. Hence, it is not unreasonable that they make the subject something other than these and something in which the contraries are less prominent.

After these philosophers, however, those who held that air was the principle spoke more wisely, for the contrary qualities found in air are less sensible. After these philosophers are those who held that water was the principle. But those who held that fire was the principle spoke most poorly, because fire has a contrary quality that is most sensible and that is very active. For in fire, there is an excellence of heat. But if the elements are compared with reference to their subtlety, those who made fire the principle seem to have spoken better, as is said elsewhere,¹ for what is more subtle seems to be more simple and prior. Hence, no one held that earth was the principle because of its density.

94. Next, at all agree in this, however (189b8), he shows how they posited contrary principles with the one material principle. He says that all who posited one material principle said that it is figured or formed by certain contraries, such as rarity and density, which are reducible to the great and the small and to excess and defect.

And, thus, the position of Plato—that the one and the great and the small are the principles of things—was also the opinion of the ancient natural philosophers, but in a different way. For the ancient philosophers, thinking that one matter was differentiated by diverse forms, held two principles on the part of form, which is the principle of action, and one on the part of matter, which is the principle of passion. But the Platonists, thinking that many individuals in one species are distinguished by a division of matter, posited one principle on the part of the form, which is the active principle, and two on the part of the matter, which is the passive principle.

And thus he draws the conclusion that he had principally intended, namely, that, by considering the above and similar positions, it seems reasonable that there are three principles of nature. And he points out that he has proceeded from probable arguments.

95. Next, at on the other hand (189b16), he shows that there are no more than three principles.

He uses two arguments.

The first is as follows. It is superfluous for that which can come to be through fewer principles to come to be through many. But the whole generation of natural things can be achieved by positing one material principle and two formal principles. For one material principle is sufficient to account for passion. But, if there were four contrary principles, and two primary contrarieties, it would be necessary that each contrariety have a different subject. For it seems that there is one primary subject for any one contrariety. And so, if, by positing two contraries and one subject, things can come to be from each other, it seems superfluous to posit another contrariety. Therefore, we must not posit more than three principles.

96. He gives the second argument at moreover, it is impossible (189b22). If there are more than three principles, it is necessary that there be many primary contrarieties. But this is impossible, because the first contrariety seems to belong to the first genus, which is one, namely, substance. Hence, all contraries that are in the genus of substance do not differ in genus, but are related as prior and posterior. For in one genus, there is only one contrariety, the first, because all other contrarieties seem to be reduced to the first one. For there are certain first contrary differentiae by which a genus is divided. Therefore, it seems that there are no more than three principles.

It must be noted, however, that each of the following statements is probable: that there is no contrariety in substances and that, in substances, there is only one primary contrariety. For if we take “substance” to mean that which is, it has no contrary. If, however, we take “substance” to mean formal differentiae in the genus of substance, then contrariety is found in them.

97. Finally, by way of summary, he concludes that there is not just one principle, nor are there more than two or three. But deciding which of these is true—that is, whether there are only two principles or three—involves much difficulty, as is clear from the foregoing.

In every coming to be, three principles are found

We will now give our own account, approaching the question first with reference to generation in its widest sense, for we shall be following the natural order of inquiry if we speak first of common characteristics and then investigate the characteristics of special cases.

We say that one thing comes to be from another thing, and one sort of thing from another sort of thing, in the case both of simple and of complex things. I mean the following. We can say, “man becomes musical,” “the non-musical becomes musical,” or “the non-musical man becomes musical.” Now, what becomes in the first and second—“man” and “non-musical”—I call simple, and what each becomes—“musical”—simple also. But, when we say, “the non-musical man becomes a musical man,” both what becomes and what it becomes are complex.

As regards one of these simple “things that become,” we say not only, “this becomes so-and-so,” but also “from being this comes to be so-and-so,” as “from being not-musical comes to be musical”; as regards the other, we do not say this in all cases, as we do not say, “from being a man he came to be musical,” but only, “the man became musical.”

When a “simple” thing is said to become something, in one case it survives through the process, but in the other it does not. For man remains a man and is such even when he becomes musical, whereas what is not musical or is unmusical does not continue to exist, either simply or combined with the subject.

With these distinctions drawn, one can gather from surveying the various cases of becoming in the way we are describing that, as we say, there must always be an underlying something—namely, that which becomes—and that this, though always one numerically, in form at least is not one. (By that I mean that it can be described in different ways.) For “to be man” is not the same as “to be unmusical.”

One part survives, while the other does not: what is not an opposite survives (for “man” survives), but “not-musical” or “unmusical” does not survive, nor does the compound of the two, namely “unmusical man.”

We speak of “becoming that from this,” instead of “this becoming that,” more in the case of what does not survive the change—“becoming musical from unmusical,” not “from man”—but there are exceptions, as we sometimes use the latter form of expression even of what survives; we speak of “a statue coming to be from bronze,” not of the “bronze becoming a statue.”

The change from an opposite that does not survive, however, is described indifferently in both ways, “becoming that from this” or “this becoming that.” We say both that “the unmusical becomes musical” and that “from unmusical he becomes musical.”

And so, both forms are used of the complex, “becoming a musical man from an unmusical man” and “unmusical man becoming a musical man.”

But there are different senses of “coming to be.” In some cases, we do not use the expression “come to be,” but “come to be accidentally.” Only substances are said to “come to be” simply. Now, in all cases other than substance, it is plain that there must be some subject, namely, that which becomes.

For we know that, when a thing comes to be of such a quantity or quality or in such a relation, time, or place, a subject is always presupposed, since substance alone is not predicated of another subject, but everything else of substance.

But that substances too, as well as anything else that can be said “to be” without qualification, comes to be from some substratum, will appear on examination. For we find in every case something that underlies, from which proceeds that which comes to be, such as animals and plants from seed.

Generally, things that come to be do so in different ways: by change of shape, as a statue; by addition, as things that grow; by taking away, as the Hermes from the stone; by putting together, as a house; by alteration, as things that “turn” in respect of their material substance.

It is plain that these are all cases of coming to be from a substratum.

Thus, clearly, from what has been said, whatever comes to be is always complex. There is, on the one hand, something that comes into existence, and again something that becomes that—the latter in two senses, either the subject or the opposite. By the “opposite,” I mean the “unmusical,” and by the “subject,” “man,” and similarly I call the absence of shape or form or order the “opposite,” and the bronze or stone or gold the “subject.”

98. After the Philosopher has investigated the number of principles by means of disputation, he here begins to determine the truth.

This section is divided into two parts.

First, he determines the truth.

Second, at we will now proceed (191a23; [120]), using the already determined truth, he rules out certain difficulties and errors of the ancients.

The first part is divided into two parts.

First, he shows that, in any natural coming to be, three things are found.

Second, at thus, if there are (190b17; [110]), he shows from this that these three things are principles.

Concerning the first part, he makes two points.

First, he states his intention;

second, he pursues his intention at we say that (189b32; [100]).

99. Because he had said above¹ that the question of whether there are only two principles of nature or three involves much difficulty, he concludes that he must first speak of generation and production as common to all the species of change. For in any change, there is found a certain coming to be. For example, when something is altered from white to black, the non-white comes to be from the white, and the black comes to be from the non-black. And the same is true of other change.

He also points out the reason for this order of procedure. It is necessary to speak first of those things that are common, and afterwards to think of those things that are proper to each thing, as was said in the beginning of the book.¹

100. Next, at we say that one thing (189b32), he develops his position.

Concerning this, he makes two points.

First, he sets forth certain things that are necessary to prove his position.

Second, at with these distinctions drawn (190a13; [103]), he proves his point.

Concerning the first part, he makes two points.

First, he sets up a certain division;

second, at as regards one (190a5; [102]), he points out the differences among the parts of the division.

101. He therefore says first (189b32) that, in any coming to be, one thing is said to come to be from another thing with reference to coming to be in regard to substantial being, or one comes to be from another with reference to coming to be in regard to accidental being. Hence, every change has two termini. The word “terminus,” however, is used in two ways, for the termini of a production or change can be taken as either simple or composite.

He explains this as follows. Sometimes we say, man becomes musical, and then the two termini of the production are simple. It is the same when we say that the non-musical becomes musical. But, when we say that the non-musical man becomes a musical man, each of the termini is a composite. For when coming to be is attributed to man or to the nonmusical, each is simple. And thus, that which becomes—namely, that to which coming to be is attributed—is said to come to be simply.

But that in which the very coming to be is terminated, which also means “to come to be simply,” is musical. Thus we say, man becomes musical, or the non-musical becomes musical.

But, when each is signified as coming to be as composed (both what becomes, or that to which the coming to be is attributed, and what it becomes, or that in which the coming to be is terminated), then we say that the non-musical man becomes musical.

For then, there is composition on the part of the subject only, and simplicity on the part of the predicate. But, when I say that the non-musical man becomes a musical man, then there is composition on the part of each.

102. Next, at as regards one (190a5), he points out two differences between the things said above. The first is that, in some of the cases mentioned above, we use two modes of speech: we say, this becomes this, and from this, this comes to be. For we say, the non-musical becomes musical, and from the non-musical, the musical comes to be. But we do not speak this way in all cases. For we do not say, the musical comes to be from man, but man becomes musical.

He points out the second difference at when a “simple” thing (190a9). He says that, when coming to be is attributed to two simple things—namely, the subject and the opposite—one of these is permanent but the other is not. For when someone has already been made musical, “man” remains. But the opposite does not remain, whether it be opposed negatively, as the non-musical, or privatively or as a contrary, as the unmusical.

Nor is the composite of subject and the opposite permanent, for the non-musical man does not remain after man has been made musical. And so coming to be is attributed to these three things, for it was said that man becomes musical, that the non-musical becomes musical, and that the non-musical man becomes musical. Of these three subjects, only the first remains complete in a production; the other two do not remain.

103. Next, at with these distinctions drawn (190a13), having assumed the foregoing, he proves his position, namely, that three things are found in any natural production.

Concerning this, he makes three points.

First, he enumerates two things that are found in any natural production.

Second, at one part survives (190a17; [105]), he proves what he had supposed.

Third, where he says, thus, clearly (190b10; [109]), he draws his conclusion.

104. He therefore first (190a13) says that, if anyone, taking for granted what was said above, wishes to consider coming to be in all the things that come to be naturally, he will agree that there must always be some subject to which the coming to be is attributed, and that that subject, although one in number and subject, is not the same in species or nature.

For when it is said of a man that he becomes musical, the man is indeed one in subject, but two in account. For man and the non-musical are not the same according to account. Aristotle does not, however, mention here the third point—that, in every generation, there must be something generated—for this is obvious.

105. Next, at one part survives (190a17), he proves the two things that he had assumed.

He shows first that the subject to which the coming to be is attributed is two in account.

Second, at but there are different (190a31; [107]), he shows that it is necessary to assume a subject in every coming to be.

He shows the first point in two ways. First (190a17), he points out that, in the subject to which the coming to be is attributed, there is something that is permanent and something that is not permanent. For that which is not an opposite of the terminus of the production is permanent, for man remains when he becomes musical, but the non-musical does not remain. And from this it is clear that man and the non-musical are not the same in account, since the one remains but the other does not.

106. Second, at we speak of (190a21), he shows the same thing in another way. With reference to the non-permanent things, it is much better to say, this comes to be from this, than it is to say, this becomes this (although this latter also may be said, but not as properly). For we say that the musical comes to be from the non-musical. We also say that the non-musical becomes musical, but this is accidental, insofar as that which happens to be non-musical becomes musical.

But, in permanent things, this is not said. For we do not say that the musical comes to be from man; rather, we say that the man becomes musical.

Even in reference to permanent things, we sometimes say, this comes to be from this, as we say that a statue comes to be from bronze. But this happens because, by the name “bronze,” we understand the “unshaped,” and so this is said by reason of the privation that is understood.

And, although we say, this comes to be from this, with reference to permanent things, yet it is better to say with reference to non-permanent things both that this becomes this and that this comes to be from this, whether non-permanent things are taken as opposites or as composed of the opposite and the subject. Thus, from this very fact that we use different modes of speech with reference to the subject and the opposite, it is clear that the subject and the opposite, such as man and the non-musical, are two in account.

107. Next, at but there are different (190a31), he proves the other point that he had assumed: in every natural production, there must be a subject. The proof of this point by argumentation belongs to metaphysics. Hence this is proved in Metaphysics 7.¹ He proves it here only by induction.

He does this first in regard to the things that come to be;

second, in regard to the modes of coming to be, at generally, things (190b4; [108]).

He therefore first (190a31) says that, since “to come to be” is used in many ways, “to come to be simply” is said only of the coming to be of substances, whereas other things are said to come to be accidentally. This is so because “to come to be” implies the beginning of existing.

Therefore, in order for something to come to be simply, it is required that previously it was not simply, which happens in those things that come to be substantially. For when a man comes to be, not only was he previously not a man, but it is true to say that he simply was not. But when a man becomes white, it is not true to say that he previously was not, but that he previously was not such.

However, those things that come to be accidentally clearly depend upon a subject. For quantity and quality and the other accidents, whose coming to be is accidental, cannot be without a subject. For only substance does not exist in a subject. Further, it is clear, if one considers the point, that even substances come to be from a subject. For we see that plants and animals come to be from seed.

108. Next, at generally, things (190b4), he shows the same thing by induction from the modes of coming to be. He says that, of things that come to be, some come to be by change of figure, as the statue comes to be from the bronze; others come to be by addition, as is clear in all instances of increase, as the river comes to be from many streams; others come to be by subtraction, as an image of Mercury comes to be from stone by sculpture; still other things come to be by composition, such as a house; and others come to be by alteration, as those things whose matter is changed, either by nature or by art. And, in all of these cases, it is apparent that they come to be from some subject.

Hence it is clear that everything that comes to be comes to be from a subject. But it must be noted that artificial things are here enumerated along with those things that come to be simply (even though artificial forms are accidents), because artificial things are in some way in the genus of substance by reason of their matter.

Or else perhaps he lists them because of the opinion of the ancients, who thought of natural things and artificial things in the same way, as will be said in book 2.¹

109. Next, at thus, clearly, from what (190b10), he draws his conclusion. He says that it has been shown from what was said above that that to which coming to be is attributed is always composed.

And since, in any production, there is “that at which the coming to be is terminated” and “that to which the coming to be is attributed,” the latter of which has two parts—namely, the subject and the opposite—it is then clear that there are three things in any coming to be: the subject, the terminus of the production, and the opposite of this terminus.

Thus, when a man becomes musical, the opposite is the non-musical, the subject is the man, and musical is the terminus of the production. And, in like manner, shapelessness and lack of figure and lack of order are opposites, while bronze and gold and stone are subjects in artificial productions.

Matter, form, and privation, the per se and per accidens principles in natural coming-to-be

Thus, if there are causes and first principles that constitute natural objects and from which they primarily are or have come to be—meaning have come to be what each is said to be in its essential nature, not what each is accidentally—then everything plainly comes to be from both subject and form.

For “musical man” is composed (in a way) of “man” and “musical”: you can analyze it into the definitions of its elements. It is clear, then, that what comes to be will come to be from these elements.

Now, the subject is one numerically, though it is two in form. (For it is the man, the gold—the “matter” generally—that is counted, for it is more of the nature of a “this,” and what comes to be does not come from it accidentally; the privation, on the other hand, and the contrary are accidental in the process.) And the positive form is one—the order, the acquired art of music, or any similar predicate.

Thus, there is one sense in which we must declare the principles to be two and another in which they are three—that is, one sense in which the contraries are the principles, such as the musical and the unmusical, the hot and the cold, or the tuned and the untuned,

and another sense in which the contraries are not the principle, since it is impossible for the contraries to be acted on by each other. But this difficulty also is solved by the fact that the substratum is different from the contraries, for it is itself not a contrary.

And so, the principles are, in a way, not more in number than the contraries, but as it were two; nor yet are they precisely two, since there is a difference of essential nature, but three. For “to be man” is different from “to be unmusical,” and “to be unformed” from “to be bronze.”

We have now stated the number of the principles of natural objects that are subject to generation and how the number is reached, and it is clear that there must be a substratum for the contraries, and that the contraries must be two.

(Yet, in another way of putting it, this is not necessary, as one of the contraries will serve to effect the change by its successive absence and presence.)

The underlying nature is an object of scientific knowledge by analogy. For as the bronze is to the statue, the wood to the bed, or the matter and the formless before receiving form to any thing that has form, so is the underlying nature to substance, that is, the “this” or existent. This, then, is one principle (though not one or existent in the same sense as the “this something”), and the definition was one, as we agreed; then, further, there is its contrary, the privation. In what sense these are two, and in what sense more, has been stated above.

Briefly, we explained first that only the contraries were principles, and later that a substratum was indispensable, and that the principles were three; our last statement has elucidated the difference between the contraries, the mutual relation of the principles, and the nature of the substratum.

Whether the form or the substratum is the essential nature of a physical object is not yet clear. But that the principles are three, and in what sense, and the way in which each is a principle, is clear. So much, then, for the question of the number and the nature of the principles.

110. After the Philosopher has shown that three things are found in every natural coming to be, he intends here to show from the foregoing how many principles of nature there are.

Concerning this, he makes two points.

First, he explains his position.

Second, at briefly, we explained (191a15; [119]), in recapitulation, he explains what has already been said and what remains to be said.

Concerning the first part, he makes two points.

First, he shows that there are three principles of nature.

Second, he names them, at the underlying nature (191a7; [118]).

Concerning the first part, he makes three points.

First, he explains the truth about the first principles of nature.

Second, at thus, there is one sense (190b29; [114]), from this disclosure of the truth, he answers the problems about the principles that were raised above.

Third, since the ancients had said that the principles are contraries, he shows whether or not contraries are always required, at we have now stated (191a3; [115]).

Concerning the first part, he makes two points.

First, he shows that there are two per se principles of nature.

Second, at now the subject (190b23; [112]), he shows that the third principle is a per accidens principle of nature.

111. With reference to the first point, he uses the following argument (190b17). Those things from which natural things are and come to be per se, and not per accidens, are said to be the principles and causes of natural things.

Whatever comes to be exists and comes to be both from subject and from form. Therefore, the subject and the form are per se causes and principles of everything that comes to be according to nature.

He proves as follows that what comes to be according to nature comes to be from subject and form. Those things into which the definition of a thing is resolved are the components of that thing, because each thing is resolved into the things of which it is composed.

But the definition of that which comes to be according to nature is resolved into subject and form. For the definition of musical man is resolved into the definition of man and the definition of musical. For if anyone wishes to define musical man, he will have to give the definitions of man and musical. Therefore, that which comes to be according to nature both is and comes to be from subject and form.

And it must be noted that he intends here to inquire not only into the principles of the coming to be but also into the principles of the being.

Hence he says significantly that things primarily are or have come to be from these first principles. And, by first principles, he means per se and not per accidens principles. Therefore, the per se principles of everything that comes to be according to nature are subject and form.

112. Next, at now, the subject (190b23), he adds the third, per accidens principle. He says that, although the subject is one in number, it is nevertheless two in species and account, as was said above.¹ For man and gold and any matter has some sort of number. This is a consideration of the subject itself, such as man or gold, which is something positive, and from which something comes to be per se and not per accidens. It is another thing, however, to consider that which happens to the subject, namely, contrariety and privation, such as to be unmusical and unshaped.

The third principle, then, is a species or form, as arrangement is the form of a house or musical is the form of a musical man, or as any of the other things that are predicated in this way. Therefore, the subject and the form are per se principles of that which comes to be according to nature, but privation or the contrary is a per accidens principle, insofar as it happens to the subject. In this way, we say that the builder is the per se active cause of the house, but the musician is a per accidens active cause of the house insofar as the builder also happens to be musical. Hence, the man is the per se cause as subject of musical man, but the non-musical is a per accidens cause and principle.

113. However, someone may object that privation does not belong to a subject while it is under some form, and thus privation is not a per accidens principle of being. Hence it must be said that matter is never without privation. For when matter has one form, it is in privation of some other form. And so, while it is coming to be that which it becomes (such as musical man), there is in the subject, which does not yet have the form, the privation of the musical itself. And so, the per accidens principle of a musical man, while he is coming to be musical, is the non-musical. For he is a non-musical man while he is coming to be musical. But when this latter form has already come to him, then there is joined to him the privation of the other form. And thus the privation of the opposite form is a per accidens principle of being.

It is clear, therefore, according to the opinion of Aristotle, that privation, which is set down as a per accidens principle of nature, is not a capacity for a form, nor an inchoate form, nor some imperfect active principle, as some say. Rather, it is the very absence of form or the contrary of form that occurs in the subject.

114. Next, at thus, there is one sense (190b29), he resolves, in the light of the truth already determined, all the preceding difficulties. He concludes from the foregoing that, in a certain respect, it must be said that there are two principles—namely, the per se principles—and that in another respect there are three, if we accept along with the per se principles also the per accidens principle.

And, in a certain respect, the principles are contraries, if one takes the musical and the non-musical, the hot and the cold, or the harmonious and the inharmonious. Yet, in another respect, if they are taken without the subject, the principles are not contraries, for contraries cannot be acted upon by each other, unless it be held that some subject is supposed for the contraries by reason of which they are acted upon by one another. And thus he concludes that the principles are not more than the contraries, for there are only two per se principles.

But there are not just two principles, for one of them according to its being is other, for the subject according to account is two, as was said.¹ And thus, there are three principles, because man and the non-musical, and bronze and the unshaped, differ according to account. Therefore, it is clear that the early opinions that argued for either part of the truth were in a certain respect true, but not altogether true.

115. Next, at we have now stated (191a3), he shows in what way two contraries are necessary and in what way they are not necessary. He says that, from what has been said, the number of natural generation’s principles is clear, and how it happens that there are this number.

For it was shown that it is necessary that two of the principles be contraries, of which one is a per se principle and the other a per accidens principle, and that something be the subject of the contraries, which is also a per se principle. But, in a certain respect, one of the contraries is not necessary for generation, for at times, it is sufficient if one of the contraries bring about the change by its absence and its presence.

116. As evidence of this we must note that, as will be said in book 5,¹ there are three species of change: generation, corruption, and motion. The difference among these is as follows.

Motion is from one positive state to another positive state, as from white to black.

Generation, however, is from the negative to the positive, as from the non-white to the white, or from non-man to man.

Corruption, on the other hand, is from the positive to the negative, as from the white to the non-white, or from man to non-man.

Therefore, it is clear that, in motion, two contraries and one subject are required. But, in generation and corruption, there is required the presence of one contrary and its absence, which is privation.

Generation and corruption, however, are found in motion. For when something is moved from white to black, white is corrupted and black comes to be. Therefore, in every natural change, subject and form and privation are required.

However, the account of motion is not found in every generation and corruption, as is clear in the generation and corruption of substances. Hence subject and form and privation are found in every change, but not a subject and two contraries.

117. This opposition is also found in substances, which are the first genus, but the opposition of contrariety is not. For substantial forms are not contraries, even though differentiae in the genus of substance are contrary, insofar as one is received along with the privation of the other, as is clear in the animate and the inanimate.

118. Next, at the underlying nature (191a7), he clarifies the above-mentioned principles. He says that the nature that is first subject to change—prime matter—cannot be known through itself, since everything that is known is known through its form. Prime matter is, moreover, considered to be the subject of every form. But it is known by analogy, that is, according to proportion.

For we know that wood is other than the form of a bench and a bed, for sometimes it underlies the one form, but at other times it underlies the other. Therefore, when we see that air at times becomes water, it is necessary to say that there is something that sometimes exists under the form of air, and at other times under the form of water. And thus, this something is other than the form of water and other than the form of air, as wood is something other than the form of a bench and other than the form of a bed. This something, then, is related to these natural substances as bronze is related to the statue, and wood to the bed, and anything material and unformed to form. And this is called “prime matter.”

This, then, is one principle of nature. It is not one as the “this something”—that is, as some determinate individual, as though it had form and unity in act—but is rather called “being” and “one” insofar as it is in potency to form. The other principle, then, is the account or form, and the third is privation, which is contrary to the form. And how these principles are two and how they are three was explained above.

119. Next, at briefly, we explained (191a15), he summarizes what has been said and points out what remains to be said.

He says, therefore, that it was said first that the contraries are principles, and afterwards that something is subjected to them, and thus there are three principles. And, from what was said just now, it is clear what the difference is between the contraries: one of them is a per se principle, and the other a per accidens principle.

And then it was pointed out how the principles are related to each other, since the subject and the contrary are one in number yet two in account.

Then it was pointed out what the subject is insofar as this could be made clear. But it has not yet been decided which is more substance, form or matter, for this will be explained at the beginning of book 2.¹

But it has been explained that the principles are three in number, how they are principles, and in what way.

And he finally draws the conclusion he principally intended, namely, that it is clear how many principles there are and what they are.

Solution of the ancients’ errors which arose from ignorance of matter

We will now proceed to show that the difficulty of the early thinkers, as well as our own, is solved in this way alone.

The first of those who studied science were misled in their search for truth and the nature of things by their inexperience, which, as it were, thrust them into another path. So, they say that none of the things that are either comes to be or passes out of existence, because what comes to be must do so either from what is or from what is not, both of which are impossible.

For what is cannot come to be (because it is already), and nothing could have come to be from what is not (because something must be present as a substratum).

So, too, they exaggerated the consequence of this and went so far as to deny even the existence of a plurality of things, maintaining that only being itself is. Such, then, was their opinion, and such the reason for its adoption.

But we say that the phrases “something comes to be from what is or from what is not” and “what is not or what is does something or has something done to it or becomes some particular thing” are to be taken (in the first way) in the same sense as “a doctor does something or has something done to him” or “is or becomes something from being a doctor.”

These expressions may be taken in two senses, and so too, clearly, may “from being” and “being acts or is acted on.” A doctor builds a house not qua doctor, but qua housebuilder, and he turns gray not qua doctor, but qua dark-haired. On the other hand, he doctors or fails to doctor qua doctor.

But we are using words most appropriately when we say that a doctor does something, undergoes something, or becomes something from being a doctor if he does, undergoes, or becomes qua doctor. Clearly, then, “to come to be so-and-so from non-being” likewise means “qua non-being.”

It was through failure to make this distinction that those thinkers gave the matter up, and through this error that they went so much further astray as to suppose that nothing else comes to be or exists apart from being itself, thus doing away with all generation.

We agree with them in holding that nothing can be simply said to come from what is not. But we nevertheless maintain that a thing may come to be from what is not in a qualified sense.

For a thing comes to be from the privation, which in its own nature is non-being—this not surviving as a constituent of the result.

Yet this causes surprise, and it is thought impossible that something should come to be in the way described from what is not.

In the same way, we maintain that nothing comes to be from being, and that being does not come to be except in a qualified sense.

In that way, however, it does, just as animal might come to be from animal, and an animal of a certain kind from an animal of a certain kind. Thus, suppose a dog to come to be from a horse. The dog would then, it is true, come to be from animal (as well as from an animal of a certain kind) but not as animal, for that is already there.

But, if anything is to become an animal not in a qualified sense, it will not be from animal; and if being, not from being—nor from non-being either, for it has been explained that, by “from not being,” we mean from non-being qua non-being.

Note further that we do not subvert the principle that everything either is or is not. This, then, is one way of solving the difficulty.

Another consists in pointing out that the same things can be explained in terms of potentiality and act. But this has been done with greater precision elsewhere.

So, as we said, the difficulties that constrain people to deny the existence of some of the things we mentioned are now solved.

For it was this reason that also caused some of the earlier thinkers to turn so far aside from the road that leads to generation and passing away and change generally. If they had come in sight of this nature, all their ignorance would have been dispelled.

120. Having determined the truth about the principles of nature, the Philosopher here excludes certain difficulties of the ancients by means of what has been determined about the principles.

He considers first the problems or errors that stem from an ignorance of matter,

and second, at others, indeed (191b35; [129]), the problems or errors that stem from an ignorance of privation.

Third, at the accurate determination (192a34; [140]), he reserves for another science the problems that arise with reference to form.

Concerning the first part, he makes two points.

First, he states the problem and the error into which the ancients fell through their ignorance of matter.

Second, at but we say that (191a34; [122]), he answers their difficulty by means of those things that have already been determined.

121. Therefore, he says first (191a23) that, after determining the truth about the principles, it must be pointed out that only in this way is every difficulty, or problem, of the ancients solved. And this is an indication that what has been said about the principles is true. For truth excludes every falsehood and difficulty. But, when something false is granted, some difficulty must remain.

Now, the problem and error of the ancient philosophers was this. The first ones who philosophically sought the truth and the nature of things were diverted into a path other than the way of truth and the way of nature. This happened to them because of the weakness of their understanding. For they said that nothing is either generated or corrupted. This is contrary to truth and contrary to nature.

The weakness of their understanding forced them to hold this position, because they did not know how to resolve the following argument, according to which it seemed to be proven that being is not generated.

If being comes to be, it comes to be either from being or from non-being. And each of these seems to be impossible, namely, that being comes to be from being or that it comes to be from non-being.

It is clearly impossible for something to come to be from being, because that which is does not come to be, for nothing is before it comes to be. And being already is; hence it does not come to be.

It is also clearly impossible for something to come to be from non-being. For it is always necessary that there be a subject for that which comes to be, as was shown above.¹ From nothing, nothing comes to be.

And from this it was concluded that there is neither generation nor corruption of being.

And those who argued in this fashion exaggerated their position to the point where they said that there are not many beings, but only one being. And they said this for the reason already given. Since they held that there is only one material principle, and since they said that nothing is caused from that one principle by way of generation and corruption, but only by way of alteration, then it follows that it would always be one according to substance.

122. Next, at but we say that (191a34), he answers the objection just mentioned.

Concerning this, he makes two points.

First, he answers the previously mentioned objection in two ways.

Second, at so, as we said (191b30; [128]), he draws the conclusion that he principally intends.

The first point is divided into two parts according to the two solutions given; the second is found at another consists in (191b27; [127]).

