LECTURE 2 (184 b 15-185 a 19)
THE OPINIONS OF THE ANCIENT PHILOSOPHERS ABOUT THE PRINCIPLES OF NATURE AND OF BEINGS. IT DOES NOT PERTAIN TO NATURAL SCIENCE TO DISPROVE SOME OF THESE OPINIONS

12. Having completed the preface in which it was shown that natural science ought to begin with the more universal principles, here, according to the order already stated, he begins to pursue those matters which 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 this book).’ This is taken up in Book III, where he says, ‘Nature has been defined ...’ (200 b 12; L1).

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. Secondly he treats the principles of the doctrine. This he does in Book II, where he says, ‘Of things that exist...’ (192 b 8; L1).

The first part is divided into two parts. First he considers the opinions others have had concerning the common principles of mobile being. Secondly he seeks the truth concerning them, where he says, ‘All thinkers, then, agree ...’ (188 a 18; L10).

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. Secondly, where he says, ‘Now to investigate ...’ (184 b 25 #15), he shows that it does not pertain to natural science to pursue some of these opinions. Thirdly, where he says, ‘The most pertinent question...’ (185 a 20; L3), 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. Secondly, where he says, ‘A similar inquiry is made ...’ (184 b 23 #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, that it is necessary that there be 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 hbld that it was immobile, as did Parmenides and Melissus, whose opinion 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 Diogenes; others that it was water, as Thales; others that it was fire, as Heraclitus; and still others some mean between air and water, such as vapour.

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, others held that they were infinite.

Of those who held that they were finite (although more than one) some held that there were two, i.e., fire and earth, as Parmenides will say below [L 10]. Others held that there were three, i.e., fire, air and water (for ‘they thought earth to be in some way composed because of its density). Others, however, held that there were four, as Empedocles did, or even some other number, because even Empedocles himself along with the four elements posited two other principles, namely, friendship and strife.

Those who held that there was an infinite plurality of principles had a diversity of opinions. For Democritus held that indivisible bodies which are 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, 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, namely 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 and bone and other such things, as will be made clear below.

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

14. Secondly, at the point where he says, ‘A similar inquiry is made...’ (184 b 23; L9), 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 which are, i.e., about beings, wondered how many there are, i.e., 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 what is in thatfrom which things are, i.e., in inquiring about principles they sought the material causes from which beings are said to be. Whence it is clear that when they inquire about beings, whether they are one or many, their inquiry concerns the material principles which are called elements.

15. Next where he says, ‘Now to investigate ...’ (184 b 25), 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. Secondly, where he says, ‘At the same time the holders of the theory...’ (185 a 18),2 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 aforesaid opinion. Secondly, where he says, ‘... or like refuting ...’ (185 a 8 #17), he shows that it does not pertain to natural science to resolve the arguments which are brought forth to prove this opinion.

 He establishes his first point with two arguments, the second , of which begins where he says, ‘To inquire therefore ...’ (185 a 5 #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 there is no difference, according to the intention of the ancient philosophers, 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 which destroys its principles. Rather, this either pertains to some other particular science (if, indeed, geometry is subalternated to some particular science, such as music is subalternated 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 aforesaid position destroys the principles of nature. For if there is only one being, and if this being is immobile, such that from it others cannot come to be, then the very nature of a principle is taken away. For every principle is either a principle of some thing or of some things. Therefore, if we posit a principle, a multiplicity follows, because one is the principle and the other is that of which it is the principle. Whoever, therefore, denies multiplicity removes principles. Therefore natural science ought not to argue against this position.

16. Next where he says, ‘To inquire therefore...’(185 a 5), he shows the sar

gp point with another argument. It is not required of any science that it bring forth arguments against manifestly false and improbable opinions. For to worry about one who offers positions contrary to the opinions of the wise is stupid, as is said in Topics, I:11.

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 improbable 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 improbable. 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 when he says, ‘... or like refuting ...’ (185 a 8), he shows that it does not belong to natural science even to resolve the arguments of the aforementioned philosophers. And this for two reasons, the second of which begins where he says, ‘We physicists ...’ (185 a 13 #18).

First he proves his position by pointing out that it is not incumbent upon any science to resolve sophistic arguments which have an obvious defect of form or matter. He says that to deal with improbable arguments is like solving a contentious or sophistic argument. But each argument of both Melissus and Parmenides is sophistic, for they err in matter, whence he says that they have accepted what is false, i.e., they assume false propositions, and they err in form, whence he says that they are not syllogizing. But the position of Melissus is much worse, i.e., more vain and foolish and does not cause any difficulty. This will be shown below [L 5]. 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 where he says, ‘We physicists...’ (185 a 13). 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 centre 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, for nature is a principle of motion, as will be said below [II, L1].

Having established this point, that motion is supposed in natural science, he proceeds further to prove his position as follows. Not A arguments must be resolved in any science, but only those which conclude to something false from the principles of that science. Any arguments which 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, i