123. He says first (191a34) that, as far as the manner of speaking is concerned, it makes no difference whether we say that something comes to be from being or from non-being, or that being or non-being does something or is acted upon, or anything else, or whether we say this same sort of thing about a doctor (namely, that the doctor does something or is acted upon, or that something is or comes to be from the doctor).

But to say that the doctor does something or is acted upon, or that something comes to be from the doctor, has two meanings. Therefore, to say that something comes to be from being or from non-being, or that being or non-being makes something, or is acted upon, has two meanings. And the same is true regardless of the terms used; for instance, it might be said that something comes to be from white, or that the white does something or is acted upon.

That there is a twofold meaning when we use expressions such as the doctor does something or is acted upon, or that something comes to be from the doctor, he shows as follows. We say that a doctor builds. But he does not do this insofar as he is a doctor, but insofar as he is a builder. And, in like manner, we say that the doctor becomes white, but not insofar as he is a doctor, but insofar as he is black. However, in another sense, we say that the doctor heals insofar as he is a doctor, and in like manner, that the doctor becomes a non-doctor insofar as he is a doctor.

Thus we say properly and per se that the doctor does something or is acted upon, or that something comes to be from the doctor, when we attribute this to the doctor insofar as he is a doctor. But when something is attributed to him per accidens, it is not insofar as he is a doctor, but insofar as he is something else.

Therefore, it is clear that, when it is said that the doctor does something or is acted upon, or that something comes to be from doctor, this has two meanings, per se and per accidens. From this, it is clear that, when it is said that a thing comes to be from non-being, this is to be understood properly and per se if that thing should come to be from non-being insofar as it is non-being. And the same argument applies to being.

But the ancients, failing to perceive this distinction, erred insofar as they thought that nothing comes to be. And they did not think that anything other than their first material principle has substantial existence. For example, those who said that air is the first material principle held that all other things signify a certain accidental existence. Thus they excluded every substantial generation, retaining only alteration. Because of the fact that nothing comes to be per se either from non-being or from being, they thought that it would not be possible for anything to come to be from being or non-being.

124. And we also say that nothing comes to be from non-being simply and per se, but only per accidens. For what is—namely, being—is not from privation per se. And this is so because privation does not enter into the essence of the thing made. Rather a thing comes to be per se from that which is in the thing after it has already been made. Thus, the shaped comes to be from the unshaped not per se, but per accidens, for once it already has been shaped, the unshaped is not in it. But this is a remarkable way for a thing to come to be from non-being, and it seemed impossible to the ancient philosophers. Therefore, it is clear that a thing comes to be from non-being not per se, but per accidens.

125. In like manner, if it is asked whether a thing comes to be from being, we must say that a thing comes to be from being per accidens, but not per se.

He shows this by the following example. Let us suppose that a dog is generated from a horse. Granting this, it is clear that a certain animal comes to be from a certain animal, and thus animal would come to be from animal. However, animal would not come to be from animal per se, but per accidens. For it does not come to be insofar as it is animal, but insofar as it is this animal. For animal already is before the dog comes to be. For the horse already is, but is not a dog. Hence the dog comes to be per se from that which is not a dog. And if animal were to come to be per se, and not per accidens, it would be necessary for it to come to be from non-animal.

And the same is true of being. For a being comes to be from that non-being that is not that which the being comes to be. Hence a thing does not come to be per se from being or per se from non-being. For this expression per se signifies that a thing comes to be from non-being in the sense that it comes to be from non-being insofar as it is non-being, as was said.

And thus, when this animal comes to be from this animal or when this body comes to be from this body, not all animal or non-animal, nor all body or non-body, is removed from that from which the thing comes to be. And likewise, neither all being nor all non-being is removed from that from which this being comes to be. For that from which fire comes to be has some being, because it is air, and also has some non-being, because it is not fire.

126. This, then, is one way of resolving the problem raised above. But this approach is not sufficient. For if being comes to be per accidens both from being and from non-being, it is necessary to posit something from which being comes to be per se. For everything that is per accidens is reduced to that which is per se.

127. In order to designate that from which a thing comes to be per se, he adds a second approach at another consists (191b27). He says that the same thing can be explained in terms of potency and act, as is clearly indicated in another place, in Metaphysics 9.¹ Thus a thing comes to be per se from being in potency, but a thing comes to be per accidens from being in act or from non-being. He says this because matter, which is being in potency, is that from which a thing comes to be per se. For matter enters into the substance of the thing that is made.

But, from privation or from the preceding form, a thing comes to be per accidens insofar as the matter, from which the thing comes to be per se, happened to be under such a form or under such a privation.

Thus, a statue comes to be per se from bronze, but the statue comes to be per accidens both from that which does not have such a shape and from that which has another shape.

128. Finally, at so, as we said (191b30), he draws the conclusion that he principally intended. He says that we can truly say that all the difficulties, or problems, are answered by what has been said above. Driven on by certain difficulties, some of the ancients denied some of the things mentioned above, namely, generation and corruption and a plurality of substantially different things. But, once this nature (namely, matter) is understood, all of their ignorance is removed.

Matter is distinguished from privation and is neither generable nor corruptible per se

Others, indeed, have apprehended the nature in question, but not adequately. In the first place, they allow that a thing may come to be without qualification from not being, accepting on this point the statement of Parmenides. Second, they think that, if the substratum is one numerically, it must be also one in potency.

But this is a very different thing. For we distinguish matter and privation and hold that one of these, the matter, is non-being only accidentally, while the privation in its own nature is non-being, and that the matter is nearly, in a sense is, substance, while the privation in no sense is.

They, on the other hand, identify their great and small alike with not being, and that whether they are taken together as one or separately. Their triad is, therefore, of quite a different kind from ours. For they got so far as to see that there must be some underlying nature, but they make it one, and even if one philosopher makes a dyad of it, which he calls great and small, the effect is the same, for he overlooked the other nature.

For the one that persists is a joint cause, with the form, of what comes to be—a mother, as it were. But the negative part of the contrariety may often seem, if you concentrate your attention on it as an evil agent, not to exist at all. For admitting with them that there is something divine, good, and desirable, we hold that there is a principle contrary to it.

But there is another principle, which of its own nature desires and yearns for it.

But the consequence of their view is that the contrary desires its extinction. Yet the form cannot desire itself, for it is not defective; nor can the contrary desire it, for contraries are mutually destructive. The truth is that what desires the form is matter, as the female desires the male and the ugly the beautiful—only the ugly or the female not per se, but per accidens.

The matter comes to be and ceases to be in one sense, while in another it does not. As that which contains the privation, it ceases to be in its own nature, for what ceases to be—the privation—is contained within it.

But, as potentiality, it does not cease to be in its own nature, but is necessarily outside the sphere of becoming and ceasing to be.

For if it came to be, something must have existed as a primary substratum from which it should come and that should persist in it; but this is its own special nature, so that it will be before coming to be.

(For my definition of matter is just this—the primary substratum of each thing, from which it comes to be without qualification, and that persists in the result.)

And, if it ceases to be, it will pass into that at the last, so it will have ceased to be before ceasing to be.

The accurate determination of the first principle in respect of form, whether it is one or many and what it is or what they are, is the province of first philosophy, so these questions may stand over till then. But of the natural (that is, perishable) forms, we shall speak in the expositions that follow.

The above, then, may be taken as sufficient to establish that there are principles and what they are and how many there are. Now let us make a fresh start and proceed.

129. Having excluded the problems and errors of the ancient philosophers that stem from their ignorance of matter, the Philosopher here excludes the errors that stem from their ignorance of privation.

Concerning this, he makes three points.

First, he sets forth the mistakes of those who erred.

Second, at but this is a very different (192a2; [132]), he shows how this position differs from the truth determined by him above.

Third, at for the one that persists (192a13; [134]), he proves that his own opinion is true.

130. He therefore says first (191b35) that some philosophers touched upon matter but did not understand it sufficiently. For they did not distinguish between matter and privation. Hence, they attributed to matter what belongs to privation. And because privation, considered in itself, is non-being, they said that matter, considered in itself, is non-being. And so, just as a thing comes to be simply and per se from matter, so they believed that a thing comes to be simply and per se from non-being.

And they were led to hold this position for two reasons.

First, they were influenced by the argument of Parmenides, who said that whatever is other than being is non-being. Since, then, matter is other than being, because it is not being in act, they said that it is non-being simply.

Second, it seemed to them that that which is one in number or subject is also one in account. And Aristotle calls this a state of being one in potency, because things that are one in account are such that each has the same power. But things that are one in subject but not one in account do not have the same potency or power, as is clear in the white and the musical. But subject and privation are one in number, such as the bronze and the unshaped. Hence it seemed to them that they would be the same in account or in power. Hence this position accepts the unity of potency.

131. But, lest anyone, because of these words, be in doubt about what the potency of matter is and whether it is one or many, it must be pointed out that act and potency divide every genus of beings, as is clear in Metaphysics 9,¹ and in book 3 of the present work.² Hence, just as the potency for quality is not something outside the genus of quality, so the potency for substantial being is not outside the genus of substance. Therefore, the potency of matter is not some property added to its essence. Rather, matter in its very substance is potency for substantial being. Moreover, the potency of matter is one in subject with respect to many forms. But, in its account, there are many potencies according to its relation to different forms. Hence, in book 3, it will be said that to be able to be healed and to be able to be ill differ according to account.³

132. Next, at but this is a very different (192a2), he explains the difference between his own opinion and the opinion just given.

Concerning this, he makes two points.

First, he clarifies our understanding of his own opinion.

Second, at they, on the other hand (192a6; [133]), he shows what the other opinion holds.

He therefore says first that there is a great difference between a thing’s being one in number or subject and its being one in potency or account. For as is clear from the above, we say that matter and privation, although one in subject, are other in account.¹

And this is clear for two reasons.

First, matter is non-being accidentally, whereas privation is non-being per se. For “unshaped” signifies non-being, but “bronze” does not signify non-being except insofar as “unshaped” happens to be in it.

Second, matter is near to the thing and exists in some respect, because it is in potency to the thing and is in some respect the substance of the thing, since it enters into the constitution of the substance. But this cannot be said of privation.

133. Next, at they, on the other hand (192a6), he clarifies his understanding of the opinion of the Platonists. He says that the Platonists also held a certain duality on the part of matter, namely, the great and the small. But this duality is different from that of Aristotle. For Aristotle held that the duality was matter and privation, which are one in subject but different in account. But the Platonists did not hold that one of these is privation and the other matter; rather, they joined privation to both, namely, to the great and the small. They either took both of them together, not distinguishing in their speech between the great and the small, or else they took each one separately.

Hence it is clear that the Platonists, who posited form and the great and the small, held three principles completely different from those of Aristotle, who posited matter and privation and form. The Platonists realized more than the other ancient philosophers that it is necessary to suppose some one nature for all natural forms, which nature is prime matter. But they made it one both in subject and in account, not distinguishing between it and privation. For although they held a duality on the part of matter—namely, the great and the small—they made no distinction at all between matter and privation. Rather, they spoke only of matter, under which they included the great and the small. And they ignored privation, making no mention of it.

134. Next, at for the one which persists (192a13), he proves that his opinion is true.

Concerning this, he makes two points.

First, he states his position, namely, that it is necessary to distinguish privation from matter.

Second, at the matter comes to be (192a25; [139]), he shows how matter is corrupted or generated.

He treats the first point in two ways:

first, by presenting it;

second, by reducing the opposite opinion to the impossible, at but there is another principle (192a18; [136]).

135. Therefore, he says first (192a6) that this nature that is the subject—namely, matter—together with form, is a cause of the things that come to be according to nature after the manner of a mother. For just as a mother is a cause of generation by receiving, so also is matter.

But if one takes the other part of the contrariety—namely, the privation—we can imagine, by stretching our understanding, that it does not pertain to the constitution of the thing, but rather to some sort of evil for the thing. For privation is altogether non-being, since it is nothing other than the negation of a form in a subject and is outside the whole being. Thus, the argument of Parmenides that whatever is other than being is non-being has a place in regard to privation, but not in regard to matter, as the Platonists said.

He shows that privation would pertain to evil as follows. Form is something divine and very good and desirable. It is divine, because every form is a certain participation in the likeness of the divine being, which is pure act. For each thing is in act insofar as it has form. Form is very good, because act is the perfection of potency and is its good. It follows as a consequence of this that form is desirable, because every thing desires its own perfection. Privation, on the other hand, is opposed to form, since it is nothing other than the removal of form. Hence, since that which is opposed to the good and removes it is evil, it is clear that privation pertains to evil. Hence it follows that privation is not the same as matter, which is the cause of a thing like a mother.

136. Next, at but there is another principle (192a18), he proves the same thing by an argument that reduces the opposite position to the impossible in this way. Since form is a sort of good and is desirable, matter, which is other than privation and other than form, naturally seeks and desires form according to its nature. But, for those who do not distinguish matter from privation, this involves the problem that a contrary seeks its own corruption, which is absurd.

That this is so he shows as follows. If matter seeks form, it does not seek a form insofar as it is under this form. For in this latter case, the matter does not stand in need of being through this form (but every appetite exists because of a need, for an appetite is a desire for what is not possessed.)

In like manner, matter does not seek form insofar as it is under the contrary or privation, for one of the contraries is corruptive of the other, and thus something would seek its own corruption.

It is clear, therefore, that matter, which seeks form, is other in account than both form and privation. For if matter seeks form according to its proper nature, as was said, and if it is held that matter and privation are the same in account, it follows that privation seeks form, and thus seeks its own corruption, which is impossible.

Hence it is also impossible that matter and privation be the same in account. Nevertheless, matter is a this, namely, something having privation.

Hence, if the feminine seeks the masculine, and if the base seeks the good, this is not because baseness itself seeks the good, which is its contrary; rather, it seeks it accidentally, because that in which baseness happens to be seeks to be good.

And likewise femininity does not seek masculinity; rather, that in which the feminine happens to be seeks the masculine.

And in like manner, privation does not seek to be form; rather, that in which privation happens to be, matter, seeks to be form.

137. But Avicenna opposes this position of the Philosopher in three ways.

First, because matter has neither animal appetite (as is obvious in itself) nor natural appetite, whereby it would seek form. For matter does not have any form or power inclining it to anything—it is through form that, for example, the heavy naturally seeks the lowest place, insofar as it is inclined by its heaviness to such a place.

Second, he objects that, if matter seeks form, this is so because it lacks every form, or because it seeks to possess many forms at once—both of which are impossible—or because it dislikes the form that it has and seeks to have another form, and this also is meaningless. Hence it seems that we must say that matter in no way seeks form.

His third objection is as follows. To say that matter seeks form as the feminine seeks the masculine is to speak figuratively, namely, as a poet, not as a philosopher.

138. But it is easy to resolve objections of this sort. For we must note that everything that seeks something either knows that which it seeks and orders itself to it or else tends toward it by the ordination and direction of someone who knows, as the arrow tends toward a determinate mark by the direction and ordination of the archer. Therefore, natural appetite is nothing but the ordination of things to their end in accordance with their proper natures. However, a being in act is ordered to its end not only by an active power but also by its matter, insofar as it is potency. For form is the end of matter. Therefore, for matter to seek form is nothing other than matter being ordered to form as potency to act.

And, because matter still remains in potency to another form while it is under some form, there is always in it an appetite for form. This is not because of a dislike for the form that it has, nor because it seeks to be the contrary at the same time, but because it is in potency to other forms while it has some form in act.

Nor does he use a figure of speech here; rather, he uses an example. For it was said above¹ that prime matter is knowable by way of proportion, insofar as it is related to substantial forms as sensible matters are related to accidental forms. And thus, in order to explain prime matter, it is necessary to use an example taken from sensible substances. Therefore, just as he used the example of unshaped bronze and the example of the non-musical man to explain matter, so now to explain matter he uses the example of the appetite of the woman for the man and the example of appetite of the base for the good. For this happens to these things insofar as they have something that is of the account of matter.

However, it must be noted that Aristotle is here arguing against Plato, who used such metaphorical expressions, likening matter to a mother and the feminine, and form to the masculine. And so, Aristotle uses Plato’s own metaphors against him.

139. Next, at the matter comes to be (192a25), he shows how matter is corrupted. He says that in a certain respect matter is corrupted and, in a certain respect, it is not. For insofar as privation is in it, it is corrupted when the privation ceases to be in it, as if we should say that unshaped bronze is corrupted when it ceases to be unshaped. But in itself, insofar as it is a certain being in potency, it is neither generated nor corruptible.

This is clear as follows. If matter should come to be, there would have to be something that is the subject from which it comes to be, as is clear from what was said above.¹

But that which is the first subject in generation is matter. For we say that matter is the first subject from which a thing comes to be per se and not per accidens, and is in the thing after it has come to be. (And privation differs from matter on both of these points. For privation is that from which a thing comes to be per accidens and is not in the thing after it has come to be.) It follows, therefore, that matter would be before it would come to be, which is impossible.

And, in like manner, everything that is corrupted is resolved into prime matter.

Therefore, at the very time that prime matter began to exist, it would be corrupted; and, thus, if prime matter is corrupted, it will have been corrupted before it is corrupted, which is impossible.

Therefore, it is impossible for prime matter to be generated and corrupted. But by this we do not deny that it comes into existence through creation.

140. Next, at the accurate determination (192a34), he indicates that, since the errors about matter and privation have been eliminated, then the errors and problems about form should also be eliminated.¹ For some have posited separated forms (that is, ideas), which they reduced to one first idea.

And so he says that first philosophy treats questions such as whether the formal principle is one or many, and how many there are, and what kind there are. Hence, these questions will be reserved for first philosophy. For form is a principle of existing, and being as such is the subject of first philosophy. But matter and privation are principles of mutable being, which is considered by the natural philosopher. Nevertheless, we shall treat of natural and corruptible forms in the following books on this discipline.

Finally, he summarizes what has been said. It has been determined that there are principles, what the principles are, and how many there are. But it is necessary to make a new start in our study of natural science, inquiring into the principles of the science.

What is nature, and what things have it?

Of things that exist, some exist by nature and some from other causes. “By nature,” the animals and their parts exist, and the plants and the simple bodies (earth, fire, air, water)—for we say that these and the like exist “by nature.”

All the things mentioned present a feature in which they differ from things that are not constituted by nature. Each of them has within itself a principle of motion and of stationariness (in respect of place, or of growth and decrease, or by way of alteration).

On the other hand, a bed and a coat and anything else of that sort, by merit of receiving these designations—that is, insofar as they are products of art—have no innate impulse to change. But, insofar as they happen to be composed of stone or of earth or of a mixture of the two, they do have such an impulse, and just to that extent.

And this seems to indicate that nature is a principle and cause of motion and rest in that in which it is primarily and per se, and not per accidens.

I say, “not per accidens,” because (for instance) a man who is a doctor might cure himself. Nevertheless, it is not insofar as he is a patient that he possesses the art of medicine: it merely has happened that the same man is doctor and patient—and that is why these attributes are not always found together.

So it is with all other artificial products. None of them has in itself the source of its own production.

But, while that principle is in something else external to the thing in some cases (for instance, houses and the other products of manual labor),

in other cases—those that may cause a change in themselves accidentally—it lies in the things themselves (but not in virtue of what they are). Nature, then, is what has been stated.

Things have a nature that have a principle of this kind. Each of them is a substance, for it is a subject, and nature always implies a subject in which it inheres.

The term “according to nature” is applied to all these things and also to the attributes that belong to them in virtue of what they are—for instance, the property of fire to be carried upward, which neither is a nature nor has a nature, but is “by nature” or “according to nature.” What nature is, then, and the meaning of the terms “by nature” and “according to nature,” has been stated.

That nature exists it would be absurd to try to prove; for it is obvious that there are many things of this kind, and to prove what is obvious by what is not is the mark of a man who is unable to distinguish what is self-evident from what is not. (This state of mind is clearly possible. A man blind from birth might reason about colors. Presumably, therefore, such persons must be talking about words without any thought to correspond.)

141. After the Philosopher has treated the principles of natural things in book 1, he here treats the principles of natural science. Now, the things that we ought to know first in any science are its subject and the middle term by which it demonstrates.

Hence book 2 is divided into two parts.

First, he determines what things belong to the consideration of natural science;

second, at now that we have established (194b16; [176]), he points out the causes from which it demonstrates.

The first part is divided into two parts.

First, he shows what nature is.

Second, at we have distinguished (193b22; [157]), he determines what things natural science considers.

The first part is divided into two parts.

First, he shows what nature is;

second, the number of ways in which nature is used is pointed out, at some identify (193a9; [149]).

The first part is divided into two parts.

First, he shows what nature is.

Second, at that nature exists (193b3; [148]), he refutes the position of those who attempt to demonstrate that nature exists.

Concerning the first part, he makes two points.

First, he states what nature is;

second, at things have a nature (192b32; [146]), he designates those things which are called “nature.”

Concerning the first part, he makes three points.

First, he inquires into the definition of nature;

second, he arrives at the definition at and this seems to indicate (192b20; [145]);

third, he explains this definition at I say (192b23; [145]).

142. He first says, therefore, that we say that, of all beings, some are from nature, while others are from other causes, such as from art or from chance. Now, we say that the following things are from nature: every sort of animal, and their parts, such as flesh and blood, and also plants and simple bodies (namely, the elements, such as earth, fire, air, and water, which are not resolved into any prior bodies). For these and all things like them are said to be from nature. All of these things differ from the things that are not from nature, because all things of this sort seem to have in themselves a principle of motion and rest: some according to place (such as the heavy and the light, and also the celestial bodies), some according to increase and decrease (such as the animals and plants), and some according to alteration (such as the simple bodies and everything that is composed of them). But things that are not from nature, such as a bed and clothing and like things, which are spoken of as not from nature because they are from art, have in themselves no principle of change except per accidens, insofar as the matter and substance of artificial bodies are natural things. Thus, insofar as artificial things happen to be iron or stone, they have a principle of motion in them, but not insofar as they are artifacts. For a knife has in itself a principle of downward motion not insofar as it is a knife, but insofar as it is iron.

143. But it does not seem to be true that, in every change of natural things, a principle of motion is in that which is moved. For in the alteration and the generation of simple bodies, the whole principle of motion seems to be from an external agent. For example, when water is heated or air is converted into fire, the principle of the change is from an external agent.

Therefore, some say that, even in changes of this sort, an active principle of motion is in that which is moved, not perfectly, but imperfectly, which principle helps the action of the external agent. For they say that, in matter, there is a certain inchoateness of form, which they say is privation, the third principle of nature. And the generations and alterations of simple bodies are said to be from this intrinsic principle.

But this cannot be. Since a thing acts only insofar as it is in act, the named inchoate state of form cannot be an active principle, since it is not act, but a certain disposition for act. And, furthermore, even if it were a complete form, it would not act on its own subject by altering it. For the form does not act; rather, the composite acts. And the composite cannot alter itself unless there are two parts in it, one that alters and the other that is altered.

144. And so it must be said that a principle of motion is in natural things in the way in which motion belongs to them. Therefore, in those things to which it belongs to move, there is an active principle of motion. But in those things to which it belongs to be moved, there is a passive principle, which is matter. And this principle, insofar as it has a natural potency for such a form and motion, makes the motion to be natural.

And, for this reason, the production of artificial things is not natural. For even though the material principle is in that which comes to be, it does not have a natural potency for such a form. So also the local motion of the celestial bodies is natural, even though it is from a separated mover, inasmuch as there is in the celestial body itself a natural potency for such a motion. However, in heavy and light bodies, there is a formal principle of motion. (But a formal principle of this sort cannot be called the active potency to which this motion pertains. Rather, it is understood as a passive potency. For heaviness in earth is not a principle for moving, but rather for being moved.) For just as the other accidents are consequent upon substantial form, so also is place, and thus also to be moved to place. However, the natural form is not the mover. Rather, the mover is that which generates and gives such and such a form upon which such a motion follows.

145. Next, at and this seems to indicate (192b20), he concludes from the above the definition of nature in the following manner. Natural things differ from the non-natural insofar as they have a nature. But they differ from the non-natural only insofar as they have in themselves a principle of motion. Therefore, nature is nothing other than a principle and cause of motion and rest in that in which it is primarily and per se, and not per accidens.

Now principle is placed in the definition of nature as a sort of genus, and not as something absolute, for the name “nature” involves a relation to a principle. For those things are said to be born that are generated after having been joined to a generator, as is clear in plants and animals. Thus, the principle of generation or motion is called “nature.” Hence they are to be laughed at who, wishing to correct the definition of Aristotle, tried to define nature by something absolute, saying that nature is a power seated in things or something of this sort. Moreover, nature is called a principle and cause in order to point out that, in that which is moved, nature is not a principle of all motions in the same way, but in different ways, as was said above.

Moreover, he says that nature is a principle of motion and rest. For those things that are naturally moved to a place similarly, or even more so, naturally rest in that place. Because of this, fire is naturally moved upward, since it is natural for it to be there. And, for the same reason, everything can be said to be moved naturally and to rest naturally in its place. Nevertheless, this must not be understood to mean that, in everything that is moved naturally, nature is also a principle of coming to rest. For a heavenly body is indeed moved naturally, but it does not naturally come to rest. But, on the whole, it can be said that nature is a principle not only of motion but also of rest.

Further, he says in which it is in order to differentiate nature from artificial things, in which there is motion only per accidens. Then he adds primarily because, even though nature is a principle of the motion of composite things, it nevertheless is not such primarily. Hence, an animal is moved downward not because of the nature of animal insofar as it is animal, but because of the nature of the dominant element.

He explains why he says, per se and not per accidens, at I say “not in virtue of” (192b23). It sometimes happens that a doctor is the cause of his own health, and so the principle of his own coming to health is in him, but per accidens. Hence, in him the principle of coming to health is not nature. For it is not insofar as he is cured that he has the art of medicine, but insofar as he is a doctor. Hence, the same being happens to be a doctor and to be cured, and he is cured insofar as he is sick. And, so, because these things are joined per accidens, they are also at times separated per accidens. For it is one thing to be a doctor who cures, and another thing to be a sick person who is cured.

But the principle of a natural motion is in the natural body that is moved insofar as it is moved. For insofar as fire has lightness, it is carried upward. And these two things are not divided from each other such that the lightness is different than the body that is moved upward. Rather, they are always one and the same.

And all artificial things are like the doctor who cures. For none of them has in itself the principle of its own making. Rather, some of them come to be from something outside, as a house and other things that are carved by hand, while others come to be through an intrinsic principle, but per accidens, as was said. And so it has been stated what nature is.

146. Next, at things have a nature (192b32), he defines those things that are given the name “nature.” He says that those things that have in themselves a principle of their motion have a nature. And such are all subjects of nature. For nature is a subject, and so it is called matter, and nature is in a subject, and so it is called form.

147. Next, at the term “according to nature” (192b35), he explains what is according to nature. He says that to be according to nature is said both of subjects whose existence is from nature and also of the accidents that are in them and caused by such a principle. Thus, to be carried upward is not a nature itself, nor does it have nature, but it is caused by nature. And thus it has been stated what nature is, and what it is that has nature, and what is according to nature.

148. Next, at that nature exists (193b3), he denies the presumptuous position of those who wish to demonstrate that nature exists. He says that it is ridiculous for anyone to attempt to demonstrate that nature exists. For it is manifest to the senses that many things are from nature that have in themselves the principle of their own motion. Moreover, to wish to demonstrate the obvious by what is not obvious is the mark of a man who cannot judge what is known in itself from what is not known in itself. For when he wishes to demonstrate that which is known in itself, he uses that which is known in itself as if it were not known in itself.

And it is clear that some people do this. A man who is born blind may sometimes reason about colors. But that which he uses as a principle is not known to him per se, because he has no understanding of the thing. Rather, he only uses names. For our knowledge has its origin from the senses, and he who lacks one sense lacks one science. Hence those who are born blind and who never sense color cannot understand anything about color, and so they use the unknown as if it were known. And the converse applies to those who wish to demonstrate that nature exists. For they use the known as if it were not known. The existence of nature is known per se, insofar as natural things are manifest to the senses. But what the nature of each thing is, or what the principle of its motion is, is not manifest.

Hence it is clear from this that Avicenna unreasonably attempted to disprove what Aristotle has said, wishing that it were possible to prove the existence of nature. However, Avicenna did not wish to prove this from natural things, for no science proves its own principles. But ignorance of moving principles does not mean that the existence of nature is not known through itself, as was said.

Nature is both matter and form, but primarily form

Some identify the nature or substance of a natural object with that immediate constituent of it that, taken by itself, is without arrangement—for instance, the wood is the “nature” of the bed and the bronze the “nature” of the statue.

As an indication of this, Antiphon points out that, if you planted a bed and the rotting wood acquired the power of sending up a shoot, it would not be a bed that would come up, but wood—which shows that the arrangement in accordance with the rules of the art is accidental, while the real nature is the other, which, further, persists continuously through the process of making.

But, if the material of each of these objects has itself the same relation to something else—say bronze (or gold) to water, bones (or wood) to earth and so on—they say that would be their nature and essence.

Consequently, some assert earth, and others fire or air or water or some or all of these, to be the nature of the things that are. For whatever any one of them supposed to have this character—whether one thing or more than one thing—this or such is said to be the whole of substance, all else being its passions, states, or dispositions. Every such thing they held to be eternal (for it could not pass into anything else), but they held other things to come into being and cease to be times without number. This, then, is one account of nature—namely, that it is the immediate material substratum of things that have in themselves a principle of motion or change.

In another way, nature is the form and species which is according to the account. For the word “nature” is applied to what is according to nature and the natural in the same way as “art” is applied to what is artificial or a work of art. We should not say in the latter case that there is anything artificial about a thing, if it is a bed only potentially, not yet having the form of a bed; nor should we call it a work of art. The same is true of natural compounds.

What is potentially flesh or bone has not yet its own nature and does not exist until it receives the form specified in the account, which we name in defining what flesh or bone is. Thus, in the second sense of “nature,” it would be the form and species (not separable except in account) of things that have in themselves a source of motion.

(The combination of the two, such as man, is not “nature,” but “from nature” or “natural.”)

The form indeed is nature more than is the matter; for a thing is more properly said to be what it is when it has attained to fulfilment than when it exists potentially.

Again, man is born from man, but not bed from bed. That is why people say that the figure is not the nature of a bed, but the wood is—if the bed sprouted, a bed would not come up, but wood. But, even if the figure is art, then on the same principle, the form of man is his nature. For man is born from man.

We also speak of a thing’s nature in the sense of generation by which its nature is attained.

“Nature” in this sense is not like doctoring, which leads not to the art of doctoring, but to health. Doctoring must start from the art, not lead to it.

But it is not in this way that nature [in the one sense] is related to nature [in the other].

What grows, qua growing, grows from something into something. Into what, then, does it grow?

Not into that from which it arose, but into that to which it tends. The form, then, is nature.

“Form” and “nature,” it should be added, are in two senses. For the privation too is in a way form. But whether in unqualified generation there is privation—that is, a contrary to what comes to be—we must consider later.

149. Having shown what nature is, the Philosopher here points out the number of ways in which “nature” is used.

He shows first that nature is predicated of matter;

second, that it is predicated of form, at another account (193a30; [151]).

Concerning the first point, we must note that the ancient natural philosophers, being unable to arrive at prime matter, as was said above,¹ held that some sensible body, such as fire or air or water, is the prime matter of all things. And so it followed that all forms come to matter as to something existing in act, as happens in artificial things. For the form of knife comes to iron already existing in act. And so they adopted an opinion about natural forms similar to that which is true of artificial forms.

Therefore, he says first that it seems to some that that which is primarily in each thing and that, considered in itself, is unformed is the substance and nature of natural things, as if we would say that the nature of a bed is wood, and the nature of a statue is bronze. For wood is in the bed and is, when considered in itself, not formed. And Antiphon said that the following is a sign of this. If one should bury a bed in the earth, and if the wood by rotting should acquire the potency to germinate something, that which is generated will not be a bed, but wood. Now, since the substance is that which remains permanent, and since it belongs to nature to generate what is like itself, he concluded that every disposition in respect to any law of reason or art is an accident. And that which remains permanent is substance, which continually undergoes change of dispositions of this sort.

Having supposed, therefore, that the forms of artificial things are accidents, and that matter is substance, Antiphon assumed the other proposition: just as the bed and statue are related to bronze and wood, so also each natural thing is related to some other thing that is its matter. Thus, bronze and gold are related to water (because the matter of all meltable things seems to be water), and bone and wood are related to earth, and it is the same with all other natural things. Hence, he concluded that the material things that subsist under natural forms are their nature and substance. And, because of this, some have said that earth is the nature and substance of all things (for example, the first theological poets); but the later philosophers chose fire or air or water, or some of these or all of them, as is clear from what was said above.¹

For they said that there are as many substances of things as there are material principles. And they said that all other things are accidents of these material principles, either as passions, or as habits, or as dispositions, or as anything else that is reduced to the genus of accident. Thus, one difference they posited between material and formal principles is that they said that they differed as substance and accident. There is, however, another difference, for they also said that these principles differ as the permanent and the corruptible. Since they held that each of the aforementioned simple bodies is a material principle, they said it was permanent, for they did not say that they were changed into each other. But they said that all other things come to be and are corrupted infinitely. For example, if water is the material principle, they said that water is never corrupted, but remains water in all things as their substance. But they said that bronze and gold and other things of this sort are corrupted and generated infinitely.

150. This position is in part true and in part false. With reference to the point that matter is the substance and the nature of natural things, it is true. For matter enters into the constitution of the substance of each natural thing. But, insofar as they said that all forms are accidents, this position is false. Thus, from this opinion and from his argument, Aristotle comes to the true conclusion: nature in one way is called matter, which underlies each natural thing that has in itself a principle of motion or of some sort of change. For motion is a species of change, as will be said in book 5.¹

151. Next, at another account (193a30), he shows that the form is also called nature.

Concerning this, he makes two points.

First, he states his position, namely, that form is nature;

second, at “form” and “nature” (193b18; [156]), he explains the diversity of forms.

He explains the first point with three arguments.

He first says, therefore, that “nature” is used in another way to refer to the form and species, which is according to the account—that is, from which the account of the thing is constituted. He proves this by the following argument.

Just as art belongs to a thing insofar as it is according to art and the artificial, so also nature belongs to a thing insofar as it is according to nature and the natural. But we do not say that that which is only in potency to that which is artificial has anything of art, because it does not yet have the species of a bed (for instance). Therefore, in natural things, that which is potentially flesh and bone does not have the nature of flesh and bone before it takes on the form in respect to which the definitive account of the thing is established (namely, that through which we know what flesh and bone are).

The nature is not yet in it before it has the form. Therefore, the nature of natural things that have in themselves a principle of motion is in another way the form. And this form, although it is not separated from the matter in the thing, still differs from the matter by reason. For as bronze and the shapeless, although one in subject, are different in account, so also are matter and form. He says this because, unless form were other than matter according to the account, the ways in which matter is called nature and form is called nature would not be different.

152. Moreover, one might believe that, since both matter and form are called nature, then the composite could also be called nature. For substance is predicated of form and of matter and of the composite. But he denies this, saying that the composite of matter and form, such as a man, is not the nature itself, but is some thing from nature. For nature has the account of a principle, but the composite has the account of being from a principle.

153. From the foregoing argument, he proceeds further to show that form is nature more than is matter. For a thing is said to be greater insofar as it is in act, rather than insofar as it is in potency. Hence form, according to which a thing is natural in act, is nature more than matter, according to which a thing is something natural in potency.

154. He gives the second argument at again, man is (193b8). He says that, although a bed does not come to be from a bed, as Antiphon said, man does come to be from man.

Hence, what they say is true, namely, that the form of bed is not the nature, but the wood is. For if wood should germinate, a bed would not come to be, but wood. Therefore, as this form, which does not arise through germination, is not nature, but art, so the form that arises from generation is nature. But the form of a natural thing does arise through generation, for man comes to be from man. Therefore, the form of a natural thing is nature.

155. He gives his third argument at we also speak (193b12). Nature can be signified as a generation—for instance, if we should call it birth. Thus, “nature” in the sense of generation—that is, birth—is the way to nature. For the difference between actions and passions is that actions are named from their principles while passions are named from their terminations. For each thing is named from act, which is the principle of action and the termination of passion.

But naming is not the same in passions and actions. For medication is not called the way to medicine, but the way to health. It is necessary for medication to proceed from medicine, not to medicine. But nature in the sense of generation, or birth, is not related to nature in the way in which medication is related to medicine.

Rather, it is related to nature as to a termination, since it is a passion. For that which is born, insofar as it is born, comes from something to something. Hence, that which is born is named from that to which it proceeds, and not from that from which it proceeds. But that to which birth tends is form. Therefore, form is nature.

156. Next, at “form” and “nature” (193b18), he shows that the nature that is form is used in two ways, namely, of the incomplete form and the complete form. This is clear in accidental generation, for example, when something becomes white. For whiteness is a complete form, and the privation of whiteness is in some way a species, insofar as it is joined to blackness, which is an imperfect form. But whether or not, in simple generation, which is the generation of substances, there is something that is a privation and also a contrary, such that substantial forms are contraries, must be considered later in book 5 and in De generatione et corruptione.¹

How physics and mathematics differ

We have distinguished, then, the different ways in which the term “nature” is used. The next point to consider is how the mathematician differs from the physicist.

Obviously, physical bodies contain surfaces and volumes and lines and points, and these are the subject matter of mathematics.

Further, is astronomy different from physics, or a department of it? It seems absurd that the physicist should be supposed to know the nature of sun or moon but not to know any of their essential attributes, particularly as the writers on physics obviously do discuss their shape also and whether the earth and the world are spherical or not.

Now, the mathematician, though he too treats of these things, nevertheless does not treat of them as the limits of a physical body; nor does he consider the accidents indicated as the accidents of such bodies.

That is why he separates them. For in thought, they are separable from motion, and it makes no difference if they are separated, nor does any falsity result.

The holders of the theory of Forms do the same, though they are not aware of it, for they separate the objects of physics, which are less separable than those of mathematics.

This becomes plain if one tries to state in each of the two cases the definitions of the things and of their accidents. “Odd” and “even,” “straight” and “curved,” and likewise “number,” “line,” and “figure,” do not involve motion. Not so “flesh” and “bone” and “man”—these are defined like “snub nose,” not like “curved.”

Similar evidence is supplied by the more physical of the branches of mathematics, such as optics, harmonics, and astronomy. These are in a way the converse of geometry. While geometry investigates physical lines, but not qua physical, optics investigates mathematical lines, but qua physical, not qua mathematical.

157. After the Philosopher has explained what nature is and how many ways the name is used, he here intends to show what it is that natural science considers.

This section is divided into two parts.

First, he shows how the natural philosopher differs from the mathematician;

second, at since “nature” has (194a12; [166]), he designates that to which the consideration of natural science extends.

Concerning the first part, he makes three points.

First, he states the question;

second, at obviously, physical bodies (193b23; [158]), he gives his reasons for raising the question;

third, he answers the question at now, the mathematician (193b31; [159]).

He therefore first says that, after the uses of the name “nature” have been determined, it is necessary to consider how the mathematician differs from the natural philosopher.

158. Next, at obviously, physical bodies (193b24), he gives his reasons for raising the question.

The first of these is as follows. Whenever sciences consider the same subjects, either they are the same science or one is a part of the other. But the mathematical philosopher considers points and lines and surfaces and bodies, and so does the natural philosopher. (For the latter proves from the fact that natural bodies have surfaces and volumes—that is, surfaces and solidity—and lengths and points. Moreover, the natural philosopher must consider all things that are in natural bodies.) Therefore, it seems either that natural science and mathematics are the same or that one is a part of the other.

He gives the second reason at further, is astronomy (193b25). In connection with this reason, he raises the question whether astronomy is altogether other than natural philosophy or a part of it. For it is clear that astronomy is a part of mathematics. Hence, if it is also a part of natural philosophy, it follows that mathematics and physics agree at least in this part.

That astronomy is a part of physics he proves in two ways.

First, by the following argument. To whomever it belongs to know the substances and natures of certain things also belongs the consideration of their accidents. But it belongs to the natural philosopher to consider the nature and substance of the sun and the moon, since they are certain natural bodies. Therefore, it belongs to the natural philosopher to consider their per se accidents.

He proves this also from the custom of the philosophers. For natural philosophers are found to have treated the shape of the sun and of the moon and of the earth and of the whole world. And these are topics that claim the attention of the astronomers. Therefore, astronomy and natural science agree not only in having the same subjects but also in considering the same accidents and in demonstrating the same conclusions. Hence it seems that astronomy is a part of physics, and as a result, physics does not differ totally from mathematics.

159. Next, at now, the mathematician (193b31), he answers the question raised above.

Concerning this, he makes two points.

First, he gives his solution;

second, he confirms it at this becomes plain (194a1; [163]).

Concerning the first part, he makes three points.

First, he answers the question;

second, at that is why he separates (193b33; [161]), he draws a sort of corollary from the above;

third, at the holders of (193b35; [162]), he excludes an error.

160. He first (193b31) says, therefore, that the mathematician and the natural philosopher treat the same things—namely, points, lines, surfaces, and things of this sort—but not in the same way.

For the mathematician does not treat these things insofar as each of them is a boundary of a natural body, nor does he consider those things that belong to them insofar as they are the boundaries of a natural body. But this is the way in which natural science considers them. And it is not inconsistent that the same thing should fall under the consideration of different sciences according to different points of view.

161. Next, at that is why he separates (193b33), he infers a sort of corollary from what he has just said. Because the mathematician does not consider lines, points, surfaces, and things of this sort, or their accidents, insofar as they are the boundaries of a natural body, he is said to abstract from sensible and natural matter. And the reason why he is able to abstract is this: according to the intellect, these things are abstracted from motion.

As evidence for this reason, we must note that many things are joined in the thing, but the understanding of one of them is not derived from the understanding of another.

Thus, white and musical are joined in the same subject, but nevertheless the understanding of one of these is not derived from an understanding of the other. And, so, one can be separately understood without the other. And this one is understood as abstracted from the other.

It is clear, however, that the posterior is not in the notion of the prior, but conversely. Hence, the prior can be understood without the posterior, but not conversely.

Thus it is clear that animal is prior to man, and man is prior to this man (for man is had by addition to animal, and this man by addition to man).

And because of this, man is not in the notion of animal nor Socrates in the notion of man.

Hence, animal can be understood without man, and man without Socrates and other individuals. And this is to abstract the universal from the particular.

In like manner, among all the accidents that come to substance, quantity comes first, and then the sensible qualities, and actions and passions, and the motions consequent upon sensible qualities. Therefore quantity does not embrace in its intelligibility the sensible qualities or the passions or the motions. Yet it does include substance in its intelligibility. Therefore, quantity can be understood without matter, which is subject to motion, and without sensible qualities, but not without substance. And thus quantities and those things that belong to them are understood as abstracted from motion and sensible matter, but not from intelligible matter, as is said in Metaphysics 7.¹

Since, therefore, the objects of mathematics are abstracted from motion according to the intellect, and since they do not include in their intelligibility sensible matter, which is a subject of motion, the mathematician can abstract them from sensible matter. And it makes no difference as far as the truth is concerned whether they are considered one way or the other.

For although the objects of mathematics are not separated according to existence, the mathematicians do not lie in abstracting them in their understanding, because they do not assert that these things exist apart from sensible matter (for this would be a lie). But they consider them without any consideration of sensible matter, which can be done without lying. Thus, one can truly consider the white without the musical, even though they exist together in the same subject. But it would not be a true consideration if one were to assert that the white is not musical.

162. Next, at the holders of the theory (193b35), he excludes one of Plato’s errors from what he has said. Since Plato was puzzled as to how the intellect could truly separate those things that were not separated in their existence, he held that all things that are separated in the understanding are separated in reality.

Hence, he not only held that mathematical entities are separated because the mathematician abstracts from sensible matter, but he even held that natural things themselves are separated, because natural science is of universals and not of singulars. Hence he held that man is separated, and horse, and stone, and other such things. And he said these separated things are ideas, although natural things are less abstract than mathematical entities. For mathematical entities are altogether separated from sensible matter in the understanding, because sensible matter is included in the understanding of the mathematicals neither in the universal nor in the particular. But some sensible matter, though not individual matter, is included in the understanding of natural things. For in the understanding of man, flesh and bone is included, but not this flesh and this bone.

163. Next, at this becomes plain (194a1), he clarifies the solution he has given in two ways:

first, by means of the difference in the definitions that the mathematician and the natural philosopher assign;

second, by means of the intermediate sciences, at similar evidence (194a7; [164]).

He therefore first says that what has been said of the different modes of consideration of the mathematician and the natural philosopher will become evident if one attempts to give definitions of the mathematicals, and of natural things and of their accidents.

For the mathematicals—such as equal and unequal, straight and curved, and number, line, and figure—are defined without motion and matter, but this is not so with flesh and bone and man.

Rather, the definition of these latter is like the definition of the snub, in which definition a sensible subject is placed, namely, nose. But this is not the case with the definition of the curved, in which definition a sensible subject is not placed.

And, thus, from the very definitions of natural things and of the mathematicals, what was said above about the difference between the mathematician and the natural philosopher is apparent.

164. Next, at similar evidence (194a7), he proves the same thing by means of those sciences that are intermediates between mathematics and natural philosophy. Those sciences are called intermediate sciences that take principles abstracted by the purely mathematical sciences and apply them to sensible matter.

For example, perspective applies to the visual line those things that are demonstrated by geometry about the abstracted line, and harmony (or music) applies to sound those things that arithmetic considers about the proportions of numbers, and astronomy applies the consideration of geometry and arithmetic to the heavens and its parts.

However, although sciences of this sort are intermediates between natural science and mathematics, they are here said by the Philosopher to be more natural than mathematical, because each thing is named and takes its species from its terminus. Hence, since the consideration of these sciences is terminated in natural matter, they are more natural than mathematical sciences, even though they proceed by mathematical principles.

He says, therefore, that sciences of this sort are established in a way contrary to the sciences that are purely mathematical, such as geometry or arithmetic. For geometry considers the line that has existence in sensible matter, which is the natural line. But it does not consider it insofar as it is in sensible matter, insofar as it is natural, but abstractly, as was said. But perspective conversely takes the abstract line that is in the consideration of mathematics and applies it to sensible matter, thus treating it not insofar as it is a mathematical, but insofar as it is a physical thing. Therefore, from this difference between intermediate sciences and the purely mathematical sciences, what was said above is clear. For if intermediate sciences of this sort apply the abstract to sensible matter, it is clear that mathematics conversely abstracts those things that are in sensible matter.

165. And from this it is clear what his answer is to the objection raised above concerning astronomy. For astronomy is a natural science more than a mathematical science.

Hence it is no wonder that astronomy agrees in its conclusions with natural science. However, since it is not a purely natural science, it demonstrates the same conclusion through another middle term.

Thus, the fact that the earth is spherical is demonstrated by natural science by a natural middle term, namely, because its parts equally and in all directions come together at the center. But this is demonstrated by astronomy from the figure of the lunar eclipse, or from the fact that the same stars are not seen from every part of the earth.

Physics considers not only matter but also every form existing in matter

Since “nature” has two senses, the form and the matter, we must investigate its objects as we would the essence of snubness. That is, such things neither are independent of matter nor can be defined in terms of matter only.

Here too, indeed, one might raise a difficulty. Since there are two natures, with which is the physicist concerned? Or should he investigate the combination of the two? But if the combination of the two, then also each severally. Does it belong then to the same or to different sciences to know each severally?

If we look at the ancients, physics would seem to be concerned with the matter. (It was only very slightly that Empedocles and Democritus touched on the forms and the essence.)

But if, on the other hand, art imitates nature, and it is the part of the same discipline to know the form and the matter up to a point—for instance, the doctor has a knowledge of health and also of bile and phlegm, in which health is realized, and the builder both of the form of the house and of the matter, namely that it is bricks and beams, and so forth—if this is so, it would be the part of physics also to know nature in both its senses.

Again, “that for the sake of which the thing comes to be,” or the end, belongs to the same department of knowledge as the means. But the nature is the end or “that for the sake of which.”

For if a thing undergoes a continuous change and there is a stage that is last, this stage is the end or “that for the sake of which.” (That is why the poet was carried away into making an absurd statement when he said, “he has the end for the sake of which he was born.” For not every stage that is last claims to be an end, but only that which is best.)

For the arts make their material (some simply make it, others make it operative), and we use everything as if it was there for our sake. (We also are in a sense an end. “That for the sake of which” has two senses; the distinction is made in the Metaphysics.)

Therefore, the arts that govern the matter and have knowledge are two: the art that uses the product, and the art that directs the production of it and is architectonic.

That is why the using art also is in a sense architectonic; but it differs in that it knows the form, while the art that is architectonic as being concerned with production knows the matter.

For the navigator knows and prescribes what sort of form a helm should have, but the ship builder knows from what wood it should be made and by means of what operations.

In the products of art, however, we make the material with a view to the function, while in the products of nature the matter is there all along.

Again, matter is a relative term: to each form there corresponds a special matter.

How far, then, must the physicist know the form or essence? Up to a point, perhaps, as the doctor must know sinew or the smith bronze (that is, until he understands the purpose of each);

and the physicist is concerned only with things whose forms are separable indeed but do not exist apart from matter. Man is begotten by man and by the sun as well. The mode of existence and essence of the separable it is the business of the primary type of philosophy to define.

166. Having shown the difference between natural science and mathematics, the Philosopher here explains that to which the consideration of natural science extends.

Concerning this, he makes two points.

First, he shows that it pertains to natural science to consider both form and matter;

second, at how far then (194b9; [175]), he points out the limits of natural science in its consideration of form.

Concerning the first part, he makes two points.

First, he draws his conclusion from what has gone before;

second, at here too, indeed (194a15; [168]), he raises difficulties against his own position.

167. He therefore says first (194a12) that, since nature is said in two ways—namely, of the matter and of the form, as was said above¹—so must it be considered in natural science. Thus, when we consider what the snub is, we not only consider its form, its curvature, but we also consider its matter, namely, the nose. Hence, in natural science, nothing is considered without sensible matter, in respect both to matter and to form.

And it must be noted that this argument of Aristotle includes two approaches.

In one way, we can argue as follows. The natural philosopher ought to consider nature. But nature is both form and matter. Therefore, he ought to consider both matter and form.

The other way is as follows.

The natural philosopher differs from the mathematician, as was said above,¹ because the consideration of the natural philosopher is like the consideration of the snub, whereas that of the mathematician is like the consideration of the curved.

But the consideration of the snub is a consideration of the form and the matter. Therefore, the consideration of the natural philosopher is a consideration of both.

168. Next, at here too, indeed (194a15), he raises two questions about to what he has just said.

The first is as follows. Since “nature” is used for matter and form, is natural science about the matter alone, or the form alone, or about that which is a composite of both?

The second problem is as follows. Supposing that natural science does consider both, is it the same natural science that considers form and matter, or are there different sciences that consider each?

169. Next, at if we look at the ancients (194a18), he answers the above-mentioned problems, and especially the second, showing that it pertains to the consideration of the same natural science to consider both form and matter. For the first question seems to have been adequately answered by what he has said, namely, that the consideration of natural science is the same as the consideration of what the snub is.

Concerning this, therefore, he makes two points.

First, he states what the ancients seem to have thought. He says that, if one wishes to look at the sayings of the ancient natural philosophers, it seems that, for them, natural science is concerned only with matter. For they said either nothing about form, or some small bit, as when Democritus and Empedocles touched upon it insofar as they held that a thing comes to be from many according to a determinate mode of mixing or joining.

170. Second, at but if on the other hand (194a21), he proves his position with three arguments.

The first of these is as follows. Art imitates nature. Therefore, natural science must be related to natural things as the science of the artificial is related to artificial things. But it belongs to the same science of the artificial to know the matter and the form up to a certain point, as the doctor knows health as a form and bile and phlegm and such things as the matter in which health is. For health consists in a harmony of humors. And, in like manner, the builder considers the form of the house and also the bricks and the wood that are the matter of the house. And so it is in all the other arts. Therefore, it belongs to the same natural science to know both the matter and the form.

171. The reason for saying that art imitates nature is as follows. Knowledge is the principle of operation in art. But all of our knowledge is through the senses and taken from sensible, natural things. Hence, in artificial things, we work to a likeness of natural things. And so, imitable natural things are produced through art, because all nature is ordered to its end by some intellective principle, such that the work of nature thus seems to be the work of intelligence as it proceeds to certain ends through determinate means. And this order is imitated by art in its operation.

172. He gives the second argument at again, “that for the sake of which” (194a27). It belongs to the same science to consider the end and those things that are for the end. This is so because the reason for those things that are for the end is taken from the end.

But nature, which is form, is the end of matter. Therefore, it belongs to the same natural science to consider matter and form.

173. That form is the end of matter he proves as follows. In order for something to be the end of a continuous motion, two things are required.

First, it must be the final stage of the motion;

second, it must be that for the sake of which the thing comes to be.

For something can be last but not be that for the sake of which something comes to be, and hence not have the account of an end.

And, because it is in the account of an end that it be that for the sake of which something comes to be, the poet maintained that it would be a jest to say that he has the end for the sake of which he was born.

This seemed to him to be a trifle, for just as if we were to say man animal because animal is in the account of man, so also that for the sake of which something comes to be is in the account of end.

For the poet wished to say that not every last thing is an end, but rather only that which is last and best. This is that for the sake of which something comes to be.

And, indeed, that the form is last in generation is per se evident. But that it is that for the sake of which something comes to be with respect to matter is made clear by a simile taken from the arts. Certain arts make matter, and of these, some make it simply (as the art of the potter makes tiles that are the matter of a house), while others make it operative, that is, they dispose matter preexisting in nature for the reception of a form (as the art of the carpenter prepares wood for the form of a ship). It must further be noted that we use all things that are made by art as though they exist for us. For we are, in a sense, the end of all artificial things. And he says in a sense because, as is said in first philosophy,¹ that for the sake of which something comes to be is used in two ways: “of which” and “for which.” Thus, the end of a house as “of which” is the dweller, as “for which” it is a dwelling.

From this, therefore, we can conclude that there are two arts that govern the matter and have knowledge, that is, those that direct the arts that make matter and those that pass judgment on the former.

Thus, there is one art that uses and another art that makes the artifact, namely, by inducing the form. And this latter art is architectonic with reference to that which disposes matter.

Thus the art of the ship builder is architectonic with respect to the art of the carpenter who cuts wood. Hence it is necessary that the art that uses be in a sense architectonic, the principal art, with respect to the productive art.

Therefore, although both are architectonic, meaning the art that uses and the productive art, they nevertheless differ. For the art that uses is architectonic insofar as it knows and passes judgment on the form, whereas the other, which is architectonic as productive of the form, knows the matter, that is, passes judgment on the matter.

He makes this clear by an example. The use of a ship pertains to the navigator; thus, the art of the navigator is an art that uses, and hence it is architectonic with respect to the art of the ship builder and knows and passes judgment on the form. He says that the navigator knows and judges what the shape of the rudder should be.

The other art, however—namely, the art of the ship builder—knows and judges from what wood and from what kind of wood the ship should be made. It is clear, therefore, that the art that produces the form directs the art that makes or disposes the matter. However, the art that uses the completed artifact directs the art that produces the form.

From this, then, we can conclude that matter is related to form as form is related to use. But use is that for the sake of which the artifact comes to be. Therefore, form also is that for the sake of which matter is in artificial things. And so, just as in those things that are according to art we make matter for the sake of the work of art, which is the artifact itself, likewise matter is in natural things from nature, and not made by us. Nevertheless, it has the same ordination to form: it is for the sake of form.

Hence, it follows that it belongs to the same natural science to consider the matter and the form.

174. He gives the third argument at again, matter is (194b8). The argument is as follows. Things that are related belong to one science. But matter is one of the things that are related, because it is spoken of in relation to form. However, it is not spoken of as if matter itself were in the genus of relation, but rather because a proper matter is determined for each form. And he adds that there must be a different matter under a different form. Hence, it follows that the same natural science considers form and matter.

175. Next, at how far, then (194b9), he shows to what extent natural science considers form.

Concerning this, he makes two points.

First, he raises the question of to what extent natural science should consider the form and quiddity of a thing. (For to consider the forms and quiddities of things absolutely seems to belong to first philosophy.)

Second, he answers the question by saying that, as the doctor considers nerves, and the smith considers bronze, up to a certain point, so also the natural philosopher considers forms. For the doctor does not consider nerve insofar as it is nerve, for this belongs to the natural philosopher. Rather, he considers it as a subject of health. So also the smith does not consider bronze insofar as it is bronze, but insofar as it is the subject of a statue or something of the sort.

So also the natural philosopher does not consider form insofar as it is form, but insofar as it is in matter. And thus, as the doctor considers nerve only insofar as it pertains to health, for the sake of which he considers nerve, so also the natural philosopher considers form only insofar as it has existence in matter.

And so, the last things considered by natural science are forms that are, indeed, in some way separated but that have existence in matter. And rational souls are forms of this sort. For such souls are indeed separated, insofar as the intellective power is not the act of a corporeal organ, as the power of seeing is the act of an eye. But they are in matter insofar as they give natural existence to such a body. That such souls are in matter he proves as follows. The form of anything generated from matter is a form that is in matter. For the generation is terminated when the form is in matter. But man is generated from matter and by man, as by a proper agent, and by the sun, as by a universal agent with respect to the generable. Hence, it follows that the soul, which is the human form, is a form in matter. Thus, the consideration of natural science about forms extends to the rational soul.

But how forms are totally separated from matter, and what they are, or even how this form, the rational soul, exists insofar as it is separable and capable of existence without a body, and what it is according to its separable essence, are questions that pertain to first philosophy.

Physics determines what and how many causes there are

Now that we have established these distinctions, we must proceed to consider causes, their character and number. Knowledge is the object of our inquiry, and men do not think they know a thing till they have grasped the why of it (which is to grasp its primary cause). So clearly we too must do this as regards both generation and passing away and every kind of physical change, in order that, knowing their principles, we may try to refer to these principles each of our problems.

In one sense, then, that from which something comes to be when it is in it is called “cause”—for instance, the bronze of the statue, the silver of the bowl, and the genera of these things.

In another sense, the form or the exemplar—the statement of the essence—and its genera are called “causes” (i.e., of the octave, the relation of 2:1, and generally number), and the parts in the definition.

Again, that from which there is a beginning of motion or rest is a cause, such as the man who gave advice, the father as cause of the child, and generally what makes of what is made and what causes change of what is changed.

Again, the end or “that for the sake of which” a thing is done is a cause: health is the cause of walking about.

(“Why does he walk?” we say, “That he may become healthy,” and, having said that, we think we have assigned the cause.)

The same is true also of all the intermediate steps that are brought about through the action of something else as means toward the end, such as reduction of flesh, purging, drugs, or surgical instruments as means toward health.

All these things are for the sake of the end, though they differ from one another in that some are activities and others are instruments. This perhaps exhausts the number of ways in which the term “cause” is used.

As the word has several senses, it follows that there are several causes of the same thing (not merely accidentally):

for instance, both the art of the sculptor and the bronze are causes of the statue. These are causes of the statue qua statue, not in virtue of anything else that it may be—only not in the same way, the one being the material cause, the other the cause from which the motion comes.

Some things cause each other reciprocally, as hard work causes fitness and vice versa, but not in the same way: the one is the end, and the other is the origin of change.

Further, the same thing is the cause of contrary results. For that which brings about one result by its presence is sometimes blamed for bringing about the contrary by its absence. Thus, we ascribe the wreck of a ship to the absence of the pilot, whose presence was the cause of its safety.

All the causes now mentioned fall into four obvious divisions. The elements are the causes of syllables, earth of vases, fire and the like of bodies, the parts of the whole, and the premises of the conclusion, all in the sense of “that from which.”

Of these pairs, the one set are causes in the sense of substratum, such as the parts, and the other set in the sense of essence—the whole and the combination and the form.

But the seed and the doctor and the adviser, and generally the maker, are all sources from which the change or stationariness originates, while the others are causes in the sense of the end or the good of the rest, for “that for the sake of which” means what is best and the end of the things that lead up to it.

(Whether we say “the good itself” or the “apparent good” makes no difference.) Such, then, is the number and nature of the kinds of cause.

176. Having shown what natural science considers, the Philosopher here begins to designate the causes from which it should demonstrate.

This section is divided into two parts.

First, he treats the causes;

second, at now the causes (198a22; [241]), he points out the causes from which natural science should demonstrate.

Concerning the first part, he makes two points.

First, he shows the need for treating the causes;

second, at in one sense (194b23; [177]), he begins to treat the causes.

He says first (194b16) that, after it has been determined what falls under the consideration of natural science, there remains to be considered the causes—what they are and how many there are. This is so because the business of studying nature is not ordered to operation, but to science. For we are not able to make natural things, but only to have science of them. Now, we do not think that we know anything unless we grasp the why, which is to grasp the cause. Hence it is clear that we must observe generation, corruption, and every natural change in such a way that we know the causes and reduce each one about which we seek the why to its proximate cause.

He says this because the consideration of causes insofar as they are causes is proper to first philosophy. For insofar as it is a cause, a cause does not depend upon matter for its existence, because the account of cause is found also in those things that are separated from matter. But the consideration of causes is taken up by the natural philosopher because of a certain necessity. However, he considers causes only insofar as they are the causes of natural changes.

177. Next, at in one sense (194b23), he treats the causes.

Concerning this, he makes three points.

First, he names the clearly diverse species of causes;

second, at but chance also (195b31; [198]), he treats certain less obvious causes;

third, at it is clear, then (198a14; [239]), he shows that the causes are neither more nor less.

The first part is divided into two parts.

First, he treats the species of causes;

second, at now the modes (195a27; [187]), he treats the modes of diverse causes in each species.

Concerning the first part, he makes two points.

First, he sets forth the different species of causes;

second, at all the causes (195a15; [183]), he reduces them to four.

Concerning the first part, he makes two points.

First, he sets forth the different causes;

second, at as the word (195a4; [182]), he points out certain consequences that follow from the above-mentioned diversity.

178. He says first (194b23) that, in one way, a cause is said to be that from which something comes to be when it is in it, as bronze is said to be the cause of a statue and silver the cause of a vase. The genera of these things, such as the metallic or the liquifiable and such things, are also called causes of these same things.

He adds when it is in it in order to differentiate this cause from the privation and the contrary. For the statue indeed comes to be from bronze, which is in the statue when it is made. But it also comes to be from the unshaped, which is not in the statue when it is made. Hence, bronze is a cause of statue but the unshaped is not, since it is only a per accidens principle, as was said in book 1.¹

179. Second, a cause is said to be the species and exemplar (194b26). This is called a cause insofar as it is the quidditative account of the thing, for this is that through which we know of each thing what it is. And, as was said above, just as even the genera of matter are called causes, so also the genera of a species are called causes.

His example is that harmony of music called the octave. The form of an octave is a proportion of the double, which is a relation of two to one. For musical harmonies are constituted by the application of numerical proportions to sounds as to matter. And, since two or the double is the form of that harmony that is the octave, the genus of two, which is number, is also a cause. Thus, just as we say that the form of the octave is that proportion of two to one (which is the proportion of the double), so also we can say that the form of the octave is that proportion of two to one, which is multiplicity.

And so, all of the parts that are placed in the definition are reduced to this mode of cause. For the parts of the species are placed in the definition, but not the parts of the matter, as is said in Metaphysics 7.10.¹

Nor is this contrary to what was said above about matter being placed in the definitions of natural things.¹ For individual matter is not placed in the definition of the species, but common matter is. Thus, flesh and bones are placed in the definition of man, but not this flesh and these bones. The nature of the species, therefore, which is constituted of form and common matter, is related as a formal cause to the individual that participates in such a nature, and to this extent, it is said that the parts that are placed in the definition pertain to the formal cause.

It should also be noted that he posits two things that pertain to the quiddity of the thing: the species and the exemplar. For there is a diversity of opinions concerning the essences of things. Plato held that the natures of species are certain abstract forms, which he called exemplars and ideas, and because of this, he posited the exemplar or paradigm. However, those natural philosophers who said something about form placed the forms in matter, and because of this, he named them species.

180. Next, he says that that from which there is a beginning of motion or rest is in some way called a cause. Thus, one who gives advice is a cause, and the father is a cause of the son, and everything that brings about a change is a cause of that which is changed.

It must be noted with reference to causes of this sort that there are four kinds of efficient cause: the perfecting, the preparing, the assisting, and the advising causes.

The perfecting cause is that which gives fulfilment to motion or change, as that which introduces the substantial form in generation.

The preparing or disposing cause is that which renders matter or the subject suitable for its ultimate completion.

The assisting cause is that which does not operate for its own proper end, but for the end of another.

The advising cause, which operates in those things that act because of something proposed to them, is that which gives to the agent the form through which it acts.

For the agent acts because of something proposed to him through his knowledge, which the advisor has given to him, just as in natural things, the generator is said to move the heavy or the light insofar as it gives the form through which they are moved.

181. Further, he posits a fourth mode of cause. A thing is called a cause as an end. This is that for the sake of which something comes to be, as health is said to be a cause of walking. And this is evident because it answers the proposed question of why. For when we ask, “Why does he walk?” we say, “That he may become healthy”; and we say this thinking that we assign a cause. And thus he gives more proof that the end is a cause than that the other things are causes, because the end is less evident, inasmuch as it is last in generation.

And he adds further that all things that are intermediates between the first mover and the ultimate end are in some way ends. Thus, the doctor makes the body thinner in order to produce health, and so health is the end of thinness. But thinness is produced by purgation, and purgation is produced by a drug, and the drug is prepared by instruments. Hence, all of these things are in some way ends, for the thinness is the end of the purging, the purging is the end of the drug, the drug is the end of the instruments, and the instruments are the ends in the operation or in the seeking for the instruments. And thus it is clear that these intermediate things differ from each other, insofar as some of them are instruments and some of them are operations performed by instruments.

And he brings this out lest anyone think that only that which is last is a cause in the sense of that for the sake of which. For the name “end” seems to refer to something that is last. Thus, every end is last not simply, but in respect to something.

He finally concludes that this is perhaps all the ways in which the name “cause” is used. He adds perhaps because of the causes that are per accidens, such as chance and fortune.

182. Next, at as the word has (195a4), he makes clear three things that follow from what he has said about the different causes. The first point is that, since there are many causes, one and the same thing has many causes per se, and not per accidens. Thus, the art of the sculptor is a cause of a statue as an efficient cause but bronze is a cause as matter. And so it is that many definitions of one thing are sometimes given in accordance with the different causes. But the perfect definition embraces all of the causes.

The second point is that some things are causes of each other in respect to different species of cause. Thus, work is an efficient cause of a good habit, yet a good habit is a final cause of work. For nothing prevents a thing from being both prior and posterior to another according to different accounts. The end is prior according to account, but posterior in existence; the converse is true of the agent. And in like manner, the form is prior to matter with respect to the account of being a complement, but the matter is prior to form with respect to generation and time in everything that is moved from potency to act.

The third point is that the same thing is, at times, the cause of contraries. Thus, through his presence, the navigator is the cause of the safety of the ship; through his absence, however, he is a cause of its sinking.

183. Next, at all the causes (195a15), he reduces all the causes mentioned above to four species. He says that all the causes enumerated above are reduced to four modes that are evident. For elements such as letters are causes of syllables, and in like manner earth is a cause of vases, and silver of a vial, and fire and such things (the simple bodies) are causes of bodies. And, in the same way, every part is a cause of the whole, and the premises—that is, the propositions in a syllogism—are a cause of the conclusion. And all these are understood as causes in the same way, namely, as a cause is that from which something comes to be: for this is common to everything mentioned. However, of all the things just enumerated, some are causes as matter and some as form, which causes the quiddity of the thing. Thus, all parts, such as the elements of syllables and the four elements of mixed bodies, are causes as matter. But those things that imply a whole or a composition or some species are understood as form. Thus species is referred to the forms of simple things, and the whole and composition are referred to the forms of composites.

184. But there seem to be two difficulties here.

The first is that he says the parts are material causes of the whole, when above he reduced the parts of the definition to the formal cause. It can be said that he spoke above of the parts of the species that fall in the definition of the whole, but here he speaks of the parts of the matter in whose definition falls the whole. Thus, circle falls in the definition of semicircle. But it would be better to say that, although the parts of the species that are placed in the definition are related to the suppositum of nature as a formal cause, they are nevertheless related to the very nature of which they are parts as matter. For all parts are related to the whole as the imperfect to the perfect, which is, indeed, the relation of matter to form.

Further, a difficulty can be raised with reference to what he says about propositions being the matter of conclusions. For matter is in that of which it is the matter. Hence, speaking of the material cause above, he said that it is that from which something comes to be when it is in it. But propositions are apart from the conclusion. But it must be pointed out that the conclusion is formed from the terms of the propositions.

Hence, in view of this, the propositions are said to be the matter of the conclusion insofar as the terms that are the matter of the propositions are also the matter of the conclusion, although they are not in the same order as they are in the propositions. In this same way, flour is called the matter of bread, but not insofar as it stands under the form of flour.

And so propositions are better called the matter of the conclusion than conversely. For the terms that are joined in the conclusion are posited separately in the premises. Thus we have two modes of cause.

185. Some things are called causes for another reason: because they are a principle of motion and rest. And, in this way, the seed that is active in generation is called a cause. Likewise, the doctor is called a cause of health according to this mode, and so also the adviser is a cause according to this mode, and everyone who makes something.

Another text reads, and propositions. For although propositions, insofar as their terms are concerned, are the matter of the conclusion, as was said above, nevertheless insofar as their inferential power is concerned, they are reduced to this genus of cause. For the principle of the discourse of reason to its conclusion is from propositions.

186. Another meaning of “cause” is found in other causes, namely, insofar as the end or the good has the account of a cause. And this species of cause is the most powerful of all the causes, for the final cause is the cause of the other causes. It is clear that the agent acts for the sake of the end.

And likewise it was shown above¹ in regard to artificial things that the form is ordered to use as to an end, and matter is ordered to form as to an end. And, to this extent, the end is called the cause of causes. Now, since he has said that this species of cause has the account of a good, while it sometimes happens in those things that act by choice that the end is evil, he forestalls this difficulty by saying that it makes no difference whether the final cause is a true or an apparent good, because what seems to be good can only move under the account of being good.

And thus he finally concludes that the species of cause are as many as were mentioned.

Now, the modes of causation are many, but when brought under headings, they too can be reduced in number.

For “cause” is used in many senses, and even within the same kind, one may be prior to another—for instance, the doctor and the expert are causes of health, and the relation 2:1 and number of the octave, and always what is inclusive to what is particular.

Another mode of causation is the accidental and its genera: for instance, “Polycletus” is the cause of a statue in one way but “sculptor” in another, because “being Polycletus” and being “sculptor” are accidentally conjoined.

It is likewise with the classes in which the accident is included; thus “a man” could be said to be the cause of a statue or, generally, “a living creature.”

An accident too may be more or less remote: for instance, suppose that “a pale man” or “a musical man” were said to be the cause of the statue.

All causes, both proper and accidental, may be spoken of either as potential or as actual; for example, the cause of a house being built is either “house builder” or “house builder building.” Similar distinctions can be made in the things of which the causes are causes, such as of “this statue” or of “statue” or of “image” generally, of “this bronze” or of “bronze,” or of “material” generally. And it is also so with the accidents.

Again, we may use a complex expression for either and say, for instance, neither “Polycletus” nor “sculptor” but “Polycletus, sculptor.”

All these various uses, however, come to six in number, under each of which again the usage is twofold. “Cause” means either what is particular or a genus, or an accident or a genus of that, and these either as a complex or each by itself—and all six either as actual or as potential.

The difference is that causes that are actually at work and singular exist and cease to exist simultaneously with their effect: for instance, this healing person with this being-healed person and that house-building man with that being-built house; but this is not always true of potential causes—the house and the house builder do not pass away simultaneously.

In investigating the cause of each thing, it is always necessary to seek what is most precise (as also in other things): thus, man builds because he is a builder and a builder builds in virtue of his art of building. This last cause, then, is prior (and so generally).

Further, generic effects should be assigned to generic causes, particular effects to particular causes (such as statue to sculptor, this statue to this sculptor), powers relative to possible effects, and actually operating causes to things that are actually being effected. This must suffice for our account of the number of causes and the modes of causation.

187. After the Philosopher has distinguished the species of causes, he here distinguishes the various modes of causes in respect to the same species of cause.

Concerning this, he makes two points.

First, he distinguishes the different modes of causes.

Second, at the difference is (195b16; [195]), he treats certain consequences of this distinction.

Concerning the first part, he makes two points.

First, he distinguishes the different modes of causes;

second, at all these various (195b12; [194]), he reduces them to a certain number.

Concerning the first part, he distinguishes the modes of causes according to four divisions.

He says first (195a27) that, while the modes of causes are numerous, if they are reduced to headings, either under some highest or under some common aspect, they are found to be fewer.

Or headings may be taken as a combination, for it is obvious that combinations of the modes are fewer than the modes.

188. Therefore, the first division or combination of modes is that, in the same species of cause, one cause is said to be prior to another, as when we understand that the more universal cause is prior. Thus, the doctor is the proper and posterior cause of health, whereas the artisan is the more common and prior cause. This is in the species of efficient cause. And the same thing is true in the species of formal cause. For the proper and posterior formal cause of the octave is the proportion of the double, whereas the more common and prior is the numerical proportion that is called multiplicity. And, in like manner, a cause that contains any cause in the entirety of its extension is a prior cause.

189. It must be noted, however, that the “universal,” “proper,” “prior,” and “posterior” causes can be taken either according to a commonness in predication (as in the example given about the doctor and the artisan), or according to a commonness in causality (as if we say the sun is a universal cause of heating while fire is a proper cause).

And these two divisions correspond to each other. For it is clear that any power extends to certain things insofar as they share in one account, and the farther that that power extends, the more common that account must be. And, since a power is proportioned to its object according to its account, it follows that a higher cause acts according to a form that is more universal and less contracted.

And this can be seen in the order of things. For to the extent that some things are superior among beings, they have forms that are less contracted and more dominant over matter, which contracts the power of form. And so, that which is prior in causing is found to be prior in some way under the account of a more universal predication. For example, if fire is the first in heating, then the heavens are not only the first in heating but also the first in producing alteration.

190. He gives the second division at another mode of causation (195a32). He says that, just as per se causes are divided into prior and posterior or common and proper, so also are per accidens causes. For besides per se causes, there are per accidens causes and their genera. Thus, Polycletus is a per accidens cause of the statue, while the sculptor is a per se cause. For Polycletus is a cause of statue insofar as he happens to be a sculptor. And, in like manner, those things that contain Polycletus in their commonness, such as man and animal, are per accidens causes of the statue.

Moreover, it must be noted that, among per accidens causes, some are closer to the per se causes and some are more removed. For everything that is joined to the per se cause but is not of its account is called a per accidens cause. Now, a thing can be closer to the account of the per se cause or more removed from it, and the per accidens causes are closer or more removed to this extent. Thus, if a sculptor happens to be white and musical, the musical is closer, because it is in the same subject in respect to the same thing—that is, in respect to the soul in which are both the art of the musician and that of statue making. But the subject itself is still more closely related than the other accidents. Thus, Polycletus is closer than white or musical, for these latter are not joined to this sculptor except through the subject.

191. He gives the third division at all causes (195b3). He says that, besides the proper causes—that is, the causes per se and the causes per accidens—some things are said to be causes in potency, such as being able to operate, while other things are actually operating causes. Thus, either the builder in habit or the builder in act can be called the cause of the building of a house.

192. And, just as causes are distinguished according to the above-mentioned modes, so also the things of which they are the causes are distinguished. For one thing is caused posteriorly and more properly, and another priorly and more commonly.

Thus, something might be called the cause of this statue, or of statue in general, or it might still more commonly be called the cause of an image. And, likewise, something might be called the moving cause of this bronze, or of bronze in the universal, or of matter. So also, in per accidens effects, it can be said that one thing is more common and another less common. An effect is said to be per accidens when it is joined to a per se effect and is outside its account. Thus, the per se effect of cooking is delectable food, but the per accidens effect is healthful food. However, the converse is true of medicine.

193. He gives the fourth division at again, we may use (195b10). He says that per se causes are sometimes taken as a complex with per accidens causes, as when we do not say that Polycletus, who is a per accidens cause, is the cause of the statue, nor that the sculptor, who is the cause per se, is the cause, but rather that the sculptor Polycletus is the cause.

194. Next, at all these various uses (195b12), he reduces the above-mentioned modes to a certain number. He says that they are six in number, but each of them is used in two ways. These are the six modes: the singular and the genus, which above he called the prior and the posterior; the accident and the genus of the accident; the simple and the complex. And each of these is divided by potency and act; thus, all the modes become twelve. He distinguishes all the modes by potency and act because what is in potency is not simply.

195. Next, at the difference is (195b16), he treats three things that follow from the distinction of modes just made.

The first point is that causes in act and causes in potency differ as follows. Causes operating in act exist and do not exist simultaneously with those things of which they are the causes in act.

For example, if we take singular causes—that is, proper causes—then this healer exists and does not exist simultaneously with the person who becomes healed, and this builder exists simultaneously with that which is built.

But this is not true if we take causes in act, which are not proper causes. For it is not true that the builder exists and does not exist simultaneously with that which is built. For it can happen that the builder is in act but this building is not being built, but some other.

But, if we take the one who is building this building, and if we take this building insofar as it is being built, then it is necessary that, when one is posited, the other must be posited also, and when one is removed the other is removed.

But this does not always happen in regard to causes that are in potency. For a home and the man who built it are not corrupted simultaneously.

And thus it follows that, just as inferior agents, which are causes of the coming to be of things, must exist simultaneously with the things that come to be as long as they are coming to be, so also the divine agent, which is the cause of existing in act, is simultaneous with the existence of the thing in act.

Hence if the divine action were removed from things, things would fall into nothingness, just as light ceases to be in the air when the presence of the sun is removed.

196. He sets forth the second point at in investigating the cause (195b21). He says that it is necessary to seek in natural things the first cause of each thing, just as we do in artificial things. So, if we should ask why it is that a man builds, we answer, “because he is a builder.” Likewise, if we ask why he is a builder, we answer, “because he possesses the builder’s art.” And the inquiry stops at this point, because this is the first cause in this order. Hence, in natural things, we should proceed to the first cause. This is so because the effect is not known unless the cause is known. Hence, if the cause of an effect is itself the effect of some yet other cause, then it cannot be known unless its cause is known, and so on until we arrive at a first cause.

197. He sets forth the third point at further, generic effects (195b25). Effects should correspond proportionally to causes such that general effects be referred to general causes and singular effects to singular causes. For example, if it is said that the cause of statue is sculptor, then the cause of this statue is this sculptor. In like manner, effects in potency should correspond to causes in potency and effects in act to causes in act.

And finally in summary he concludes that this is a sufficient treatment of the species and modes of causes.

But fortune also and chance are reckoned among causes: many things are said both to be and to come to be as a result of fortune and chance.

We must inquire, therefore, in what manner fortune and chance are present among the causes enumerated and whether they are the same or different, and generally what fortune and chance are.

Some people even question whether they are real or not. They say that nothing happens by fortune, but that everything that we ascribe to fortune or chance has some definite cause—for instance, coming by fortune into the market and finding there a man whom one wanted but did not expect to meet is due to one’s wish to go and buy in the market.

Similarly, in other cases of fortune, it is always possible, they maintain, to find something that is the cause, but not fortune.

For if fortune were real, it would seem strange indeed, and the question might be raised of why on earth none of the wise men of old, in speaking of the causes of generation and decay, took account of fortune, whence it would seem that they too did not believe that anything is by fortune.

But there is a further circumstance that is surprising. Many things both come to be and are by fortune and chance, and although all know that each of them can be ascribed to some cause (as the old argument said which denied fortune), they nevertheless speak of some of these things as happening by fortune and others not. For this reason also, they ought to have at least referred to the matter in some way or other. Certainly the early physicists found no place for fortune among the causes that they recognized—love, strife, mind, fire, or the like.

This is strange, whether they supposed that there is no such thing as fortune or whether they thought there is but omitted to mention it—and that too when they sometimes used it, as Empedocles does when he says that the air is not always separated into the highest region, but “as it may chance.”

At any rate he says in his cosmogony that “it happened to run that way at that time, but it often ran otherwise.” He tells us also that most of the parts of animals came to be by fortune.

There are some too who ascribe this heavenly sphere and all the worlds to chance. They say that the vortex arose by chance (that is, the motion that separated and arranged in its present order all that exists).

This statement might well cause surprise. For they are asserting that fortune is not responsible for the existence or generation of animals and plants, nature or mind or something of the kind being the cause of them (for it is not any chance thing that comes from a given seed but an olive from one kind and a man from another).

Yet, at the same time, they assert that the heavenly sphere and the divinest of visible things arose by chance, having no such cause as is assigned to animals and plants. Yet, if this is so, it is a fact that deserves to be dwelt upon, and something might well have been said about it.

For besides the other absurdities of the statement, it is the more absurd that people should make it when they see nothing coming to be by chance in the heavens, but much happening by chance among the things that, as they say, are not due to fortune, when we should have expected exactly the opposite.

Others there are who, indeed, believe that fortune is a cause but that it is inscrutable to human intelligence, as being a divine thing and full of mystery. Thus we must inquire what fortune and chance are, whether they are the same or different, and how they fit into our division of causes.

198. Having treated the obvious species and modes of cause, the Philosopher here takes up certain hidden modes, namely, fortune and chance.

Concerning this, he makes two points.

First, he states his intention;

second, he pursues what he has proposed, at some people even question (195b36; [199]).

He says first that fortune and chance are also reckoned among the causes, since many things are said to come to be or to exist because of fortune and chance.

And, so, with respect to fortune and chance, three things must be considered:

how they are reduced to the causes mentioned above;

whether fortune and chance are the same or different;

and finally, what chance and fortune are.

Next, at some people even question (195b36; [199]), he begins his treatment of fortune and chance.

First, he sets forth the opinions of others.

Second, at first, then, we observe (196b10; [207]), he establishes the truth.

Concerning the first part, he sets forth three opinions.

The second begins at there are some (196a24; [203]),

and the third at others there are (196b5; [206]).

Concerning the first part, he makes two points.

First, he sets forth the opinions and arguments of those who deny fortune and chance.

Second, at but there is a further circumstance (196a11; [201]), he argues about the second of these reasons.

199. He says first (195b36) that some have questioned whether fortune and chance exist.

They deny that they exist for two reasons.

The first argument is that all of those things that are said to come to be by chance or fortune are found to have some determinate cause other than fortune. He gives an example of this sort of thing. If someone coming to the market place should find some man whom he wished to find, but who he did not previously believe would be found, we say that his finding of this man was due to fortune. But the cause of this finding is his will to buy, for the sake of which he went to the market where the man whom he sought was. And the same is true of all other things that are said to be by fortune, for they have some cause other than fortune. And, so, fortune does not seem to be a cause of anything, and consequently is nothing. For we do not posit fortune except insofar as we hold that some things exist by fortune.

200. He gives the second argument at for if chance were real (196a7). He says that, if fortune were something, it seems to be inconsistent (and that it is truly inconsistent is shown below) and puzzling that none of the ancient wise men who treated the causes of generation and corruption treated fortune. But, as it seems, those ancients thought that nothing exists by fortune. And thus this second argument is taken from the opinion of the ancient natural philosophers.

201. Next, at but there is a further circumstance (196a11), he argues about this second proof, showing what he had assumed above, that it is inconsistent that the ancient natural philosophers did not treat chance and fortune.

He proves this with two arguments.

His first argument is as follows. It seems remarkable, and indeed it is, that the ancient natural philosophers did not treat chance and fortune. For they assumed that they treated the causes of those things that come to be, yet there are many things that come to be by fortune and chance. Hence they should have treated fortune and chance. Nor are they to be excused by the argument given above that denies fortune and chance. For although men know that every effect is reduced to some cause, as the above opinion that denies fortune and chance stated, nevertheless, regardless of this argument, these philosophers held that some things come to be by fortune and other things do not.

Hence, these natural philosophers must make mention of fortune and chance at least in order to show that it is false that some things come to be by fortune and chance, and in order to point out the reason that some things are said to be by fortune and some not. Nor can they be excused by reason of the fact that chance and fortune would be reduced to one of the causes that they posited. For they did not think that fortune is one of the things that they thought to be causes, such as friendship or strife or some other such thing.

202. He gives his second argument at this is strange (196a19). He says that, whether they thought that fortune existed or not, it is inconsistent that the ancient natural philosophers neglected to treat fortune. For if they thought that there was fortune, it is inconsistent that they did not treat it; but if they thought that there was no fortune, it is inconsistent that they sometimes used it.

For example, Empedocles said that air is not always united on high above the earth, as if this were natural to it, but rather this happens by chance. For he says that, when the earth was made by strife distinguishing the elements, it happened that air gathered together in this place, and as it came together then, it will hold this course so long as the world remains.

But, in other worlds, which he held come to be and are corrupted to infinity, as was said above,¹ air would be differently related in many ways to the parts of the universe. And he said likewise that the many parts of animals come to be by fortune, such that, in the first production of the world, heads came to be without necks.

203. Next, at these are some (196a24), he gives the second opinion.

Concerning this, he makes two points.

First, he sets forth the opinion;

second, he disproves it, at this statement might (196a28; [204]).

Thus, he first says (196a24) that some have said that chance is the cause of the heavens and all the parts of the world. And they said that the revolution of the world—the motion of the stars distinguishing and constituting the whole universe below according to this order—is by chance. This seems to be the opinion of Democritus, who says that the heavens and the whole world are constituted by chance through the motion of atoms, which are per se mobile.

204. Next, at this statement might (196a28), he disproves this position with two arguments.

The first argument is that it would seem to be worthy of great wonder that animals and plants are not from fortune, but from intellect or nature or some other determinate cause. For it is clear that a thing is not generated from any seed whatsoever, but man from a determinate seed and the olive from a determinate seed. And, since these inferior things do not come to be by fortune, it is worthy of wonder that the heavens and those things that are more divine among the sensible things known to us, namely, the sempiternal parts of the world, are by chance and should not have any determinate cause, as do animals and plants. And, if this is true, it would have been worthwhile to insist and to give a reason why this is so. But the ancients failed to do this.

205. He gives the second argument at for besides the other (196b1). How can it be true that the celestial bodies are by chance while inferior bodies are not? This seems to be inconsistent first from the fact that they are the nobler; second, it is even more inconsistent in the light of what is seen. For we see that, in the heavens, nothing comes to be by chance, whereas in inferior bodies, which are not said to be by chance, many things seem to happen by fortune. According to their position, it would be more reasonable if the converse were true, such that, in those things whose cause is chance or fortune, some things would be found to come to be by chance or by fortune, but not in those things whose cause is not chance or fortune.

206. Next, at others there are (196b5), he sets forth the third opinion about fortune. He says that it seems to some that fortune is a cause, but it is hidden to the human intellect, as if it were something divine and above men. For they wanted to hold the position that all fortuitous events are reduced to some divine ordaining cause, as we hold that all things are ordered by divine providence.

But, although this opinion has a radical truth, they did not use the name “fortune” well. For that divine thing that orders cannot be called or named fortune, for to the extent that a thing participates in reason or order, it no longer falls under the idea of fortune. Hence, the inferior cause, which of itself does not have an ordination to the fortuitous event, should much more be called fortune than the superior cause, if such a cause is the one that orders. He omits an inquiry about this opinion, both because it exceeds the bounds of natural science and because he shows below that fortune is not a per se cause, but a per accidens cause.¹ Hence, how he evaluates these opinions will be made more clear in what follows. And so he concludes that, for the clarification of these opinions, we must consider what fortune and chance are and whether they are the same or different, and how they are reduced to the causes mentioned above.

The definition of fortune

First, then, we observe that some things come to pass in the same way always, but others for the most part.

It is clearly of neither of these that fortune is said to be the cause, nor can the effect of fortune be identified with any of the things that come to pass by necessity and always, or those that do so for the most part.

But, as there is a third class of events besides these two—events that all say are by fortune—it is plain that there is such a thing as fortune and chance; for we know that things of this kind are due to fortune and that things due to fortune are of this kind.

But, second, some events are for the sake of something, others not.

Again, some of the former class are in accordance with deliberate intention, others not, but both are in the class of things that are for the sake of something.

Hence, it is clear that, even among the things that are outside the necessary and the normal, there are some in connection with which the phrase “for the sake of something” is applicable. (Events that are for the sake of something include whatever may be done as a result of thought or of nature.)

Things of this kind, then, when they come to pass accidentally, are said to be “by fortune.” For just as a thing is something either in virtue of itself or accidentally, so may it be a cause.

For instance, the house-building faculty is in virtue of itself the cause of a house, whereas the pale or the musical is the accidental cause. That which is the per se cause of the effect is determinate, but the accidental cause is indeterminable, for the possible accidents of an individual are innumerable.

To resume, then: when a thing of this kind comes to pass among events that are for the sake of something, it is said to be by chance or by fortune. (The distinction between the two must be made later—for the present, it is sufficient if it is plain that both are in the sphere of things done for the sake of something.)

For example, a man is engaged in collecting subscriptions for a feast. He would have gone to such and such a place for the purpose of getting the money, if he had known.

He actually went there for another purpose, and it was only accidentally that he got his money by going there; and this was not due to the fact that he went there as a rule or necessarily,

nor is the end effected (getting the money) a cause present in himself—it belongs to the class of things that are intentional and the result of intelligent deliberation.

It is when these conditions are satisfied that the man is said to have gone by fortune.

If he had gone of deliberate purpose and for the sake of this—if he always or normally went there when he was collecting payments—he would not be said to have gone “by fortune.”

It is clear, then, that fortune is a per accidens cause in those things that come to be in a few instances according to what is proposed for the sake of an end. Thus, intelligent reflection and fortune are in the same sphere, for purpose implies intelligent reflection.

207. Having set forth the opinions of others about fortune and chance, the Philosopher here determines the truth.

This section is divided into three parts.

First, he shows what fortune is;

second, at they differ (197a36; [226]), he shows how fortune and chance differ;

third, at both belong to (198a2; [236]), he points out the genus of cause to which chance and fortune are reduced.

The first part is divided into two parts.

First, he shows what fortune is;

second, at it is necessary (197a8; [217]), he explains the meaning of those things that are said about fortune from the definition of fortune.

Concerning the first part, he makes three points.

First, he sets forth certain divisions needed for the investigation of the definition of fortune;

second, at to resume, then (196b29; [215]), he shows under which members of these divisions fortune is contained;

third, at it is clear (197a5; [216]), he finishes the definition of fortune.

Now, since fortune is posited as a kind of cause, and since it is necessary in order to understand a cause, to know that of which it is the cause, he first sets forth a division on the part of that of which fortune is the cause.

Second, at things of this kind (196b23; [214]), he sets forth a division on the part of the cause itself.

208. With reference to the first point, he sets forth three divisions.

The first of these (196b10) is that certain things always come to be, like the rising of the sun, while certain other things come to be frequently, such as a man born with eyes. But neither of these is said to be by fortune. But certain things besides these two occur in fewer instances, as when a man is born with six fingers or without eyes. And everyone says that things of this sort come to be by fortune. Hence, it is clear that fortune is something, for to be by fortune and to be in fewer instances are convertible. And he brings this up in opposition to the first opinion that denied fortune.

209. However, it seems that this division of the Philosopher is insufficient, for there are some happenings that are indeterminate. Therefore, Avicenna said that, in those things that are indeterminate, a thing happens to be by fortune, such as those things that happen less often.

And it is no objection that it is not said that Socrates sits by fortune, since this is indeterminate. For although this is indeterminate with respect to the moving potency, it is not indeterminate with respect to the appetitive potency, which tends determinately to one thing. And, if something should happen outside of the appetitive potency, it would be said to be fortuitous.

Now, just as the moving potency, which is indeterminate, does not move to act unless it is determined to one thing by the appetitive potency, so also nothing that is indeterminate moves to act unless it is determined to one thing by something. For that which is indeterminate is, as it were, being in potency.

However, potency is not a principle of action; only act is such. Hence, from that which is indeterminate, nothing follows unless it is determined to one thing by something, either always or frequently. And because of this, he omitted things that are indeterminate from his discussion of things that come to be.

210. It must also be noted that some define the necessary as that which is never impeded and the contingent as that which occurs frequently but may be impeded in a few instances.

But this is unreasonable. “Necessary” is said of what has in its nature that which cannot not be, but “contingent” of what happens frequently, which is able to not be. But to have or not have some impediment is itself contingent. For nature does not prepare an impediment for that which cannot not be, since this would be superfluous.

211. He gives the second division at but, second (196b17). He says that some things come to be for the sake of an end while other things do not. This division, however, raises a difficulty, because every agent acts for an end; it acts either by nature or by intellect.

But we must note that he is saying that those things that come to be for themselves do not come to be for the sake of something, insofar as they have in themselves a pleasure or perfection because of which they are pleasing in themselves. Or else he is speaking of those things that do not occur for the sake of a deliberate end—for example, stroking the beard or some other such thing that takes place at times without deliberation and solely from the motion of the imagination. Hence, they have an imagined end, but not a deliberated end.

212. He gives the third division at again, some of the former (196b18). He says that, of the things that come to be for the sake of an end, some happen in accordance with will and others do not.

Both of these are found among those things that come to be for the sake of something. For not only those things that come to be by will but also those things that come to be by nature come to be for the sake of something.

213. Now, since those things that come to be either necessarily or frequently come to be from nature or from that which is proposed,¹ it is clear that, both in those things that always happen and in those things that happen frequently, there are some things that come to be for an end. For both nature and that which is proposed act for the sake of an end.

And thus it is clear that these three divisions include each other. For those things that come to be from what is proposed or from nature come to be for the sake of an end, and those things that come to be for the sake of an end come to be always or frequently.

214. Next, at things of this kind (196b23), he gives the division from the part of the cause. He says that, when things of this kind—that is, things that are from what is proposed for the sake of something and that are in few instances—come to be through a per accidens cause, we say that they are by fortune. For as certain aspects of beings are per se and others per accidens, the same is true of causes. Thus, the per se cause of a house is the builder’s art, while the per accidens cause is the white or the musical.

But it must be noted that a per accidens cause is taken in two ways:

in one way on the part of the cause,

and in another way on the part of the effect.

On the part of the cause, that which is called a per accidens cause is joined to the per se cause. Thus, if the white and the musical are called causes of a house, it is because they are accidentally joined to the builder.

On the part of the effect, we sometimes refer to something that is accidentally joined to the effect, as when we say that a builder is the cause of strife because strife arises from the building of a house. In this sense, fortune is said to be a per accidens cause when something is accidentally joined to the effect—for example, if the discovery of a treasure is accidentally joined to the digging of a grave.

Thus, the per se effect of a natural cause is what follows according to the exigencies of its form such that the effect of the agent who acts through something proposed is that which happens because of the intention of the agent. Hence, whatever takes place in the effect outside this intention is per accidens.

And I say that this is true if what is outside the intention follows in few cases. For what is always or frequently joined to the effect falls under the intention itself. For it is stupid to say that someone intends something but does not will that which is always or frequently joined to it.

Moreover, he points out a difference between the per se cause and the per accidens cause. The per se cause is limited and determinate, whereas the per accidens cause is unlimited and indeterminate, because an infinity of things can happen to be united.

215. Next, at to resume, then (196b29), he points out those members of the above divisions under which fortune is contained and what fortune is. He says first that fortune and chance, as was said above, pertain to those things that happen for the sake of something. However, the difference between fortune and chance will be determined later.¹ But now it should be clear that each of them is contained among those things that act for the sake of an end.

Thus, if one knows that he will receive money in the forum, and if he goes there to take it away, but if he did not go there for this purpose, it is per accidens that his arrival should have this effect, that he got his money. And thus it is clear that fortune is a per accidens cause of things that are for the sake of something.

Further, it is clear that fortune is a cause of things that occur in few instances. For carrying money away is said to be by fortune when he who takes money away comes to the house neither necessarily nor frequently.

Moreover, fortune pertains to those things that come to be because of what is proposed. For taking money away, which is said to be by fortune, is the end of some causes, but not in itself, as in those things that happen by nature.

Rather, it is the end of those things that come to be as proposed by the intellect. But, if someone acting under such a proposal should go in order to take money away, or if he always or frequently takes money away when he comes, this would not be said to be by fortune, just as, if anyone frequently or always soaks his feet when he goes to a muddy place, it would not be said that this is due to fortune, even though he did not intend it.

216. Next, at it is clear (197a5), he gives a definition of fortune that is drawn from what was said above. He says that it is clear from the foregoing that fortune is a per accidens cause in those things that come to be in a few instances according to what is proposed for the sake of an end. And from this it is clear that fortune and intellect pertain to the same thing. For only those who have an intellect act by fortune, for there is no proposal or will without intellect. And, although only those who have an intellect act by fortune, still the more something is subject to the intellect, the less is it subject to fortune.

The meaning of what is said about fortune

It is necessary, no doubt, that the causes of what comes to pass by fortune be indefinite, and that is why fortune is supposed to belong to the class of the indefinite and to be inscrutable to man.

And this is also why it might be thought that, in a way, nothing occurs by fortune. For all these statements are correct, because they are well grounded.

Things do, in a way, occur by fortune, for they occur accidentally and fortune is an accidental cause.

But, strictly, it is not the cause—without qualification—of anything;

for instance, a house builder is the cause of a house, but accidentally, a flute player may be so.

And the causes of the man’s coming and getting the money (when he did not come for the sake of that) are innumerable.

He may have wished to see somebody or been following somebody or avoiding somebody, or may have gone to see a spectacle.

Thus, to say that fortune is a thing contrary to rule is correct. For rule applies to what is always true or true for the most part, whereas fortune belongs to a third type of event. Hence, to conclude, since causes of this kind are indefinite, fortune too is indefinite.

(Yet, in some cases, one might raise the question whether any accidental fact might be the cause of the fortune occurrence, such as when the cause of health may be the fresh air or the sun’s heat, but having had one’s hair cut cannot be; for some accidental causes are more relevant to the effect than others.)

Fortune is called “good” when the result is good, and “evil” when it is evil.

The terms “good fortune” and “ill fortune” are used when either result is of considerable magnitude. Thus, one who comes within an ace of some great evil or great good is said to be fortunate or unfortunate. The mind affirms the essence of the attribute, ignoring the hair’s breadth of difference.

Further, it is with reason that good fortune is regarded as unstable; for fortune is unstable, as none of the things that result from it can be invariable or normal.

Both fortune and chance are, then, as I have said, accidental causes in the sphere of things that are capable of coming to pass neither simply nor frequently, and with reference to such of these as might come to pass for the sake of something.

217. Having given the definition of fortune, he establishes from this definition the meaning of those things that are said about fortune.

First, he considers those things that the ancient philosophers said about fortune.

Second, at thus, to say (197a18; [219]), he considers those things that the common man says about fortune.

He has given above three opinions concerning fortune and chance.¹ And he disproved the second of these opinions as being altogether false, for this position held that fortune is the cause of the heavens and of all worldly things.

Thus, having rejected the second opinion, he here shows that the third opinion, which holds that fortune is hidden to man, is true.

Second, at and this is also why (197a10; [218]), he shows how the first opinion, which holds that nothing comes to be by fortune or chance, might be true.

Since it was said above¹ that per accidens causes are infinite, and also that fortune is a per accidens cause, he concludes from this that the causes of that which is by fortune are infinite. And, since the infinite, insofar as it is infinite, is unknown, it follows that fortune is hidden to man.

218. Next, at and this is also why (197a10), he shows how the first opinion might be true. He says that, in a way, it is true to say that nothing comes to be by fortune. For all of those things that others say about fortune are in a certain respect true, because they have some reason. Since fortune is a per accidens cause, it follows that what is by fortune is something per accidens. But what is per accidens is not simply. Hence it follows that fortune is not the cause of anything simply.

And he clarifies what he has said about each of these opinions through an example. He says that, as the builder is the per se cause of a house and is the cause simply, whereas the flute player is a per accidens cause of the house, in like manner, the fact that someone should come to a place with no intention of taking money away is a per accidens cause of carrying it away.

But this per accidens cause is infinite, because it is possible for a man to go to that place because of an infinity of other reasons, such as if he came to visit someone, or to pursue an enemy, or to escape from a pursuer, or to see a show of some sort. Now, all these things and anything similar are causes of the taking of money that happens by chance.

219. Next, at thus, to say (197a18), he explains the meaning of those things that are commonly said about fortune.

First, he explains why it is said that what is by fortune is without reason;

second, at fortune is called (197a25; [222]), he explains why it is said that fortune is good or bad.

Concerning the first part, he makes two points.

First, he lays out his position;

second, he raises a certain difficulty, at yet, in some cases (197a21; [221]).

220. He says first (197a18) that fortune is rightly said to be without reason. For we can reason only about those things that happen always or in most instances. But fortune lies outside of both of these. And so, since such causes, which occur in exceptional cases, are per accidens and infinite and without reason, it follows that causes by fortune are infinite and without reason. For every per se cause produces its effect either always or in most cases.

221. Next, at yet in some cases (197a21), he raises a certain difficulty. He says that, although it may be said that fortune is a per accidens cause, some will question, or doubt, this. The problem is whether everything that happens to be a per accidens cause ought to be called a cause of that which comes to be by fortune. Thus, it is clear that the per se cause of health can be either nature or the art of the doctor.

However, can all those things with which the coming to be of health happens to be connected, such as the fresh air (or wind), and the heat, and shaving of the head, be called causes per accidens? The question, therefore, is whether each of these is a cause per accidens.

Now, since we said above that fortune is most properly called a per accidens cause on the part of the effect, since a thing is said to be a cause of that which happens to the effect, it is clear that a fortuitous cause produces something in the fortuitous effect even though it does not intend that, but rather something else connected with the effect. According to this, wind or heat can be called fortuitous causes of health, insofar as they produce some change in the body, upon which change health follows. But removing the hair or some other such thing does not produce anything clearly related to health. But, among the per accidens causes, some are nearer and others are more remote. Those that are more remote seem less to be causes.

222. Next, at fortune is called (197a25), he explains why fortune is said to be good or bad.

First, he explains why fortune is said to be good or bad simply. He says that fortune is said to be good when something good happens and bad when something bad happens.

223. Second, at the terms “good fortune” (197a26), he explains the meaning of good fortune and misfortune. He says that we refer to good fortune and misfortune when the fortuitous event has some great good or great evil. For an event is called good fortune when some great good follows; it is called misfortune when some great evil follows.

And, since being deprived of a good is included in the account of evil and being deprived of evil is included in the account of the good, then, when one is a little removed from a great good, he is said to be unfortunate if he misses it.

On the other hand, if one is close to a great evil and is freed from it, he is said to be fortunate. This is so because the intellect takes that which is only a little removed as if it were not removed at all, but already possessed.

224. Third, at further, it is with reason (197a30), he explains why good fortune is uncertain. He says that this is so because good fortune is a kind of fortune. But fortune is uncertain, because it pertains to things that are neither always nor frequent, as was said. Hence it follows that good fortune is uncertain.

225. Finally, at both fortune and chance (197a32), he concludes as a sort of recapitulation that each (chance and fortune) is a cause per accidens, and that each pertains to things that do not happen simply, neither always nor frequently, and that each pertains to things that come to be for the sake of something, as is clear from what was said above.¹

The difference between chance and fortune

They differ in that “chance” is the wider term. Every result of fortune is from chance, but not everything that is from chance is from fortune.

Fortune and what results from fortune are appropriate to agents that are capable of good fortune and of moral action generally. Therefore, fortune is necessarily in the sphere of moral actions.

This is indicated by the fact that good fortune is thought to be the same, or nearly the same, as happiness, and happiness to be a kind of moral action, since it is well-doing. Hence, what is not capable of moral action cannot do anything by fortune.

Thus, an inanimate thing or a lower animal or a child cannot do anything by fortune, because it does not have that which is proposed; nor can “good fortune” or “ill fortune” be ascribed to them, except metaphorically—as Protarchus, for example, said that the stones of which altars are made are fortunate because they are held in honor while their fellows are trodden under foot. Even these things, however, can in a way be affected by fortune, when one who is dealing with them does something to them by fortune, but not otherwise.

That which is by chance, on the other hand, is found both in the lower animals and in many inanimate objects.

We say, for example, that the horse came “by chance,” because, though his coming saved him, he did not come for the sake of safety.

Again, the tripod fell “of itself,” because, though when it fell it stood on its feet so as to serve for a seat, it did not fall for the sake of that.

Hence, it is clear that when things that come to be simply for the sake of something do not come to be for the sake of that which happens, but for the sake of something extrinsic, then we say that these things come to be by chance.

These chance events are said to be from fortune if they have the further characteristics of being the objects of deliberate intention and are due to agents capable of that mode of action.

This is indicated by the phrase “in vain,” which is used when A, which is for the sake of B, does not result in B. For instance: taking a walk is for the sake of evacuation of the bowels; if this does not follow after walking, we say that we have walked “in vain” and that the walking was “vain.”

This implies that what is naturally the means to an end is “in vain” when it does not effect the end toward which it was the natural means, for it would be absurd for a man to say that he had bathed in vain because the sun was not eclipsed, since the one was not done with a view to the other.

Thus, that which is by chance is, even according to its derivation, the case in which the thing itself happens in vain.

The stone that struck the man did not fall for the purpose of striking him; therefore, it fell by chance, because it might have fallen by the action of an agent and for the purpose of striking.

The difference between chance and what results by fortune is greatest in things that come to be by nature. For when anything comes to be contrary to nature, we do not say that it came to be by fortune, but from what is per se frustrated.

Yet, strictly, this too is different from what is per se frustrated; for the cause of the latter is external, that of the former internal. We have now explained what fortune is and what chance is, and in what they differ from each other.

Both belong to the mode of causation “source of change,” for either some natural or some intelligent agent is always the cause; but in this sort of causation, the number of possible causes is infinite.

Chance and fortune are causes of effects that, though they might result from intelligence or nature, have in fact been caused by something accidentally. Now, since nothing which is accidental is prior to what is per se, it is clear that no accidental cause can be prior to a cause per se. Chance and fortune, therefore, are posterior to intelligence and nature. Hence, however true it may be that the heavens are due to chance, it will still be true that intelligence and nature will be prior causes of this [whole] and of many things in it besides.

It is clear, then, that there are causes and that the number of them is what we have stated. The number is the same as that of the things comprehended under the question “why?”

The why is reduced finally to what the thing is in things that do not involve motion, like mathematics (to the definition of “straight line” or “commensurable,” etc.); or to what initiated a motion (such as, “Why does someone fight?” “Because he has stolen”); or to inquiring, “for the sake of what?” (e.g., “that they may rule”); or in the case of things that come into being, to looking for the matter. The causes, therefore, are these and so many in number.

226. Having treated fortune and chance with reference to those aspects in which they are alike, the Philosopher here explains the difference between them.

This section is divided into two parts.

First, he explains the difference between fortune and chance;

second, at the difference between (197b32; [235]), he explains that in which this difference primarily consists.

The first part is divided into two parts.

First, he explains the difference between chance and fortune;

second, at hence, it is clear (197b18; [233]), he summarizes what he has said about each of them.

227. Concerning the first part, he makes two points.

First (197a36), he explains the difference between chance and fortune. He says that they differ by reason of the fact that chance pertains to more things than fortune, because everything that is by fortune is by chance, but not conversely.

228. Second, at fortune and what results (197b1), he clarifies the difference mentioned above.

First, he designates the things in which fortune is found.

Second, at that which is by chance (197b13; [231]), he shows that chance is found in more things.

Concerning the first part, he makes two points.

First, he designates the things in which fortune is found.

Second, at thus, an inanimate thing (197b6; [230]), he draws a conclusion about those things in which fortune is not found.

229. He says first that fortune and that which is by fortune are found in those things in which something is said to happen well. For fortune is found in those things in which there can be good fortune and misfortune. Now, a thing is said to happen well for him to whom action belongs.

However, action belongs properly to the one who has dominion over his action. For what does not have dominion over its action is that which is acted upon, rather than that which acts. And, thus, action is not in the power of that which is acted upon, but rather in the power of that which acts.

Now, since the active or practical life pertains to those who have dominion over their acts (for here is where operation according to virtue or vice is found), it is necessary that fortune pertains to the practical.

A sign of this is the fact that fortune seems to be the same as happiness, or very nearly so. Hence, the happy are commonly called the fortunate. For according to those who think that happiness consists in external goods, happiness is the same as fortune; but according to those who say that external goods, in which fortune plays a great part, help as instruments in the attainment of happiness, good fortune is close to happiness because it helps one attain it. Hence, since happiness is a certain operation, since it is good operation—namely, that of perfected virtue, as is said in Ethics 1.8¹—it follows that fortune pertains to the actions in which one happens to act well or is impeded from acting well. And this means that things turn out either well or badly. Hence, since one has dominion over his actions insofar as he acts voluntarily, it follows that, in those actions alone where one acts voluntarily should something happen by fortune, but not in others.

230. Next, at thus, an inanimate thing (197b6), he draws from the above a conclusion about the things in which fortune is not found.

He says that, since fortune is found only in those who act voluntarily, it follows that neither an inanimate thing nor a child nor a beast act by fortune, since they do not act voluntarily as having free choice (which is here called that which is proposed).

Hence, neither good fortune nor misfortune can happen to them except metaphorically. Thus, someone said that the stones from which altars are built are fortunate because honor and reverence are shown them, but the stones next to the altar stones are walked upon.

This is said because of a certain likeness to men, among whom the honored seemed to be fortunate, whereas those stones that are walked upon are called unfortunate.

But, although it follows from the foregoing that such things do not act by fortune, there is nothing to prevent them from being acted upon by fortune. For some voluntary agent may act upon them. Thus, we say that it is good fortune when a man finds a treasure or that it is a misfortune when he is struck by a falling stone.

231. Next, at that which is by chance (197b13), he points out that chance is found also in other things.

Concerning this, he makes three points.

First, he shows that chance is found in other things;

second, at hence, it is clear (197b18; [233]), he draws a certain conclusion from what was said above;

third, at this is indicated (197b22; [234]), he uses an example to clarify the point.

232. He says first that chance is found not only in men, who act voluntarily, but also in other animals, and even in inanimate things. He gives an example dealing with other animals. It is said that a horse comes by chance when his coming is conducive to his safety, although he did not come for the sake of safety. He gives another example taken from inanimate things. We say that a tripod falls by chance because, as it stands, it is suitable for sitting, although it did not fall for the sake of this, namely, so that someone might sit on it.

233. Next, at hence, it is clear (197b18), he draws the following conclusion from the above: when things that come to be simply for the sake of something do not come to be for the sake of that which happens, but for the sake of something extrinsic, then we say that these things come to be by chance. But we say that, among the things that come to be by chance, only those things that happen in those who have free choice come to be by fortune.

234. Next, at this is indicated (197b22), he clarifies what he has stated in this conclusion, that chance occurs in those things that happen for the sake of something. A sign of this is the fact that the word vain is used, which is close to “chance” in the Greek.

For we use the term vain when that which is for the sake of something does not come to be because of that something, that is, when that thing on account of which it comes to be does not occur.

Thus, if one should walk in order to evacuate the bowels, and if this should not happen to the walker, then he is said to have walked in vain, and his walking would be vain. Thus, that which is suitable for the coming to be of something is vain and frustrated when it does not accomplish that for whose coming to be it is suitable.

He explains why he says that for whose coming to be it is suitable. If someone were to say that he bathed in vain because the sun was not eclipsed while he bathed, he would speak ridiculously, because bathing oneself is not apt for producing an eclipse of the sun.

Hence chance, which in the Greek is called automatum—that is, per se frustrated—occurs in those things that are for the sake of something. This is also true of that which is frustrated or vain. For the name per se frustrated signifies the very thing that is frustrated, just as per se man signifies man himself and per se good signifies good itself.

He gives an example of things that happen by chance. Thus, it is chance when it is said that a stone that strikes someone when falling did not fall for the purpose of striking him. Therefore, it fell because of that which is per se vain or per se frustrated, for the stone does not naturally fall for this purpose. However, at times a stone does fall as thrown by someone for the purpose of hitting another.

However, although chance and the vain are alike insofar as each is among the things that are for the sake of something, they nevertheless also differ. For a thing is called vain because of the fact that that which was intended does not follow, whereas a thing is called chance because of the fact that something else that was not intended does follow.

Hence, sometimes a thing is vain and chance at the same time, such as when that which was intended does not occur but something else does occur. However, sometimes there is chance but not the vain, as when both that which was intended and something else occur. And there is the vain and no chance when neither that which was intended nor anything else occurs.

235. Next, at the difference (197b32), he explains that in which chance most of all differs from fortune. He says that they differ most of all in the things that happen by nature, because chance has a place here but fortune does not. For when in the operations of nature something happens outside of nature—for example, when a six fingered person is born—we do not say that this happens by fortune, but rather because of that which is per se frustrated, that is, by chance.

And so we can take as another difference between chance and fortune the fact that the cause of those things that are by chance is intrinsic, just as the cause of those things that are by nature is intrinsic. But the cause of those things that are by fortune is extrinsic, just as the cause of those things that are from free choice is extrinsic.

And he finally concludes that he has now explained what the per se frustrated or chance is, what fortune is, and how they differ from each other.

236. Next, at both belong (198a2), he points out the genus of cause to which chance and fortune are reduced.

First, he states his position;

second, at chance and fortune are causes (198a5; [237]), he disproves from this a certain opinion mentioned above.¹

He therefore says first that both chance and fortune are reduced to the genus of the moving cause. For chance and fortune are causes either of those things that proceed from nature or of those things that proceed from intelligence, as is clear from what has been said.

Hence, since nature and intelligence are causes as things from which motion begins, so fortune and chance also are reduced to the same genus. But since chance and fortune are per accidens causes, their number is indeterminate, as was said above.¹

237. Next, at chance and fortune are causes (198a5), he refutes the opinion of those who maintain that fortune and chance are the causes of the heavens and of all worldly things.

He says that since chance and fortune are per accidens causes of those things of which intellect and nature are the per se causes, and since a per accidens cause is not prior to a per se cause, as nothing per accidens is prior to that which is per se, it follows that chance and fortune are causes that are posterior to intellect and nature.

Hence, if it should be held that chance is the cause of the heavens, as some maintained, as was said above,¹ it would follow that intellect and nature are first of all causes of some other things and afterwards causes of the whole universe.

Moreover, the cause of the whole universe seems to be prior to the cause of some part of the universe, since any part of the universe is ordered to the perfection of the universe. But it seems to be inconsistent that some other cause is prior to that which is the cause of the heavens. Hence, it is inconsistent that chance is the cause of the heavens.

238. Furthermore, we must consider that, if those things that happen fortuitously or by chance—that is, outside the intention of inferior causes—are reduced to some superior cause that orders them, then, in relation to this latter cause, they cannot be said to be fortuitous or by chance. Hence, that superior cause cannot be called fortune.

239. Next, at it is clear, then (198a14), he shows that the causes are not more than those mentioned. This is clarified as follows. The question of why asks for the cause. But only the above mentioned causes answer the question of why. Therefore, the causes are not more than those that were mentioned. He says that the answers to the question of why are the same in number as the above mentioned causes.

For sometimes the why is reduced finally to what the thing is, to the definition, as is clear in all immobile things. The mathematicals are of this sort, in which the why is reduced to the definition of the straight or of the commensurate, or of some other thing that is demonstrated in mathematics. Since a right angle is defined as that angle that is formed by the falling of one line upon another that makes two equal angles on each side, then, if it should be asked why an angle is a right angle, the reply would be because it is formed by a line making two equal angles on each side. And it is the same in the other instances.

Sometimes the why is reduced to the first moving cause. Thus, for instance, “Why does someone fight?” “Because he has stolen.” For this is what brought on the fight.

Sometimes it is reduced to the final cause, as if we should ask for the sake of what does someone fight, with the answer being that he might rule.

Sometimes it is reduced to the material cause, as when it is asked why this body is corruptible and the answer is that it is composed of contraries.

Thus, it is clear that these are the causes and they are just so many.

240. Furthermore, there must be four causes. A cause is that upon which the existence of another follows. Now, the existence of that which has a cause can be considered in two ways.

First, it is considered absolutely, and thus the cause of the existing is the form by which something is in act;

second, it is considered insofar as a being comes to be in act from being in potency.

And, since everything that is in potency is reduced to act by that which is a being in act, it is necessary that there be two other causes: the matter and the agent that reduces the matter from potency to act. However, the action of the agent tends toward something determinate, and thus it proceeds from some determinate principle. For every agent does that which is suitable to it. But that toward which the action of the agent tends is called the final cause. Therefore, there must be four causes. But, since the form is the cause of existing absolutely, the other three are causes of existence insofar as something receives existence. Hence, in immobile things, the other three causes are not considered, but only the formal cause is considered.

Natural philosophy demonstrates from all four causes

Now, the causes being four, it is the business of the physicist to know about them all, and if he refers his problems back to all of them, he will assign the “why” in the way proper to his science—the matter, the form, the mover, and “that for the sake of which.”

The last three often coincide, for the “what” and “that for the sake of which” are one, while the primary source of motion is the same in species as these (for man generates man).

And so too, in general, are all things that cause motion by being themselves moved;

and such as are not of this kind are no longer inside the province of physics,

for they cause motion not by possessing motion or a source of motion in themselves, but being themselves incapable of motion.

Hence there are three branches of study: the first of things that are incapable of motion; the second of things in motion but indestructible; the third of destructible things.

The question of why, then, is answered by reference to the matter, to what the thing is, and to the primary moving cause.

For in respect of generation, it is mostly in this last way that causes are investigated—“What comes to be after what? What is it that first makes, or undergoes change?” and so at each step of the series.

Now, the principles that cause motion in a physical way are two, of which one is not physical, as it has no principle of motion in itself. Of this kind is whatever causes motion but is not itself moved, such as that which is completely unchangeable, the primary reality.

Of this kind is also the essence of that which is coming to be, namely, the form. For this is the end, or “that for the sake of which.”

Hence, since nature is for the sake of something, we must know this cause also.

We must explain the “why” fully: one, that “from this” that will necessarily result (“from this” either simply or most of the time);

and “this must be so if that is to be so” (as the conclusion presupposes the premises);

and that this was the essence of the thing;

and because it is better thus (not without qualification, but with reference to the essential nature in each case).

241. Having treated the causes, the Philosopher here shows that the natural philosopher demonstrates from all the causes.

Concerning this, he makes two points.

First, he states his intention.

Second, at the last three (198a24; [242]), he explains his position.

He therefore says first (198a22) that, inasmuch as there are four causes, as was said above,¹ it pertains to natural science both to know all of them and to demonstrate naturally through all of them by reducing the question “why?” to each of the aforementioned causes: the form, the moving cause, the end, and the matter.

Next, at the last three (198a24; [242]), he explains his position.

Concerning this, he makes two points.

First, he sets forth certain things that are necessary to clarify his position.

Second, at, the question (198a31; [244]), he proves his position.

Concerning the first point, he sets forth two things that are necessary for the proof of what follows.

The first of these deals with the relationship of the causes among themselves.

The second deals with the consideration of natural philosophy and is given at and so too, in general (198a27; [243]).

242. He says first (198a24) that it often happens that three of the causes combine into one, such that the formal cause and the final cause are one in number. This must be understood to apply to the final cause of generation but not to the final cause of the thing generated. For the end of the generation of man is the human form, but this form is not the end of man. Rather, man acts for his end through this form. But the moving cause is the same as both of these according to species. And this is especially true in univocal agents, in which the agent produces something like unto itself according to species, as man generates man. For in these cases, the form of the generator, which is the principle of generation, is the same in species as the form of the generated, which is the end of the generation.

However, in non-univocal agents, the species is different. For in these cases, the things that come to be cannot reach the point where they follow upon the form of the generator according to the same kind of species. Rather, they participate in some likeness to it insofar as they are able, as is clear in those things that are generated by the sun. Therefore, the agent is not always the same in species with the form, which is the end of generation; furthermore, not every end is a form. And because of this, it is significant that he said often. But the matter is neither the same in species nor the same in number as the other causes. For matter as such is being in potency, whereas the agent as such is being in act, and the form or the end is act or perfection.

243. Next, at and so too (198a27), he makes his second point that deals with the things that natural philosophy should treat. He says that it pertains to natural philosophy to consider any movers that move in such a way that they are moved. But things that move but are not themselves moved do not belong within the consideration of natural philosophy, which properly considers natural things that have in themselves a principle of motion. For movers that are not themselves moved do not have in themselves a principle of motion, since they are not moved, but are immobile. Thus, they are not natural things, and as a result do not come under the consideration of natural philosophy.

Hence, it is clear that there are three branches of study; the study and intention of philosophy is threefold according to the three genera of things which are found.

For some things are immobile, and one philosophical study deals with them.

Another philosophical study deals with things that are mobile but incorruptible, such as the celestial bodies.

And there is a third philosophical study that deals with things that are mobile and corruptible, such as the inferior bodies.

The first of these studies pertains to metaphysics, while the other two pertain to natural science, which treats all mobile things, both corruptible and incorruptible.

Hence some have misunderstood this passage, desiring to reduce these three studies to the three parts of philosophy: mathematics, metaphysics, and physics. For astronomy, which seems to consider the incorruptible mobile things, belongs more to natural philosophy than to mathematics, as was said above.¹ For insofar as it applies mathematical principles to natural matter, it considers mobile things. Therefore, this division is taken according to the diversity of things existing outside the mind, and not according to the division of the sciences.

244. Next, at the question of why (198a31), he sets forth his position.

Concerning this, he makes two points.

First, he shows that it pertains to natural philosophy to consider all the causes and to demonstrate through them. These are the two points he has proposed above.

Second, at we must explain, then (198b10; [250]), he proves certain things that are assumed in this argument.

Concerning the first part, he makes two points.

First, he shows that natural philosophy considers all the causes.

Second, at we must explain the “why” (198b5; [247]), he shows that it demonstrates through all of them.

Concerning the first part, he makes two points.

First, he shows that natural philosophy considers the matter and the form and the moving cause.

Second, at of this kind is also (198b3; [246]), he shows that it considers the end.

Concerning the first part, he makes two points.

First, he states his intention;

second, he proves it, at for in respect of (198a33; [245]).

First (198a31) he concludes from what was said above that the “why” is assigned to natural things by reference to the matter, and to what the thing is (namely, the form), and to the first mover.

245. Next, at for in respect of (198a33), he proves his position as follows. It has been said that natural philosophy considers those things that are moved, both the generable and the corruptible. Therefore, whatever should be considered about generation should be considered by natural philosophy. But, with reference to generation, one ought to consider the form, the matter, and the moving cause.

Those who wish to consider the causes of generation consider them as follows.

First, we consider what it is that comes to be after something, as fire come to be after air, since fire is generated from air. And the form, through which the generated is what it is, is considered in this way.

Next, we consider what it is that first makes; that is, we consider that which first moves to generation. And this is the moving cause.

Next, we consider what it is that undergoes this change. And this is the subject and the matter. With reference to generation, we consider not only the first mover and the first subject, but also those things that are consequent upon them.

And thus it is clear that it pertains to natural philosophy to consider the form, the mover, and the matter. However, natural philosophy does not consider every mover. For there are two kinds of moving principles: the moved and the unmoved. Now, a mover that is not moved is not natural, because it does not have in itself a principle of motion. And such is the moving principle that is altogether immobile and the first of all movers, as will be shown in book 8.¹

246. Next, at of this kind is also (198b3), he shows that natural philosophy also considers the end. He says that the form and what the thing is also fall under the consideration of natural philosophy, insofar as the end is that for the sake of which the generation occurs. For it was said above that the form and the end coincide in the same thing. And since nature acts for the sake of something, as will be proven below,¹ it must belong to natural philosophy to consider the form not only insofar as it is form but also insofar as it is the end. If, however, nature were not to act for the sake of something, then natural philosophy would consider form insofar as it is form, but not insofar as it is an end.

247. Next, at we must explain the “why” (198b5), he shows how natural philosophy demonstrates through all the causes.

First, he shows how it demonstrates through matter and the moving cause, which are the prior causes in generation.

Second, at that “this must be so” (198b7; [248]), he shows how it demonstrates through the form.

Third, at and because it is better (198b9; [249]), he shows how it demonstrates through the end.

He says first (198b5) that, in natural things, the “why” must be elaborated fully, that is, in every genus of cause. Thus, if something has gone before—whether it be the matter or the mover—then something necessarily follows. For example, if something is generated from contraries, it is necessary that the latter be corrupted, and if the sun approaches the north pole, the days must become longer, and cold must diminish and heat increase for those who dwell in the northern part. However, we must realize that it is not always necessary that something follows from a preceding matter or mover. Rather, sometimes a thing follows simply or in every case, as in the things mentioned. But sometimes a thing follows in most instances: for instance, from human seed and a mover in generation, it follows in most instances that what is generated has two eyes, but at times this fails to happen. Similarly, because of the fact that matter is so disposed in the human body, it happens that a fever is frequently produced because of festering, but at times this is impeded.

248. Next, at and “this must be so” (198b7), he shows how, in natural things, demonstration must be made through the formal cause. In order to understand this, we must know that, when something follows from the preceding causes in generation (that is, from the matter and the mover) by necessity, then a demonstration can be established, as was said above.

However, a demonstration cannot be established when something follows in most instances. But, then, a demonstration must be taken from what is posterior in generation so that something should follow necessarily from another, as the conclusion follows from the principles of a demonstration.

Let us proceed thus in demonstration: if this should come to be, then this and that are required. For example, if man should be generated, it is necessary that human seed be an agent in the generation.

If, however, we proceed conversely by saying that human seed is an agent in generation, then the proposition that therefore, man will be generated does not follow as a conclusion follows from propositions.

But that which ought to come to be—namely, that in which the generation is terminated—was, as was said above, what the thing was to be, namely, the form.

Hence, it is clear that, when we demonstrate according to this mode—namely, that this must be so if that is to be so—we demonstrate through the formal cause.

249. Next, at and because it is better (198b9), he shows how natural philosophy demonstrates through the final cause. He says that natural philosophy sometimes also demonstrates that something is true because it is better that it be so. For example, we might demonstrate that the front teeth are sharp because, as such, they are better for cutting food, and nature does what is better. Nature does not, however, do what is better simply, but what is better with reference to what belongs to each substance; otherwise, nature would give a rational soul, which is better than an irrational soul, to each animal.

The argument of those who deny that nature acts for an end

We must explain, then, that nature belongs to the class of causes that act for the sake of something; afterward, [we must explain] about the necessary and its place in physical problems, for all writers ascribe things to this cause, arguing that, since the hot and the cold and the like are of such and such a kind, therefore certain things necessarily are and come to be—and if they mention any other cause (one, “friendship and strife,” another, “mind”), it is only to touch on it and then say good-bye to it.

A difficulty presents itself: why should not nature work neither for the sake of something nor because it is better so, but just as Jupiter rains, not in order to make the corn grow, but of necessity?

What is drawn up must cool, and what has been cooled must become water and descend, the result of this being that the corn grows. Similarly, if a man’s crop is spoiled on the threshing floor, the rain did not fall for the sake of this—in order that the crop might be spoiled—but that result just followed.

Why, then, should it not be the same with the parts in nature, such as that our teeth should come up of necessity (the front teeth sharp, fitted for tearing, the molars broad and useful for grinding down the food) since they did not arise for this end, but it was merely a coincident result? And so [we might ask] with all other parts in which we suppose that there is purpose.

Then, wherever all the parts came about as just what they would have been if they had come to be for an end, such things survived, being organized spontaneously in a fitting way; but those that grew otherwise perished and continue to perish, as Empedocles says his “man-faced ox-progeny” did. Such are the arguments (and others of the kind) that may cause difficulty on this point.

250. Having shown that natural philosophy demonstrates from all the causes, the Philosopher here clarifies certain things that he had assumed:¹ that nature acts for an end and that, in some things, necessity is not from the causes that are prior in being (which are the matter and the moving cause), but from the posterior causes, which are the form and the end.

Concerning this, he makes two points.

First, he states his intention;

second, at a difficulty presents itself (198b16; [251]), he develops his position.

He therefore says first (198b10) that it must be pointed out that nature is among the number of causes that act for the sake of something. And this is important with reference to the problem of providence. For things that do not know the end do not tend toward the end unless they are directed by one who does know, as the arrow is directed by the archer. Hence, if nature acts for an end, it is necessary that it be ordered by someone who is intelligent. This is the work of providence.

After this, it must be pointed out how necessity is present in natural things. Is the necessity of natural things always from the matter, or is it sometimes from the matter and the mover, or sometimes from the form and the end?

It is necessary to make this inquiry for the following reason. All of the ancient natural philosophers, when giving the reason for natural effects, reduced such effects to this cause, namely, that it is necessary for these things to happen because of matter. For example, since heat is by nature what it is and naturally produces a certain effect (and in like manner cold and other similar things), then those things that are caused by them must come to be or exist. And, if some of the ancient natural philosophers touched upon some cause other than the necessity of matter, they have no reason for taking any glory from the fact. For after such causes were posited by them—for instance, intellect, which Anaxagoras posited, and friendship and strife, which Empedocles posited—they did not use them except in certain general instances, such as in the constitution of the world. But they omitted such causes when discussing particular effects.

251. Next, at a difficulty presents itself (198b16), he develops his position.

First, he asks whether nature acts for the sake of something;

second, at as regards what is “of necessity” (199b34; [269]), how necessity is found in natural things.

Concerning the first part, he makes two points.

First, he gives the opinion and argument of those who hold that nature does not act for the sake of something;

second, he disproves this position, at yet it is impossible (198b34; [255]).

252. Concerning the first point, it must be noted that those who held that nature does not act for the sake of something tried to confirm their position by denying that in which nature is most clearly seen to act for the sake of something. That which most strongly demonstrates that nature acts for the sake of something is the fact that, in the operation of nature, a thing is always found to come to be as good and as suitable as it can be. Thus, the foot is made in a certain way by nature so that it may be suitable for walking. Hence if it falls short of this natural disposition, it is not fit for this use. And the same is true of other instances.

And, since they tried especially to oppose this point, Aristotle says (198b16) that it can be objected that there is nothing to prevent nature from not acting for the sake of something or from doing what is always better.

For at times, we find that, from some operation of nature, some utility results that nevertheless is not the end of that natural operation, but merely happens to occur. Thus, we might say that Jupiter rains—that is, God or universal nature—but not for the purpose that grain should grow.

Rather, rain results from the necessity of matter. For it must be that, in the lower regions, because of the closeness of the heat of the sun, vapors are drawn out from the water. Having been carried above because of the heat, when they arrive at the point where heat is lacking because of the distance from the place where the rays of the sun are reflected, it is necessary that the vaporized water that is going up freeze at that very point. When the freezing is completed, the vapors are changed into water. And, when water has been generated, it must fall down because of its weight. And, when this takes place, it happens that the grain grows.

Nevertheless, it does not rain so that grain might grow. For in the same way, grain might be destroyed in some place because of rain, as when grain is gathered on a thrashing floor. Nevertheless, rain does not fall in order to destroy grain; rather, this happens by chance when rain falls. And, in the same way, it seems to happen by chance that grain accidentally grows when rain falls.

Hence, it seems that there is nothing to prevent this from being true also in regard to animals, which seem to be disposed for the sake of some end. For example, one might say that, because of the necessity of matter, some teeth—namely, the front teeth—happen to be sharp and suitable for cutting food, and the molars happen to be broad and useful for grinding food.

Nevertheless, nature did not make the teeth such and such for the sake of these utilities. Rather, after teeth have been made by nature in such a way as they develop from the necessity of matter, it is accidental that they acquired such a form. And, once this form exists, this utility follows. And the same thing can be said of all other parts that seem to have some determinate form for the sake of some end.

253. But one might say that such utilities follow always or in many cases, and what is always or in most cases suitable exists by nature. In order to forestall this objection, they say that, from the beginning of the formation of the world, the four elements were joined in the constitution of natural things, and thus the many and varied dispositions of natural things were produced. And, in all these things, only that which happened to be suitable for some utility, as if it were made for that utility, was preserved, for such things had a disposition that made them suitable for being preserved not because of some agent intending an end, but because of that which is per se vain, that is, by chance. On the other hand, whatever did not have such a disposition was destroyed, and is destroyed daily. Thus Empedocles said that, in the beginning, things that were part ox and part man were generated.

254. Therefore, because of this argument, or because of some other similar argument, some will have a difficulty on this point. But in regard to this argument, it must be noted that they use an unsuitable example. For although rain does have a necessary cause in regard to matter, it is nevertheless ordered to some end, namely, the conservation of things generable and corruptible. For in inferior things, mutual generation and corruption are for this purpose: that perpetual existence be preserved in them. Hence, the growth of grain is poorly taken as an example. For a universal cause is referred to a particular effect. And it must also be noted that the growth and conservation of growing things on earth occur in most cases because of the rain, whereas their corruption occurs in few instances. Hence, although rain is not for their destruction, it does not follow that it is not for their preservation and growth.

Nature acts for an end

Yet it is impossible that this should be the true view. For teeth and all other natural things either invariably or normally come about in a given way; but of not one of the results of fortune or chance is this true.

We do not ascribe to chance or mere coincidence the frequency of rain in winter, but frequent rain in summer we do; nor heat in the dog days, but only if we have it in winter.

If it is agreed, then, that things are either the result of coincidence or for an end, and that these cannot be the result of fortune or chance, it follows that they must be for an end; and that such things are all due to nature even the champions of the theory that is before us would agree.

Therefore, action for an end is present in things that come to be and are by nature.

Further, where a series has a completion, all the preceding steps are for the sake of that. Now, surely, as it is in intelligent action, so it is suitably adapted; and as suitably adapted, so it is in each action if nothing interferes.

Now, intelligent action is for the sake of an end; therefore, the nature of things also is so. Thus, if a house, for instance, had been a thing made by nature, it would have been made in the same way as it is now by art, and if things made by nature were made also by art, they would come to be in the same way as by nature. Each step in the series, then, is for the sake of the next.

Art sometimes completes what nature cannot bring to a finish and at other times imitates her. If, therefore, artificial products are for the sake of an end, so clearly also are natural products. The relation of the later to the earlier terms of the series is the same in both.

This is most obvious in the animals other than man: they make things neither by art nor after inquiry or deliberation. Therefore, people discuss whether it is by intelligence or by some other faculty that spiders, ants, and the like work.

By gradual advance in this direction, we come to see clearly that, in plants too, that is produced that is conducive to the end—leaves, for example, grow to provide shade for the fruit.

If, then, it is both by nature and for an end that the swallow makes its nest and the spider its web, and plants grow leaves for the sake of the fruit and send their roots down (not up) for the sake of nourishment, it is plain that this kind of cause is operative in things that come to be and are by nature.

And, since “nature” means two things, the matter and the form, of which the latter is the end, and since all the rest is for the sake of the end, the form must be the cause in the sense of “that for the sake of which.”

255. Having stated the opinion and argument of those who say that nature does not act for an end, he here disproves this position.

He does this first through proper arguments;

second, at now, mistakes come to pass (199a33; [261]), through arguments taken from those things from which the opponents tried to prove the contrary position.

256. Concerning the first point, he sets forth five arguments.

The first (198b34) is as follows. Everything that happens naturally happens either in every instance or in most instances. But nothing that happens by fortune or by that which is per se vain—that is, by chance—happens in every instance or in most instances.

For we do not say that it rains frequently in winter by fortune or by chance. But if it rains frequently in the dog days, we would say that this happens by chance. And in like manner, we do not say that it happens by chance that there is heat during the dog days, but only if this should happen during the winter.

From these two points, he argues as follows. Everything that happens does so either by chance or for the sake of an end. Now, those things that happen outside the intention of an end are said to happen by chance.

But it is impossible for those things that happen in every instance or in most instances to happen by chance. Therefore, those things that happen in every instance or in most instances happen for the sake of an end.

Now, whatever happens according to nature happens either in every instance or in most instances, as even they admitted. Therefore, whatever happens by nature happens for the sake of something.

257. He gives the second argument at further, where a series (199a8). He says that there is an end for all things. That which is prior and all of its consequences are done for the sake of the end. Having assumed this, he argues as follows. As something is done naturally, so is it disposed to be done. For suitably adapted means naturally. And this proposition is convertible, for as something is disposed to be done, so it is done. However, it is necessary to add the condition “unless it is impeded.” Therefore, let us agree that there is no impediment. Hence, as something is done naturally, so is it disposed to be done. But things that happen naturally are done so that they lead to an end. Therefore, they are disposed to be done in such a way that they are for the sake of an end. And thus nature seeks an end; that is, nature has a natural disposition for an end. Hence, it is clear that nature acts for the sake of an end.

He clarifies what he has said by an example. One proceeds from the prior to the posterior in the same way in both art and nature. Thus, if artificial things such as houses were made by nature, they would be made according to the order in which they now are made by art. Thus, the foundation would be constructed first, and afterward the walls would be erected, and finally the roof would be placed on top. For nature proceeds this way in the things that are rooted in the earth, like plants. Their roots, like a foundation, are fixed in the earth; the trunk, after the manner of a wall, is raised on high; and the branches are on top like a roof.

And, in like manner, if the things that are produced by nature were made by art, they would be made according to the way they are disposed to be produced by nature.

This is clear in regard to health, which happens to be produced by art and by nature. For as nature heals by heating and cooling, so also does art.

Hence, it is clear that, in nature, one thing is for the sake of another; that is, the prior is for the sake of the posterior. And the same is true of art.

258. He gives the third argument at art sometimes completes (199a15). He says that art makes certain things that nature cannot make, such as a house and things of this sort. However, in regard to those things that happen to be produced by art and by nature, art imitates nature, as is clear in regard to health, as was said above.

Hence, if things that are made according to art are for the sake of an end, it is clear that things that are made according to nature also are made for an end, since the prior and the posterior in each case are similarly related. However, one might say that this is not a different argument from the one already given, but complementary to it and a clarification of it.

259. He gives the fourth argument at this is most obvious (199a20). This argument is drawn from those things in nature that more obviously seem to act for the sake of something. He says that it is most clear that nature acts for the sake of something when we consider animals that act neither through art nor through inquiry or deliberation. It is manifest in their operations that they act for the sake of something. Because of this, some have wondered whether spiders and ants and animals of this sort act through intellect or through some other principle. But, because they always act in the same way, it is clear that they do not act by intellect, but by nature. For every swallow makes a nest in the same way, and every spider a web in the same way, which would not be the case if they acted by intellect and from art. For not every builder makes a house in the same way, because the artisan judges the form of the thing built and can vary it. If we proceed beyond animals to plants, it is apparent among them that some things have been made and are useful for an end, as the leaves are useful as a covering for the fruit. Hence, if these things are due to nature and not to art—namely, that the swallow makes a nest and the spider a web, and that the plants produce leaves for the sake of the fruit, and the roots of plants are not above, but below so that they might take nourishment from the earth—it is clear that a final cause is found in things that come to be and are by nature, that is, by nature acting for the sake of something.

260. He gives the fifth argument at and, since “nature” means (199a30). He says that “nature” is used in two ways: for the matter and for the form. The form is the end of generation, as was said above.¹ And the account of an end is that other things come to be for the sake of it. Hence, it follows that to be and to come to be for the sake of something should be found in natural things.

Opponents’ arguments show that nature acts for an end

Now, mistakes come to pass even in the operations of art: the grammarian makes a mistake in writing and the doctor pours out the wrong dose.

Hence, mistakes are clearly possible in the operations of nature also. If, then, there are cases in art in which what is rightly produced serves a purpose, and if where mistakes occur there was a purpose in what was attempted but not attained, so must it be also in natural products, and monstrosities will be failures in the purposive effort.

Thus, in the original combinations, the “ox-progeny,” if they failed to reach a determinate end, must have arisen through the corruption of some principle corresponding to what is now the seed.

Further, seed must have come into being first, and not straightway the animals: the words “whole-natured first” must have meant seed.

Again, in plants, too, we find the relation of means to end, though the degree of organization is less. Were there in plants, then, also “olive-headed vine-progeny,” like the “man-headed ox-progeny,” or not? It seems an absurd suggestion, but there must have been, if there were such things among animals.

Moreover, among the seeds, anything must have come to be at random.

But the person who asserts this entirely does away with “nature” and what exists “by nature.”

For those things are natural that arrive at some completion by a continuous motion originated from an internal principle: the same completion is not reached from every principle; nor any chance completion, but always the tendency in each is towards the same end, if there is no impediment.

The end and the means toward it may come about by chance.

We say, for instance, that a stranger has come by chance and gone away after he has bathed,¹ when he does so as if he had come for that purpose, though it was not for that that he came. This is accidental, for chance is an accidental cause, as I remarked before. But, when an event takes place always or for the most part, it is not accidental or by chance. In natural products, the sequence is invariable, if there is no impediment.

It is absurd to suppose that purpose is not present because we do not observe the agent deliberating. Art does not deliberate. If the ship-building art were in the wood, it would produce the same results by nature. If, therefore, purpose is present in art, it is present also in nature. The best illustration is a doctor doctoring himself; nature is like that. It is plain, then, that nature is a cause, a cause that operates for a purpose.

261. After the Philosopher has shown by appropriate arguments that nature acts for the sake of something, he here intends to make this clear by destroying those things through which some embraced the contrary position.

This section is divided into three parts according to the three things by which some seem to be moved to deny that nature acts for an end.

The second part begins at but the person (199b14; [267]).

The third part begins at it is absurd (199b26; [268]).

262. The first thing by which some seem to be moved to deny that nature acts for an end is the following. Sometimes we see things happen otherwise than is customary, as happens in the case of monsters, which are the errors of nature. Hence, Empedocles held that, at the beginning of the constitution of things, certain things were produced that did not have this form and this order that is now commonly found in nature.

263. He brings forth four arguments to overcome this difficulty.

First (199a33), he shows that, although art acts for the sake of something, error still occurs in things that are made by art. For sometimes the grammarian does not write correctly or the doctor prescribes a drink as a medicinal potion incorrectly.

Hence, it is clear that error occurs also in things that are by nature, even though nature acts for the sake of something. Of the things that are made by art for the sake of something, some are made according to art and are made correctly.

There are other things, however, in which the artisan fails, not acting according to his art, and in these cases, error occurs, even though the art is acting for the sake of something.

For if art does not act for a determinate end, then there would be no error no matter how the art was performed. For the operation of the art would be equally related to all things. The very fact that there happens to be error in art, then, is a sign that art acts for the sake of something.

The same thing also happens in natural things, in which monsters are, as it were, the errors of nature acting for the sake of something insofar as the correct operation of nature is deficient. And this very fact that error occurs in natural things is a sign that nature acts for the sake of something. The same thing is true of those substances that Empedocles said were produced at the beginning of the world, such as the ox-progeny, half ox and half man.

For if such things were not able to arrive at some end and final state of nature such that they would be preserved in existence, this was not because nature did not intend this, but because they were not capable of being preserved.

For they were not generated according to nature, but by the corruption of some natural principle, as it now also happens that some monstrous offspring are generated because of the corruption of seed.

264. He gives the second argument at further, seed must have (199b7). The argument is as follows. Wherever there are determinate principles and a determinate order of proceeding, there must be a determinate end for the sake of which other things come to be. But in the generation of animals, there is a determinate order of proceeding. For it is necessary that seed come to be first, and there is no animal that exists immediately from the beginning. And the seed itself is not immediately hardened, but in the beginning, it is soft and tends toward perfection in a certain order. Therefore, there is a determinate end in the generation of animals. Therefore, monsters and errors do not occur in animals because of nature’s not acting for the sake of something.

265. He gives the third argument at again, in plants (199b9). The argument is as follows. Although nature acts for the sake of something in regard not only to animals but also to plants, the degree of organization is less, namely, it is less clear. Fewer things can be inferred from the operations of plants.

If, therefore, monsters and errors occur in animals because nature does not act for the sake of something, this should be even more true of plants. As the “man-faced ox-progeny” occurs in animals, does there also occur in plants an olive-headed vine-progeny, half olive and half vine? It seems absurd to say that these things occur. Nevertheless, this must be so if it is true in regard to animals that nature does not act for the sake of something. Therefore, in regard to animals it is not true that nature does not act for the sake of something.

266. He gives the fourth argument at moreover, among the seeds (199b13). The argument is as follows. As animals are generated by nature, so also are the seeds of animals.

Therefore, if what occurs in the generation of animals happens in any way whatsoever, and not by nature, as it were, acting for a determinate end, then the same would be true of seeds: any sort of seed would be produced by any sort of thing. This is obviously false. Hence, the first supposition is also false.

267. Next, at but the person (199b14), he destroys the second point by which some were moved to hold that nature does not act for the sake of something. This seemed true to some because things that happen naturally seem to proceed from the prior principles, which are the agent and the matter, and not from the intention for an end.

But Aristotle shows the contrary. He says that one who speaks in this manner—that is, one who says that nature does not act for the sake of something—destroys nature and the things that are according to nature. For those things are said to be according to nature that are moved continuously by some intrinsic principle until they arrive at some end—not to some contingent end, and not from any principle to any end, but from a determinate principle to a determinate end. For progress is always made from the same principle to the same end, unless something impedes it.

However, that for the sake of which something is done sometimes happens to occur by fortune, when it is not done for the sake of this.

For example, if some stranger should come and leave after he has bathed, we say this was by fortune. For he did not bathe himself as if he had come for this purpose, since he did not come for this.

Hence, his bathing is accidental, for fortune is a per accidens cause, as was said above.¹ But, if this should happen always or in most instances to him who comes, it would not be said to be by fortune.

But, in natural things, events occur not per accidens, but always, unless something should impede. Hence, it is clear that the determinate end that follows in nature does not follow by chance, but from the intention of nature. And from this it is clear that it is contrary to the meaning of nature to say that nature does not act for the sake of something.

268. Next, at it is absurd (199b26), he destroys the third point by which some hold the opinion that nature does not act for the sake of something. For it seems to some that nature does not act for the sake of something because nature does not deliberate.

But the Philosopher says that it is absurd to hold this opinion. For it is obvious that art acts for the sake of something, yet it is also obvious that art does not deliberate. Nor does the artisan deliberate insofar as he has the art, but insofar as he falls short of the certitude of the art.

Hence, the most certain arts do not deliberate, as the writer does not deliberate how he should form letters. Moreover, those artisans who do deliberate do not do so in the execution after they have discovered the certain principles of the art.

Thus, one who plays the harp would seem most inexperienced if he should deliberate in playing any chord. And from this it is clear that an agent does not deliberate, not because he does not act for an end, but because he has the determinate means by which he acts.

Hence, since nature has the determinate means by which it acts, it does not deliberate. For nature seems to differ from art only because nature is an intrinsic principle and art is an extrinsic principle. For if the art of ship building were intrinsic to wood, a ship would have been made by nature in the same way as it is made by art. And this is most obvious in the art that is in that which is moved, although per accidens, such as in the doctor who cures himself. For nature is most like this art.

Hence, it is clear that nature is nothing but a certain kind of art—namely, the divine art—impressed upon things, by which these things are moved to a determinate end. It is as if the ship builder were able to give to timbers that by which they would move themselves to take the form of a ship.

Finally, he concludes by saying that it is clear that nature is a cause and that it acts for the sake of something.

How necessity is found in natural things

As regards what is “of necessity,” we must ask whether the necessity is hypothetical, or simple as well.

The current view places what is of necessity in the process of production, just as if one were to suppose that the wall of a house necessarily comes to be because what is heavy is naturally carried downward and what is light to the top; thus, the stones and foundations take the lowest place, with earth above because it is lighter, and wood at the top of all as being the lightest.

Nevertheless, though the wall does not come to be without these, it is not because of these except as its material cause: it comes to be for the sake of sheltering and guarding certain things.

It is the same in all other things that involve production for an end: the product cannot come to be without things that have a necessary nature, but it is not due to these except as its material; it comes to be for an end. For instance, why is a saw this way? To effect such-and-such and for the sake of such-and-such.

This end, however, cannot be realized unless the saw is made of iron. It is therefore necessary for it to be of iron if we are to have a saw and perform the operation of sawing.

What is necessary, then, is necessary on a hypothesis; it is not a result necessarily determined by antecedents. Necessity is in the matter, while “that for the sake of which” is in the definition.

Necessity in mathematics is similar in a way to necessity in things that come to be through the operation of nature.

Since a straight line is what it is, it is necessary that the angles of a triangle should equal two right angles, but not conversely—though, if the angles are not equal to two right angles, then the straight line is not what it is either.

But, in things that come to be for an end, the reverse is true. If the end is to exist or does exist, that also that precedes it will exist or does exist; otherwise, just as the premise will not be true if the conclusion is not true, so here the end or “that for the sake of which” will not exist.

For this too is itself a starting-point, but of the reasoning, not of the action; while the starting-point in mathematics is the starting-point of the reasoning only, as there is no action.

If, then, there is to be a house, such-and-such things must be made or be there already or exist, or generally the matter relative to the end (bricks and stones if it is a house). But the end is not due to these except as the matter, nor will it come to exist because of them.

Yet, if they do not exist at all, neither will the house or the saw—the former in the absence of stones, the latter in the absence of iron—just as, in the other case, the premises will not be true if the angles of the triangle are not equal to two right angles.

The necessary in nature, then, is plainly what we call by the name of matter, and the changes in it. Both causes must be stated by the physicist, but especially the end, for that is the cause of the matter, not vice versa.

And the end is “that for the sake of which,” and the beginning starts from the definition or essence.

This is just as in artificial products: since a house is of such-and-such a kind, certain things must necessarily come to be or be there already; or, since health is this, these things must necessarily come to be or be there already.

Similarly if man is this, then these [must necessarily come to be or be there already]; if these, then those.

Perhaps the necessary is present also in the definition.

For if one defines the operation of sawing as being a certain kind of dividing, then this cannot come about unless the saw has teeth of a certain kind, and these cannot be unless they are of iron. For in the definition too there are some parts that are, as it were, its matter.

269. Having shown that nature acts for an end, the Philosopher here proceeds to inquire into the second question, that is, how necessity is found in natural things.

Concerning this, he makes three points.

First, he raises the question.

Second, at the current view (199b35; [271]), he sets forth the opinion of others.

Third, at nevertheless, though the wall (200a5; [272]), he determines the truth.

270. Thus, he asks (199b34) whether, in natural things, there is a simple necessity—that is, an absolute necessity—or a necessary by condition or by supposition. In order to understand this, it must be noted that the necessity that depends upon prior causes is an absolute necessity, as is clear from the necessity that depends upon matter. That an animal is corruptible is absolutely necessary. For to be composed of contraries is a consequence of being an animal.

In like manner, that which has necessity from the formal cause is also absolutely necessary. For example, man is rational, or a triangle has three angles equal to two right angles, which is reduced to the definition of triangle.

Similarly, that which has necessity from the efficient cause is absolutely necessary. Thus, because of the motion of the sun, it is necessary that day and night alternate. But that which has necessity from that which is posterior in existence is necessary upon condition, or by supposition.

For example, it might be said that it is necessary that this be if this ought to come to be. Necessity of this kind is from the end and from the form insofar as it is the end of generation. Therefore, to ask whether, in natural things, there is a simple necessity or a necessity by supposition is nothing else than to ask whether necessity is found in natural things from the end or from the matter.

271. Next, at the current view (199b35), he gives the opinion of others. He says that some are of the opinion that the generation of natural things arises from an absolute necessity of matter. For example, one might say that a wall or a house is such as it is by the necessity of matter, because heavy things are disposed to move downward and light things to rise above. And, because of this, the heavy and hard stones remain in the foundation, while earth, being lighter, rises above the stones, as is clear in walls constructed of tiles that are made of earth. But the timbers, which are the lightest, are placed at the highest point, at the roof. Thus, they thought that the dispositions of natural things have come to be such as they are from the necessity of matter. For example, it might be said that a man has feet below and hands above because of the heaviness or lightness of humors.

272. Next, at nevertheless, though the wall (200a5), he determines the truth.

Concerning this, he makes two points.

First, he shows what sort of necessity there is in natural things;

second, at necessity in mathematics (200a15; [273]), he compares the necessity of natural things to the necessity that is in the demonstrative sciences.

He first says that, granting that it seems absurd to say that there is such a disposition in natural things because of the matter, it also appears absurd to say that this is true of artificial things, an example of which has already been given. However, such a disposition is not produced in natural things and in artificial things unless the material principles have an aptitude for such a disposition. For a house would not stand well unless the heavier materials were placed in the foundation and the lighter materials above.

However, it must not be said because of these that the house is so disposed that one part of it is below and another above. I say because of these, meaning because of the heaviness or lightness of certain parts (except insofar as the term because of refers to the material cause, which is for the sake of the form).

Rather, the parts of a house are so disposed for the sake of an end, which is to shelter and protect men from the heat and the rain. And, just as it is with a house, so it is with all other things in which something happens to act for the sake of something. For in all things of this sort, the dispositions of what is generated or made do not follow without material principles, which have a necessary matter by which they are apt to be so disposed.

However, the things made or generated are not so disposed because the material principles are such, unless the term because refers to the material cause. Rather, they are so disposed because of the end. And the material principles seek to be apt for this disposition that the end requires, as is clear in a saw. For a saw is this way, that is, has a certain disposition or form. And, for this reason, it must have such a matter. And it has this disposition or form because of some end.

However, this end, which is cutting, could not be achieved unless the saw were of iron. Therefore, it is necessary that a saw be iron if there must be a saw and if it must be for this end, which is its operation. Thus, it is clear that there is a necessity by supposition in natural things, just as there is such a necessity in artificial things, but not such that what is necessary is the end. For that which is necessary is posited on the part of the matter, but the reason for the necessity is posited on the part of the end. For we do not say that there must be such an end because the matter is such. Rather we say that, since the end and the future form are such, the matter must be such. And, so, the necessity is placed in the matter, but the reason for the necessity is placed in the end.

273. Next, at necessity in mathematics (200a15), he compares the necessity that is in the generation of natural things to the necessity that is in the demonstrative sciences.

He does this first with reference to the order of necessity,

and second with reference to that which is the principle of the necessity, at and the end (200a34; [274]).

He says first (200a15) that, in a certain respect, necessity is found in the demonstrative sciences in the same way that it is found in things that are generated according to nature. For a priori necessity is found in the demonstrative sciences, as when we say that, since the definition of a right angle is such, it is necessary that a triangle be such and such—namely, that it have three angles equal to two right angles. Therefore, from that which is first assumed as a principle, the conclusion arises by necessity. But the converse does not follow, that, if the conclusion is true, then the principle is. For sometimes a true conclusion can be drawn from false propositions.

But it does follow that, if the conclusion is not true, then neither is the given premise true. For a false conclusion is drawn only from a false premise.

But, in things that are made for the sake of something, either according to art or according to nature, this converse does obtain.

For if the end either will be or is, then it is necessary that what is prior to the end either will have been or is.

If, however, that which is prior to the end is not, then the end will not be, just as, in demonstrative sciences, if the conclusion is not true, then the premise will not be true.

Thus, it is clear that, in things that come to be for the sake of an end, the end holds the same order that the premise holds in demonstrative sciences. This is so because the end also is a principle, not indeed of action, but of reasoning. For from the end, we begin to reason about those things that are the means to the end.

In demonstrative sciences, however, a principle of action is not considered, but only a principle of reasoning, because there are no actions in demonstrative sciences, but only reasonings.

Hence, in things that are done for the sake of an end, the end properly holds the place that the premise holds in demonstrative sciences. Hence, there is a similarity on both sides, even though they seem to be related conversely because of the fact that the end is last in action, which does not pertain to demonstration.

Therefore, he concludes that, if a house, which is the end of a generation, is to come to be, it is necessary that the matter that is for the sake of this end come to be and preexist. Thus, tiles and stones must exist first if a house is to come to be. This does not mean that the end is for the sake of the matter, but rather that the end will not be if the matter does not exist.

Thus, there will be no house if there are no stones, and there will be no saw if there is no iron. For just as, in demonstrative sciences, the premises are not true if the conclusion, which is similar to things that are for an end, is not true, so also is the beginning related to the end, as was said.

Thus it is clear that, in natural things, that is said to be necessary that is material or is a material motion. And the reason for this necessity is taken from the end, for it is necessary for the sake of the end that the matter be such. And one ought to determine both causes of a natural thing—that is, both the material and the final cause—but especially the final cause, because the end is the cause of the matter, but not conversely. For the end is not such as it is because the matter is such, but rather the matter is such as it is because the end is such, as was said above.

274. Next, at and the end (200a34), he compares the necessity of natural generation to the necessity of the demonstrative sciences with respect to that which is the principle of the necessity. It is clear that, in demonstrative sciences, the definition is the principle of the demonstration.

And in like manner the end, which is the principle and reason for necessity in things that come to be according to nature, is a sort of principle taken by reason and by definition. For the end of generation is the form of the species that the definition signifies.

This also is clear in artificial things. For as the demonstrator in demonstrating takes the definition as a principle, so also does the builder in building and the physician in curing.

Thus, because the definition of a house is such, this must come to be and exist in order that a house might come to be; because this is the definition of health, this must come to be in order for someone to be cured. And if this and that are to be, then we must accomplish those things that must come to be.

However, in demonstrative sciences, definition is threefold.

One of these is a principle of demonstration, for example, thunder is the extinguishing of fire in a cloud.

The second is the conclusion of a demonstration, for example, thunder is a continuous sound in the clouds.

The third is a combination of these two, for example, thunder is a continuous sound in the clouds caused by the extinguishing of fire in a cloud. This definition embraces within itself the whole demonstration without the order of demonstration. Hence, it is said in Posterior Analytics 1.8 that definition is a demonstration differing by position.¹

Since, therefore, in things that come to be for the sake of an end, the end is like a principle in demonstrative science, and since those things that are for the sake of the end are like the conclusion, there is also found in the definition of natural things that which is necessary because of the end.

For if one wishes to define the operation of a saw (which is a division of a certain sort that will not occur unless the saw has teeth, and these teeth are not suitable for cutting unless they are of iron), it will be necessary to place iron in the definition of saw.

For nothing prevents us from placing certain parts of matter in the definition—not individual parts, such as this flesh and these bones, but common parts, such as flesh and bones. And this is necessary in the definition of all natural things.¹

Therefore, the definition that comprises in itself the principle of the demonstration and the conclusion is the whole demonstration. Thus, the definition that draws together the end, the form, and the matter comprises the whole process of natural generation.

Natural science treats of motion and those things consequent upon it

Nature is the principle of motion and change, and it is the subject of our inquiry.

We must therefore see that we understand the meaning of motion, for if it were unknown, the meaning of nature would also be unknown.

When we have determined the nature of motion, our next task will be to attack in the same way the terms that are involved in it.

Now, motion is supposed to belong to the class of things that are continuous, and the infinite presents itself first in the continuous—that is how it comes about that “infinite” is often used in definitions of the continuous (“that which is divisible to infinity”). Besides these, place, void, and time are thought to be necessary conditions of motion.

Clearly, then, for these reasons and also because the attributes mentioned are common to and coextensive with all the objects of our science, we must first take each of them in hand and discuss it. For the investigation of special attributes comes after that of the common attributes. Thus, as we said, we begin with motion.

We may start by distinguishing what exists in a state of act only, what exists as potential, and what exists as potential and also in act—one being a “this something,” another quantity, a third quality, and similarly in each of the other modes of the predication of being. Further, the word “relation” is used with reference to excess and defect, agent and patient, and generally what can move and what can be moved. For what can cause motion is relative to what can be moved, and vice versa.

Again, there is no such thing as motion outside of things. It is always with respect to substance or to quantity or to quality or to place that what changes changes. But it is impossible, as we assert, to find anything common to these that is neither “this” nor quantity nor quality nor any of the other predicates. Hence, neither will motion and change have reference to something over and above the things mentioned, for there is nothing over and above them.

Now, each of these belongs to all its subjects in either of two ways: in substance, as either its form or its privation; in quality, such as either white and black; in quantity, as complete and incomplete; in respect of locomotion, as upward and downward or light and heavy. Hence, there are as many types of motion or change as there are meanings of the word “is.”

275. Having settled the question of the principles of natural things,¹ and that of the principles of this science,² the Philosopher here begins to pursue his original plan, which is to arrive at conclusions concerning the subject of this science, mobile being taken absolutely.

The treatment, then, is divided into two parts:

in the first, he comes to a conclusion about motion in itself;¹

in the second, he comes to a conclusion about movers and things movable, in book 7, at everything that is in motion (241b24; [884]).

The first part is divided into two:

in the first, he comes to a conclusion about motion itself;¹

in the second, he comes to a conclusion about its parts, in book 5, at everything that changes (224a21; [638]).

As to the first, he does two things:

first, he states what is under investigation;

then he explains it, at we may start (200b26; [279]).

With reference to the first of these, he does two things:

first, he says what he intends to principally treat;

second, he sets down certain things connected with it, with which he will be subsequently concerned, at when we have determined (200b15; [277]).

276. As to the first (200b12), he uses the following argument. Nature is the principle of motion and change, as is evident from the definition set down in book 2¹ (though how motion and change differ will be shown in book 5²).

And thus it is evident that, if one does not know motion, one does not know nature, since the former is placed in the definition of the latter. Therefore, since we intend to present the science of nature, we must make motion understood.

277. Then, at when we have determined (200b15), he adds certain things that accompany motion. And he employs two sets of reasons for including them.

The first is as follows: whoever determines something must determine those things that follow upon it, for the subject and its accidents are considered in a single science.

But the infinite follows upon motion intrinsically, as the following makes plain: motion is within the number of continuous things, as will be evident below in book 6.¹ But “infinite” enters into the definition of “continuum.”

And he adds first because the infinite that is found in the addition of number is caused from the infinite that is in the division of the continuum.

And that the infinite enters into the definition of the continuum he shows from the fact that those defining the continuum often use “infinite”—as, for example, when they say that the continuum is that which is divisible to infinity.

And he says often because there is also found another definition of the continuum, which is given in the Categories:¹ the continuum is that whose parts are joined at a common boundary.

Now, these two definitions differ. For the continuum, since it is a certain whole, is properly defined through its parts. But parts are compared to the whole in a twofold way: according to composition, insofar as the whole is composed out of the parts; and according to resolution, insofar as the whole is divided into the parts.

The present definition of the continuum is therefore given according to the mode of resolution, while that which is set down in the Categories is according to the mode of composition. Hence it is clear that the infinite follows upon motion intrinsically.

But there are some things that follow upon motion extrinsically, as certain external measures, such as place, the void, and time. For time is the measure of motion itself, while the measure of the mobile thing is indeed place according to truth, but the void according to the opinion of some. And therefore he adds that motion cannot be without place, the void, and time. Nor does the fact that not all motion is local affect this, since nothing is moved that is not in place. For every sensible body is in place, and to sensible body alone does it belong to be moved.

Likewise, local motion is the first of motions, and when it is removed, the other motions are removed, as will be evident below in book 8.¹ It is thus clear that the four above-mentioned properties are consequent upon motion and, hence, pertain to the consideration of the natural philosopher for the given reason.

278. This is also true for yet another reason that he adds subsequently: because the properties just stated are common to all natural things.

Accordingly, since it is the task of natural science to reach conclusions concerning all natural things, one must therefore first determine concerning each of these.

For the speculation that is directed toward proper things comes after that which is of common things, as was stated in the beginning.¹ But, among all these common things, one must first reach conclusions concerning motion itself, because the other things follow upon it, as was stated.

279. Then, at we may start (200b26), he puts his plan into execution.

And first, he reaches conclusions concerning motion and the infinite, which follows motion intrinsically;

second, he does the same in book 4 for the other three, which follow motion extrinsically, at the physicist must have a knowledge (208a27; [406]).

The first treatment is divided into two parts:

first, he comes to a conclusion about motion;

second, he does the same for the infinite, at the science of nature is concerned (202b30; [326]).

With respect to the first of these, he does two things:

first, he prefaces his treatment with certain considerations requisite for investigating the definition of motion;

second, he defines motion, at we have now (201a9; [283]).

As to the first of these, he does two things:

first, he sets down in advance certain divisions, since the most suitable path toward finding definitions is through division, as the Philosopher shows in Posterior analytics 2.12¹ and in Metaphysics 7;²

second, he shows that motion falls within the given divisions, at again, there is no such thing (200b32; [281]).

280. With respect to the first of these (200b26), he sets down three divisions.

The first of these is that being is divided by potency and act. Now, this division does not distinguish beings into genera—for potency and act are found in every genus.

The second division is of being as divided according to the ten genera. The first of these is this something, namely, substance; others are quantity or quality or some other of the predicaments.

The third division is of one genus of beings, namely, of the one which is relation. For motion seems in a certain way to pertain to this genus, insofar as the mover is referred to the movable thing.

In order to understand this third division, one must consider that, since relation has the weakest existence—consisting alone, as it does, in the fact of being something referred to something else—it is necessary that it be grounded on some other accident.

For the more perfect accidents are closer to the substance, and it is through them as intermediates that the other accidents inhere in the substance.

Now, relation is founded chiefly upon two accidents that have an order to something else: upon quantity and action. For quantity may be a measure even of something external to it; but the agent transfuses its action into something other than itself.

Accordingly, certain relations are founded upon quantity, and especially upon that species of quantity which is number, to which the basic account of measure pertains—as is evident in “double and half,” “multiple and fraction,” and other such things.

Similarly, “same,” “like,” and “equal” are founded upon unity, which is the principle of number.

Still other relations are founded upon action and passion: either according to existing act, as something is said to be heating in relation to that which is heated; or according to having acted, as a father is referred to a son because he engendered him; or else according to the possibility of acting, as a master is related to a servant because he is able to make him do something.

Now, the Philosopher clearly explains this division in Metaphysics 5,¹ but he here touches on it briefly, saying that one sort of relation is that according to excess and defect, which sort, indeed, is founded on quantity, as in the case of double and half; while the other is according to active and passive, and mover and movable, which are referred to each other, as is self-evident.

281. Then, at again, there is no such thing (200b32), he shows how motion is reduced to the given divisions.

And as to this, he does two things:

first, he shows that motion is not outside the genera of things in which motion occurs;

second, he shows that motion is divided as the genera of things are divided, at now, each of these (201a3; [282]).

As to the first of these, it should be observed that since motion is an imperfect act, as will be evident below,¹ and since everything that is imperfect falls under the same genus with that which is perfect—not, indeed, as a species, but by reduction (as prime matter is by reduction in the genus of substance)—motion is necessarily not outside the genera of things in which motion occurs.

And this is what he states, that motion is not outside of things—that is, outside the genera of things in which motion is found—in such a way as to be something extraneous to, or something common to, these genera. And he makes this plain by the fact that whatever is changed is changed according to substance, quantity, quality, or place, as will be shown in book 5.¹

Now, there is not some common univocal element in these genera that would not be found under some predicament but would be their genus; but being is common to them according to analogy, as will be shown in Metaphysics 4.¹ Hence, it is also plain that neither motion nor change is outside the given genera, since nothing is outside the latter and they sufficiently divide being. But, as to the question of how motion is related to the predicament of action or passion, this will be explained below.²

282. Then, at now, each of these (201a3), he shows that motion is divided as the genera of things are divided. For it is plain that, in all the genera, a thing may be present in two ways: either as something perfect or as something imperfect. The reason for this is that privation versus possession is the prime contrariety, which is found in all the contraries, as is stated in Metaphysics 10.¹

Hence, since all the genera are divided through contrary differences, it is necessary that in all there be the perfect and the imperfect: in substance, something is as form and something is as privation; in quality, there is something such as white, which is perfect, and something such as black, which is, as it were, imperfect; in quantity, one thing is perfect quantity and another imperfect; and in place, something is above, which is, as it were, perfect, and something is below, which is, so to speak, imperfect; or else there is light and heavy, which are placed in place by virtue of the inclination that is in them.

Hence, it is plain that, according to the divisions of being, there are corresponding divisions of motion. For the species of motion differ according to the different genera of being. Thus, increase, which is motion in quantity, differs from generation, which is motion in substance. The species of motion likewise differ according to perfect and imperfect in the same genus: generation is motion in substance toward form, while corruption is motion toward privation; and in quantity, increase is toward perfect quantity, diminution toward imperfect. But, as to the question of why there are not assigned two kinds in quality and place, this will be explained in book 5.¹

The definition of motion

We have now before us the distinctions in the various classes of being between what is full real and what is potential. The entelechy of a thing existing in potency, insofar as it is such, is motion—

namely, of what is alterable qua alterable, alteration; of what can be increased and its opposite, what can be decreased (there is no common name), increase and decrease; of what can come to be and can pass away, coming to be and passing away; of what can be carried along, locomotion.

Examples will elucidate this definition of motion. When the buildable insofar as it is buildable is in act, it is being built, and this is building. Similarly with learning, doctoring, rolling, leaping, ripening, aging, and so on.

The same thing, if it is of a certain kind, can be both potential and in act, not indeed at the same time or in the same respect, but for instance, potentially hot and actually cold.

Hence, such things will at once act and be acted on by one another in many ways: each of them will be capable at the same time of causing alteration and of being altered.

Hence, too, what effects motion as a physical agent can be moved: when a thing of this kind causes motion, it is itself also moved.

This, indeed, has led some people to suppose that every mover is moved. But this question depends on another set of arguments, and the truth will be made clear later.

It is possible for a thing to cause motion while it is itself incapable of being moved. Motion is the act of a thing in potency when it is already in act and operates not as itself but as movable.

What I mean by “as” is this: bronze is potentially a statue. But it is not the act of bronze as bronze that is motion. For “to be bronze” and “to be a certain potentiality” are not the same. If they were identical without qualification, meaning in definition, the act of bronze as bronze would have been motion. But they are not the same, as has been said.

(This is obvious in contraries. “To be capable of health” and “to be capable of illness” are not the same, for if they were, there would be no difference between being ill and being well. Yet the subject both of health and of sickness—whether it is humor or blood—is one and the same.)

We can distinguish, then, between the two—just as, to give another example, “color” and “visible” are different—and clearly it is the act of the possible insofar as it is possible that is motion. So this, precisely, is motion.

283. After first setting down certain things necessary for investigating the definition of motion, the Philosopher now defines motion:

first, in general;

second, more specifically, at what motion is, then (202b23; [325]).

With regard to the first, he does two things:

first, he shows what motion is;

second, he inquires whether motion belongs to the mover or to the mobile thing, at the mover is also moved (202a3; [297]).

As to the first of these, he does three things:

first, he gives the definition of motion;

second, he explains the parts of the definition, at examples will elucidate (201a15; [287]);

third, he shows that it is a good definition, at, further, it is evident (201b5; [292]).

As to the first, he does two things:

first, he gives the definition of motion;

second, he gives examples, at namely, of what (201a11; [286]).

284. As to the first, one must understand that some have defined motion by saying that motion is a going-out from potency to act that is not sudden. But they are found to be in error, because they have placed in the definition certain elements that are posterior to motion: for a going-out is a species of motion; sudden likewise involves time in its definition (the sudden is that which occurs in the indivisible unit of time); time, however, is defined in terms of motion.

285. Consequently, it is entirely impossible to define motion in terms of what is prior and better known otherwise than the Philosopher here does. For it has been pointed out already that every genus is divided by potency and act.¹ Now, potency and act, since they are among the first differences of being, are naturally prior to motion, and it is these that the Philosopher uses to define motion.

Consider, therefore, that something is in act only, something is in potency only, and something else is midway between potency and act. What is in potency only is not yet being moved; what is already in perfect act is not being moved, but has already been moved. Consequently, that is being moved that is midway between pure potency and act, which is partly in potency and partly in act—as is evident in alteration. For when water is only potentially hot, it is not being moved; when it has now been heated, the motion of heating is finished; but when it possesses some heat, though imperfectly, then it is being moved, since whatever is being heated gradually acquires more and more heat.

Therefore, this imperfect act of heat existing in a heatable object is motion—not, indeed, by reason of what the heatable object has already become, but inasmuch as, being already in act, it has an order to a further act. For should this order to a further act be taken away, the act already present, however imperfect, would be the term of motion and not motion itself—as happens when something becomes half-heated. This order to a further act belongs to the thing that is in potency to it. Similarly, if the imperfect act were considered solely as ordered to a further act, under the account of potency, it would not have the account of motion, but of a principle of motion—for heating can begin from either a cold or a lukewarm object.

The imperfect act, therefore, has the character of motion both insofar as it is compared, as potency, to a further act, and insofar as it is compared, as act, to something more imperfect. Hence, motion is neither the potency of a thing existing in potency nor the act of a thing in act, but it is the act of a thing in potency, where the word act designates its relation to a prior potency and the words of a thing in potency designates its relation to a further act. Hence the Philosopher most aptly defines motion as the entelechy, the act, of a thing existing in potency, insofar as it is such.

286. Then, at namely, of what (201a11), he gives examples from all the species of motion, such as that alteration is the act of the alterable insofar as it is alterable.

And, because motion in quantity and in substance does not have a single name in the same way as motion in quality is called alteration, he gives two different names for the motions in quantity and says that the act of the increasable and of its opposite, the decreasable (for which two there is no common name), is increase and decrease.

Similarly, the acts of the generable and of the corruptible are generation and corruption, and the act of what is mutable in regard to place is called change of place.

In this section, the Philosopher uses the word “motion” for any kind of change and avoids the strict usage in which motion is distinct from generation and corruption, as will be said in book 5.¹

287. Then, at examples will elucidate (201a15), he explains the several words of the definition:

first, he explains the use of the word act;

second, at the same thing (201a19; [288]), he explains of a thing existing in potency;

third, at what I mean (201a29; [289]), he explains insofar as it is such.

As to the first, he uses this reasoning.

That by which something previously existing in potency becomes actual is an act. But something becomes actual when it is being moved, although previously it was in potency. Therefore, motion is an act.

He says, therefore, that it is plain that motion is this, namely, an act, from the fact that the buildable implies a potency to something but, when the buildable is being reduced to act according to this potency that it implies, we then say it is being built—and this act is passive building. And the same thing is true in all other motions such as being taught, healing, rolling, dancing, growing up (that is, increase), growing old (that is, decrease), and so on.

For it must be remembered that, before something is being moved, it is in potency to two acts: to a perfect act that is the term of the motion, and to an imperfect act that is motion itself. Thus, before it begins to be heated, water is in potency to being heated and to having been heated. When it is being heated, it is being reduced to the imperfect act that is motion, but not yet to the perfect act that is the term of the motion—rather, in respect to this, it still remains in potency.

288. Then, at the same thing (201a19), he shows that motion is the act of a thing existing in potency. For every act is strictly the act of that in which it is always found—as light is never found but in the transparent, for which reason it is the act of the transparent. But motion is found always in a thing existing in potency. Therefore, motion is the act of a thing existing in potency.

To explain the second proposition, he says that, since certain things are the same both in potency and in act—although not at the same time or in the same respect (as, for example, something is hot actually and cold potentially)—it follows that many things mutually act and are acted upon, insofar as both are in potency and in act with respect to the other under different aspects. And, because all lower natural bodies share the same matter, there is therefore in each of them a potency to what is actual in another. Hence, in all such bodies, something simultaneously acts and is acted upon, both moves and is moved.

This fact had led some to say absolutely that every mover is likewise being moved. This point will be cleared up in a later place. For it will be shown in Physics 8¹ and in Metaphysics 12² that there exists an immobile mover, since it is not in potency but in act only. But, when that which is in potency, yet existing in a certain way in act, either acts itself or is acted upon by another insofar as it is movable, that is, is reduced to the act of motion—whether moved by itself or by another—then motion is its act. That is why things in potency, whether they act or are acted upon, are moved, since they are acted upon when acting and are being moved when moving—just as fire, when it acts on logs, is acted upon, insofar as it becomes more dense through smoke (since flame is nothing more than burning smoke).

289. Then, at what I mean (201a29), he explains this part of the definition, insofar as it is such:

first, by an example;

second, by giving a reason, at this is obvious in contraries (201a34; [290]).

He says first (201a29) that the phrase insofar as it is such had to be added because what is in potency is at the same time something in act. And, although the subject that is both in potency and in act may be the same, nevertheless to be in potency and to be in act is not contained under the same account.

Thus, although brass is a statue in potency but is brass actually, nevertheless the account of the brass as brass is not the same as the account of the brass as it is in potency to a statue.

Now, motion is not an act of the brass insofar as it is brass, but insofar as it is in potency to a statue; otherwise, during the whole time that it was brass, it would be undergoing motion, which is clearly false. That is why it is necessary to add insofar as it is such.

290. Then, at this is obvious in contraries (201a34), he explains the same thing by using an argument based on the nature of contraries. For it is clear that a given subject is in potency to contraries—as a humor or the blood is in potency to health and to sickness. But to be in potency to health is one thing and to be in potency to sickness is another, if one considers their objects. Otherwise, if to be able to be sick and to be able to be well were the same thing, it then would follow that being sick and being well would be the same. Hence, the idea of “being able to be sick” differs from “being able to be healthy,” although their actual subject is one and the same thing.

It is plain, therefore, that there is not one and the same account of the subject as it is a certain being and as it is in potency to something else. Otherwise, potency to contrary things would fall under one and the same account. In like manner, the account of that which is color and that which is visible are not one and the same. Thus, it was necessary to say that motion is the act of the possible insofar as it is possible—to prevent supposing that it is the act of what is in potency insofar as it is merely some subject.

Motion’s definition is suitably formulated

Further, it is evident that motion is an accident of a thing just when it is fully real in this way, and neither before nor after. For each thing of this kind is capable of being at one time actual and at another not.

Take, for instance, the buildable as buildable. The act of the buildable as buildable is the process of building. For the act of the buildable must be either this or the house.

But, when there is a house, the buildable is no longer buildable. On the other hand, it is the buildable that is being built. The process of being built, then, must be the kind of act required.

But building is a kind of motion, and the same account will apply to the other kinds also.

The soundness of this definition is evident both when we consider the accounts of motion that the others have given and also from the difficulty of defining it otherwise. One could not easily put motion and change in another genus.

This is plain if we consider where some people put it. They identify motion with “otherness” or “inequality” or “non-being.” But such things are not necessarily moved, whether they are “other” or “unequal” or “non-existent”; nor is change either to or from these, rather than to or from their opposites.

The reason that they put motion into these genera is that it is thought to be something indefinite, and the principles in the second column are indefinite because they are privative: none of them is either “this” or “such,” or comes under any of the other modes of predication.

In turn, the reason that motion is thought to be indeterminate is that it cannot be classed simply as a potentiality or as an act: a thing that is merely capable of having a certain size is not undergoing change, nor yet a thing that is actually of a certain size; and motion is thought to be a sort of act, but incomplete, and the reason for this view is that the potential whose act it is is incomplete.

This is why it is hard to grasp what motion is. It is necessary to class it with privation or with potentiality or with sheer act, yet none of these seems possible. There remains, then, the suggested mode of definition: that it is a sort of act, or act of the kind described, hard to grasp but not incapable of existing.

291. Having given the definition of motion and an explanation of each of the words in the definition, the Philosopher now shows it to be a good definition:

first, directly;

second, indirectly, at the soundness of this (201b16; [293]).

292. In regard to the first (201b5), he uses the following argument: everything that is in potency may at some time be in act, but the buildable is in potency. Therefore, there may at some time be an act of the buildable insofar as it is buildable. But this act is either the house itself or the building of it. But “house” is not the act of the buildable insofar as it is buildable, since the buildable as such is being reduced to act when the building is taking place, but when the house now exists, it is no longer being built. Hence, building is an act of the buildable as such. Building, however, is a certain motion. Motion, therefore, is the act of a thing existing in potency as such. The same is true of other motions. It is clear, therefore, that motion is the type of act described above,¹ and that something is being moved only when it is in such an act, and neither before nor after: not before, since, if it is only in potency, the motion has not begun; nor after, since it has now completely ceased to be in potency by virtue of being in perfect act.

293. Then, at the soundness of this definition (201b16), he shows indirectly that it is a good definition by showing that motion cannot be defined in any other way.

In regard to this, he does three things:

first, he proposes what he intends;

second, he presents definitions given by others and rejects them, at this is plain (201b19; [294]);

third, he explains why others defined motion as they did, at the reason that (201b24; [295]).

He says, therefore, that two things show why the definition given of motion is a good one:

first, because the definitions that others have given are unsuitable;

second, because it is impossible to define motion otherwise than as Aristotle has defined it because motion cannot be placed in any other genus other than that of the act of a thing existing in potency.

294. Then, at this is plain (201b19), he excludes the definitions of motion given by others.

These did three things in defining motion.

For they said that motion is otherness because the thing being moved constantly changes from one state to another.

Similarly, they said motion is inequality, because the thing being moved approaches its term always more and more.

They also said that motion is non-being, because the thing being moved does not yet have that to which it is being moved as long as it is being moved—as that which is being moved toward whiteness is not yet white.

These definitions the Philosopher destroys in three ways.

He does so first by looking at the subject of motion. For if motion were otherness, inequality, or non-being, then whatever would possess any one of these three characteristics would of necessity be undergoing motion—in whatever this motion is, that thing is being moved.

But things that are other are not necessarily being moved by the fact that they are other, nor by the fact that they are unequal, nor by the fact that they do not exist. It follows, therefore, that otherness and inequality and non-being are not motion.

Second, he shows the same thing by looking at the term to which the motion is tending, for motion and change do not tend more to otherness than to likeness, or to inequality more than to equality, or to non-being more than to being. For generation is a change to being, and corruption to non-being. Hence, motion is not otherness any more than a likeness, not inequality any more than equality, and not non-being any more than being.

Third, he shows the same thing by looking at the term from which the motion begins, since, just as some motions start from otherness and from inequality and from non-being, so others start from their opposites.

Hence, there is no reason to place motion in the aforementioned genera any more than in their opposites.

295. Then, at the reason that (201b24), he points out why some defined motion in the stated ways.

In regard to this, he does two things:

first, he assigns the reason of what has already been stated;

second, he explains a supposition he had made, at in turn, the reason (201b27; [296]).

He therefore says first (201b24) that the reason that the older philosophers placed motion in the above-mentioned genera (otherness, inequality and non-being) is that motion seems to be something indeterminate, something incomplete and imperfect, as though possessing no determinate nature. And, because it is indeterminate, its proper place seemed to be in the genus of privation. For when Pythagoras laid down two ordinations of reality, in each of which he placed ten principles, the principles in the second group were said by him to be indeterminate because they were privative. They were not, indeed, determined by a form in the genus of substance, nor by the form of quality or by any special form in either of these genera, or by the form of any of the other predicaments. In one of these groups the Pythagoreans placed ten things: finite, unequal, one, right, male, rest, straight, light, good, and equilateral triangle. In the other, they placed infinite, equal, many, left, female, motion, oblique, dark, evil, and scalene triangle.

296. Then, at in turn, the reason (201b27), he gives the reason that motion is placed among the indeterminates. And he says that the reason for this is that motion cannot be placed either in potency or in act.

For if it were placed under potency, whatever would be in potency—for example, to quantity—would be being moved according to quantity. If, on the other hand, it were included under act, then whatever things were actually quantified would be being moved according to quantity.

Now, it is indeed true that motion is act, yet it is imperfect act, a mean between potency and act. And that it is imperfect act is clear from the fact that that of which it is an act is a being in potency as stated above.¹

And that is why it is difficult to grasp what motion is. For at first sight, it seems to be either entirely act or entirely potency, or else to be contained under privation as it seemed to the ancients who called it non-being or inequality. But none of these is possible, as we have shown above.¹ Hence it follows that there is just one way to define motion: as we have said, it is the act of a thing existing in potency. It is difficult to dwell on such an act on account of the commingling of act and potency; yet that there should be such an act is not impossible, but contingent.

Motion is the act both of the mover and of the mobile object

The mover is also moved, as has been said—that is, every mover that is in potency to being a mover,

and whose immobility is rest—when a thing is subject to motion, its immobility is rest.

For to act on the movable as such is just to move it. But this it does by contact, such that it is also acted on at the same time.

Hence, we can define motion as the act of the mobile inasmuch as it is mobile, the cause of this attribute being contact with what can move such that the mover is also acted on.

The mover or agent will always be a form, either a “this” or “such” or a “quantity,” which, when it acts, will be the source and cause of the change; for instance, the fully formed man begets man from what is potentially man.

The solution of the difficulty that is raised about the motion—whether it is in the movable—is plain. It is the act of this potentiality by the action of that which has the power of causing motion.

And the act of that which has the power of causing motion is not other than the act of the movable.

For it must be the act of both. A thing is capable of causing motion because it can do this; it is a mover because it is in act.

But it actualizes the mobile. Hence, there is a single act of both alike,

just as one to two and two to one are the same interval, and the steep ascent and the steep descent are one—for these are one and the same, although they can be described in different ways. So it is with the mover and the moved.

297. After defining motion, the Philosopher now shows whose act motion is, whether it is the act of the mobile or of the mover.

Also, it may be said that he gives another definition of motion that is related to the previous one as material to formal and as a conclusion to its principle.

And this is the definition: motion is the act of the mobile inasmuch as it is mobile. This definition is a conclusion from the previous one. For since motion is the act of a thing existing in potency inasmuch as it is in potency, and since that which exists in potency as such is the mobile and not the mover (for the mover as such is in act), it follows that motion is an act of the mobile as such.

298. In regard to the main question, he does three things:

first, he shows that motion is an act of the mobile;

second, he shows how motion is related to the mover, at and the act of that (202a15; [304]);

third, he raises a difficulty, at this view has a rational defect (202a21; [308]).

About the first, he does two things:

first, he posits a definition of motion, namely, that motion is an act of the mobile;

second, he clears up a doubt, at the solution of the difficulty (202a13; [303]).

In regard to the first, he does three things:

first, he investigates the definition of motion;

second, he gives the definition, at hence, we can define (202a7; [302]);

third, he explains it, at the mover or agent (202a7; [302]).

In investigating the definition, he shows that to be moved happens even to the mover.

In regard to this, he does two things:

first, he shows that every mover is moved;

second, he shows why that happens, at for to act (202a5; [301]).

299. He shows in two ways that the mover is moved.

This is so first of all because anything that is previously in potency and then in act is somehow moved. But movers are found that are previously movers in potency and afterward movers in act; therefore, this kind of mover is moved. He states, therefore, that every mover, since it is such that it is in potency to being a mover, is likewise moved. This is clear from what has been said, for it was said¹ that motion is an act of a thing existing in potency, and this occurs in every natural mover; that is why it was said above that every physical mover is moved.²

300. Second, at and whose immobility (202a4), he brings out the same point in another way: whatsoever’s immobility is its rest is capable of motion, for rest and motion, since they are opposites, happen to the same things. But the immobility of a mover—that is, its ceasing from moving—is called rest, for there are things that are said to rest when they cease to act. Therefore, every such mover—one whose immobility is rest—is moved.

301. Then, at for to act (202a5), he shows why it happens that a mover is moved. For it does not happen precisely because it is a mover, but because it is such by touching. For to move is to act so that something may be moved, and what is so acted upon by the mover is moved. But whatever acts does so by touching, for bodies act by touching; hence it follows that what acts is at the same time acted upon, because that which touches is acted upon.

However, this must be understood of those cases where there is mutual touching—that is, when the thing touching is also touched, as happens in things that are material, where both of the things are acted upon when they touch one another.

But heavenly bodies, because they do not have the same kind of matter as the lower bodies, so act on them that they are not acted upon in return, and they touch without being touched, as is stated in De generatione 1.¹

302. Then, at hence, we can define (202a7), he posits the definition of motion, concluding from what has been said that, although the mover is moved, motion nevertheless is not an act of the mover, but of the mobile inasmuch as it is mobile. He shows this subsequently by the fact that to be moved is accidental to the mover and does not belong essentially to it. Hence, if something is moved precisely inasmuch as its act is motion, it follows that motion is an act not of the mover but of the mobile—not, indeed, insofar as it is a mover but insofar as it is a mobile.

That to be moved is accidental to the mover is clear from what was pointed out in the earlier part of this lecture; for this act of the mobile, which is motion, happens from its contact with the mover. From this, it follows that, at the same time that it is acting, it is acted upon, and thus to be moved is accidental to the mover.

That to be moved does not belong essentially to the mover is clear from the fact that some form is always seen to be the mover: the form that is in the genus of substance is the mover in substantial change; a form in the genus of quality is the mover in alteration; and a form in the genus of quantity is the mover in growth and decrease. Forms of this type are the causes and principles of motions, since every agent moves according to its form. For every agent acts inasmuch it is actual, as an actual man makes an actual man of man in potency. Hence, since it is through its form that a thing is actual, it follows that form is the moving principle. Thus, to move belongs to a thing inasmuch as it has a form through which it is actual. Therefore, since motion is the act of a thing existing in potency, as was said above,¹ it follows that motion belongs to a thing not insofar as it is a mover, but insofar as it is mobile. For that reason, the definition says that motion is an act of the mobile inasmuch as it is mobile.

303. Then, at the solution of this difficulty (202a13), he shows a difficulty that arises from what has been said. For some wonder whether motion is in the mover or in the mobile. But this doubt is solved from what went before. For it is clear that an act of anything is in that thing of which it is the act. Thus, it is plain that the act of motion is in the mobile, since it is an act of the mobile, although caused in it by the mover.

304. Then, at and the act (202a15), he shows how motion and mover are related.

He first of all proposes his intention, saying that the act of the mover is not distinct from the act of the mobile. Hence, since motion is an act of the mobile, it is somehow also an act of the mover.

305. Second, at for it must be (202a16), he explains this.

And in regard to this, he does three things.

First, he shows that there is an act of the mover as well as of the mobile. For whatever is described according to potency and act has some act corresponding to it. Now, just as that which is moved is called “mobile in potency,” since it is capable of being moved, and is called “moved according to act” inasmuch it is actually being moved, so a mover is described as a “potential mover” inasmuch as it is able to move, and moves in act inasmuch as it actually acts. Therefore, some act is competent to both, that is, to mover and to mobile.

306. Second, at but it is on the movable (202a17), he shows that the act of the mover and that of the mobile are the same act. For something is called mover inasmuch as it acts and moved inasmuch as it is being acted upon.

But what the mover causes by acting and what the moved receives as being acted upon are one and the same thing. And this is what he means when he says that the mover actualizes the mobile, that is, causes the act of the mobile.

Therefore, they must both, the mover and the moved, have the same act, for what is from the mover as agent cause is the same as what is in the moved as patient and receiver.

307. Third, at just as one to two (202a18), he illustrates this by an example. For the distance from one to two is the same as that from two to one, but they differ according to account; for in relating two to one, we have double, but in relating one to two, we have half. The same thing is true of the distance covered by one ascending and by one descending, but by reason of the diversity of starting point and term, one is called “ascent” and one “descent.” A parallel case is true of the mover and of the thing moved. For inasmuch as motion proceeds from the mover into the mobile, it is an act of the mover, but inasmuch as it is in the mobile from the mover, it is an act of the mobile.

This view has a rational defect. Perhaps it is necessary that the act of the agent and that of the patient should not be the same. The one is “agency” and the other “patiency,” and the outcome and completion of the one is an “action,” while that of the other is a “passion.”

Since, then, they are both motions, we may ask in what they are, if they are different? Either both are in what is acted on and moved, or the agency is in the agent and the patiency in the patient. (If we ought to also call the latter “agency,” the word would be used in two senses.)

Now, if the latter is so, the motion will be in the mover, for the same statement will hold of the mover and the moved. Hence, either every mover will be moved or, though having motion, it will not be moved.

If, on the other hand, both are in what is moved and acted on—both the agency and the patiency (for instance, both teaching and learning, though they are two, in the learner)—then, first, the act of each will not be present in each, and a second absurdity is that a thing will have two motions at the same time.

How will there be two alterations of quality in one subject toward one definite quality? The thing is impossible.

But will the act be one? Someone will say it is contrary to reason to suppose that there should be one identical act of two things that are different in kind.

Yet there will be, if teaching and learning are the same, and agency and patiency. To teach will be the same as to learn, and to act the same as to be acted on—the teacher will necessarily be learning everything that he teaches, and the agent will be acted on.

One may reply that it is not absurd that the act of one thing should be in another. Teaching is the activity of a person who can teach, yet the operation is performed on some patient—it is not cut adrift from a subject, but is of this on that.

There is nothing to prevent two things having one and the same act, provided the acts are not described in the same way, but are related as what can act to what is acting.

Nor is it necessary that the teacher should learn, even if to act and to be acted on are one and the same, provided they are not the same in definition (like “raiment” and “dress”), but are the same merely in the sense in which the road from Thebes to Athens and the road from Athens to Thebes are the same, as has been explained above. For it is not things that are in a way the same that have all their attributes the same, but only such as have the same definition.

But, indeed, it by no means follows from the fact that teaching is the same as learning that to learn is the same as to teach,

any more than it follows from the fact that there is one distance between two things that are at a distance from each other, that the two vectors AB and BA are one and the same.

To generalize: teaching is not the same as learning, or action as passion, in the full sense, though they belong to the same subject, the motion; for the “act of this in that” and the “act of this through the action of that” differ in definition.

What motion is, then, has been stated both generally and particularly. It is not difficult to see how each of its types will be defined—alteration is the act of the alterable qua alterable (or, more scientifically, an act of the potency of that which is active and of that which is passive, as such)—generally and again in each particular case, such as building, healing, and the like. A similar definition will apply to each of the other kinds of motion.

308. After showing that motion is the act both of the mobile and of the mover, the Philosopher now raises a difficulty on this point.

First, he raises the difficulty;

second, he solves it, at one may reply (202b5; [314]).

Regarding the first, he does two things:

first, he prefaces certain things to the difficulty;

second, he pursues the difficulty, at since, then, they are both (202a25; [310]).

309. He therefore says (202a21) that what has been said above now causes a rational—that is, logical—defect, or doubt, by virtue of there being tenable reasons for both sides. In introducing the difficulty, he says that there is an act in that which is active and there is an act in that which is passive, just as above, there was stated to be an act of the mover and of the moved.¹ As a matter of fact, the act of the active is called action and the act of the passive is called passion. This he proves by saying that the work and end of anything is its act and perfection; hence, since the work and end of the agent is action and that of the patient is passion, it follows that action is the act of the agent and passion that of the patient.

310. Then, at since, then, they are both (202a25) he pursues this doubt. For it is clear that both action and passion are motion, for each is the same as motion. Therefore, action and passion are either the same motion or diverse motions. If they are diverse, then each of them must be in some subject. Either both will be in the patient, the thing moved, or one of them is in the agent and the other is in the patient.

To say the opposite—namely, that what is in the agent is passion and what is in the patient is action—is to speak equivocally, for it would be calling passion action and vice versa.

The fourth possibility—namely, that both are in the agent—is left out, but this is because it has already been shown¹ that motion is in the mobile, which excludes the fourth possibility, that neither be in the patient, but both in the agent.

311. Of the two possibilities listed, he develops the second one first, at now, if the latter is so (202a28). For if anyone says that action is in the agent and passion in the patient, then, since action is a certain motion, as was stated, it follows that motion is in the mover. For the same thing should be true both of the mover and of the moved: if motion is in either one, it is being moved. Or else what is true of the mover and of the moved is also true of the patient and of the agent. Now, if motion is in something, that thing is being moved; therefore, it follows either that every mover is being moved or that something has motion but is not being moved. Each of these seems unreasonable.

312. Then, at if, on the other hand (202a31), he develops the other possibility given above. He says that, if anyone should say that both of them—namely, action and passion—since they are two motions, are in the patient (which is equivalent to saying that teaching, which is on the part of the teacher, and learning, which is on the part of the learner, are both in the learner), then two conflicts arise.

The first is that, if what we said previously is true—namely, that action is an act of the agent—then, if action is not in the agent but in the patient, it will follow that the proper act of each thing is not in the thing of which it is the act.

Then another conflict follows: one and the same thing is being moved according to two motions. For action and passion are now supposed to be two motions. Now, in whatever thing there is a motion, that thing is being moved according to that motion. So, if action and passion are in the mobile, it follows that the mobile is being moved according to two motions. This would be tantamount to having two alterations in one subject, both of them specifically the same, such as one subject being moved to two whitenings, which is impossible. This does not mean that one subject could not be moved by two alterations tending toward two specifically different terms, such as whitening and heating. Nevertheless, it is clear that action and passion terminate at the same specific term; for what the agent does and what the patient receives are one and the same.

313. Then, at but will the act be one (202a36), he develops the other possibility. For it could be said that action and passion are not two motions, but one.

But this leads to four difficulties.

The first is that the acts of things of different species would be the same. For it has been already pointed out that action is an act of the agent and passion an act of the patient, and that these are specifically diverse; but, if action and passion are the same motion, then the acts of specifically different things will be the same.

The second difficulty is that, if action and passion are one motion, then action is the same as passion, such that teaching, which is in the teacher, is the same as learning, which is in the learner.

The third difficulty is that acting would be the same as being acted upon, and teaching would be the same as learning.

The fourth difficulty that follows from this is that every teacher would be learning and every agent would be being acted upon.

314. Then, at one may reply (202b5), he solves the difficulty. From what was settled previously,¹ it is clear that action and passion are not two motions, but one and the same motion; for insofar as motion is from the agent, it is called action, and insofar as it is in the patient, it is called passion.

315. Hence, not all the conflicts that follow from the first case, in which it was supposed that action and passion are two motions, have to be solved. But one remains to be solved even on the supposition that action and passion are one motion: since action is an act of the agent, then, if action and passion are one motion, it follows that the act of the agent is somehow in the patient. Thus, the act of one thing will be in something else.

This remaining difficulty, together with the four listed above, leaves five to be solved.

316. He says in the first place that there is nothing wrong with an act of one thing being in something else, for teaching is an act of the teacher, an act continuously tending from him into someone else without interruption; hence, this act that is the agent’s as being from this is the very one that is in the patient as received in him. But it would be wrong if the act of the one were the act of the other in precisely the same way.

317. Then, at there is nothing to prevent (202b8), he solves another difficulty: two things would have the same act.

And he says that there is nothing to prevent one act belonging to two things, so long as it is not one and the same in thought, but only in reality, as was already explained above,¹ when it was pointed out that the distance from one to two and from two to one are the same, and of that which is in potency looking toward the agent and conversely.

For in these cases, the same one reality is assigned to two things according to different accounts: it is assigned to the agent inasmuch as it is from it and to the patient inasmuch as it is in it.

318. The three remaining difficulties, of which one followed logically from the other, he takes care of in reverse order.

He disposes first of the last difficulty introduced, because it is so evidently improper.

Thus, he settles the fifth difficulty third. He says that it is not necessary to say that one who is teaching is learning or that an agent is being acted upon just because to act and to be acted upon are the same, as long as we understand that they are not the same in the way that dress and clothing are the same (for these are the same in account), but in the way that the road from Thebes to Athens and that from Athens to Thebes are the same, being the same as to subject but differing as to account, as said above.¹

For it is not necessary that things that are somehow the same should be the same in all ways; that is true only of things that are the same in subject or reality and also in account. And, therefore, even granting that to act and to be acted upon are the same, yet, since they are not the same in account, it will not follow that it is the same for an object to act and to be acted upon.

319. Then, at but, indeed (202b16), he answers the fourth difficulty. And he says that, even though teaching and the learning of the learner were the same, it does not follow that to teach and to learn are the same, since teaching and learning are abstract terms but to teach and to learn are concrete.

Hence, they are being applied to ends or to terms that serve as the basis for the difference in account between action and passion. For just as the distance between two points is one and the same space in the abstract, yet it is not one and the same if we apply it to two concrete places, as when we say that there is a distance between here and there and between there and here.

320. Then, at to generalize (202b19), he answers the third difficulty by destroying the inference that, if action and passion are one motion, they are the same. And he says that ultimately it must be said that it does not follow that action and passion are the same, nor that teaching and learning are, but rather that both are in the same motion. This motion, as a matter of fact, is action from one viewpoint and passion from another. For it is one thing as to account to be an act of a thing as being in that and another to be the act of a thing as being from that.

Now, motion is called action inasmuch as it is an act of the agent as from the agent; it is called passion inasmuch as it is an act of the patient as in the patient. Thus, it is clear that, although the motion of the mover and that of the moved are the same thing due to the fact that motion as such abstracts from these accounts, yet action and passion differ due to the fact that these accounts are included in their signification. From this, it is also apparent that, since motion abstracts from the account of action and passion, it belongs neither in the predicament “action” nor in the predicament “passion,” as some supposed.

321. But two difficulties still remain with respect to this.

The first is this: if action and passion are one motion, and they differ merely in thought, as said above, it seems that they should not be listed as two distinct predicaments, since the predicaments are genera of things.

Second, if motion is either action or passion, motion will not be found in substance, quality, quantity, and place, as said above,¹ but only in action and passion.

322. To settle this matter, it should be known that being is divided into the ten predicaments not univocally, as a genus into species, but according to the different modes of existing. Now, the modes of existing are proportional to the modes of predicating. For in predicating something of something else, we say, “this is that”; hence, the ten genera of being are called the ten predicaments.

Now, every predication takes place in one of three ways.

One way is to predicate of a subject that which pertains to its essence, as when I say, “Socrates is man” or “man is animal.” According to this, the predicament of substance is taken.

Another way is to predicate of a subject something that is not of its essence but yet inheres in the subject. This inherent thing may be traceable to the matter in the subject, in which case one has the predicament of “quantity” (for quantity is properly a result of matter; for which reason Plato traced the “large” to matter);

or it is traceable to the form, and in this case, there is the predicament of “quality” (for which reason qualities are founded on quantity, as color in a surface, and figure in lines or in a plane);

or the predication may be due to a relation existing between subject and something else, and thus we have the predicament of “relation” (for when I say, “the man is a father,” it is not something absolute that is predicated of the man, but a relation in him to something without).

The third mode of predicating is when something outside the subject is predicated after the manner of denomination. This allows even extrinsic accidents to be predicated of substance, but yet we do not say that man is whiteness, but that man is white. To be denominated by something extrinsic can occur, generally speaking, to all things in one way or another, and in a special way in those matters that refer only to man.

Speaking generally, a thing can be denominated by something extrinsic either according to the account of cause or according to that of measure. For something is denominated “caused” or “measured” on account of its relationship to something extrinsic.

Now, there are four genera of causes, two of which are parts of the essence, namely, matter and form. Hence, any predication based on these two pertains to the predicament of “substance,” as when I say that man is rational and that man is corporeal.

In regard to the other two causes, the final cause does not cause separately from the agent, for the end is a cause only insofar as it influences the agent. Therefore, the only cause according to which a thing can be denominated something as based on something extrinsic is the agent cause.

Consequently, when something is denominated from the agent cause, it is the predicament of “passion,” for to undergo is nothing but the undergoing of something from an agent. On the other hand, if the agent cause is denominated on account of its effect, one has the predicament of “action,” for action is an act from the agent into something else, as stated above.

In regard to measures, it will be either intrinsic or extrinsic. An intrinsic measure would be a thing’s own length and width and depth. In these cases, a subject is being denominated something by reason of what inheres intrinsically; hence, this pertains to the predicament “quantity.”

The extrinsic measures are time and place. It is the predicament “when” whenever something is denominated by time; when it is denominated by place, it is the predicament “where” or the predicament “position,” which adds to “where” the order of the parts in place. Such an order of parts is not considered in regard to the measure that is time, for the order of parts in time is already implied in the account of time, since time is the number of motion according to the order of the “before” and the “after.” Thus, it is through denomination from time or place that something is said to be “when” or “where.”

There is a special predicament for human beings. In other animals, nature provided the requirements for preserving life, such as horns for defense, a tough and woolly hide as a covering, and claws or the like for proceeding without harm. Hence, when animals are said to be “armed” or “covered” or “shod” by reason of this equipment, they are somehow so called not by reason of something extrinsic, but of something intrinsic, something that is part of them. Hence, such are referred to the predicament of “substance,” as the same would be if man were said to be endowed with hands or feet.

But the other things could not be endowed upon man by nature, both because they would be out of keeping with the precise balance of his constitution and because reason makes man capable of an enormous number of works, for the performance of which nature could not have endowed him with specific instruments. In the place of all these instruments, man has reason, which he can use to make for himself the things that are intrinsic to other animals. So, when a man is said to be armed or clothed or shod, he is denominated thus by reason of something extrinsic to him that is neither a cause nor a measure. Hence it is located in a special predicament called “habit.”

But we should not fail to note that this predicament is, in certain matters, used also for other animals, not inasmuch as they are considered in their nature, but insofar as they are put at the service of man. Thus we say that a horse is caparisoned or saddled or armed.

323. This makes it clear that, although motion is one, yet there are two predicaments that are based on motion, depending on the different external things according to which the predicamental denominations are made. For an agent is one thing from which, as from something external, the predicament of “passion” is taken; and the patient is some other thing from which something is denominated an agent. This solves the first difficulty.

324. The second doubt is easy to solve. For the account of motion depends not only on that which pertains to motion in reality but also on that which reason apprehends. In reality, motion is nothing more than an imperfect act, which is a sort of beginning of a perfect act in that which is being moved; thus, in that which is becoming white, some whiteness has begun to be. But, in order that what is imperfect have the account of motion, it is further required that we understand it as a mean between two. The one mentioned earlier is compared to motion as potency to act (hence motion is called act). The consequent one is compared to motion as the perfect to the imperfect or as act to potency; hence motion is called the act of a being that exists in potency, as we said above.¹

But anything imperfect, if it is not considered to be tending on to something other as perfect, is called the terminus of motion, and one will not have a motion according to which something is being moved—as, for example, if something should start to become white and then the alteration was immediately stopped.

Therefore, in regard to what there is of motion in external reality, motion is placed reductively in that genus that terminates the motion as the imperfect is reduced to the perfect, as stated above.¹

But, in regard to what reason apprehends about motion—namely, that it is midway between two terms—here the account of cause and effect are brought in, because, for something to be reduced from potency to act, an agent cause is required. From this aspect, motion pertains to the predicaments of “action” and “passion,” for these two predicaments are based on the accounts of acting cause and of effect, as was said above.

325. Then, at what motion is, then (202b23), he defines motion more particularly. He says that we have pointed out what motion is both in general and in particular—because, from what was said about the definition of motion in general, it is clear how it can be defined in particular. For if motion is the act of the mobile as such, it follows that alteration is the act of the alterable as alterable, and so on for other particular kinds of motion. And, because there was a doubt whether motion is an act of the mover or of the mobile—and we showed that it is an act of the active as from it and of the passive as in it—then, to remove any further doubts, we can say somewhat more explicitly that motion is an act of the potency of that which is active and of that which is passive. In this way, we could have said that building is an act of the builder and of the buildable as such. The same is true of healing and of other motions.

The opinions of the ancients concerning the infinite

The science of nature is concerned with spatial magnitudes and motion and time, and each of these at least is necessarily infinite or finite, even if some things dealt with by the science are not, such as a point and a passion.

It is not necessary, perhaps, that such things should be put under either head. Hence, it is incumbent on the person who specializes in physics to discuss the infinite and to inquire whether there is such a thing or not, and if there is, what it is.

The appropriateness of this problem to the science is clearly indicated. All who have touched on this kind of science in a way worth considering have formulated views about the infinite,

and indeed, to a man, make it a principle of things. Some, as the Pythagoreans and Plato, make the infinite a principle in the sense of a self-subsistent substance, and not as a mere accident of some other thing.

Only the Pythagoreans place the infinite among the objects of sense (they do not regard number as separable from these) and assert that what is outside the heaven is infinite.

Plato, on the other hand, holds that there is no body outside—the Forms are not outside because they are nowhere—yet that the infinite is present not only in the objects of sense but in these also.

Further, the Pythagoreans identify the infinite with the even. For this, they say, when it is cut off and shut in by the odd, provides things with the element of infinity. An indication of this is what happens with numbers.

By the addition of the gnomons to one and outside it, sometimes the figure that results is different, sometimes it is the same. But Plato has two infinites, the great and the small.

The physicists, on the other hand, all of them, always regard the infinite as an attribute of a substance that is different from it and belongs to the class of the so-called elements—water or air or what is intermediate between them. Those who make them limited in number never make them infinite in amount.

But those who make the elements infinite in number, as Anaxagoras and Democritus do, say that the infinite is continuous by contact—compounded of the homogeneous parts according to the one, and of the seed-mass of the atomic shapes according to the other.

Further, Anaxagoras held that any part is a mixture in the same way as the all, on the ground of the observed fact that anything comes out of anything.

For it is probably for this reason that he maintains that, once upon a time, all things were together.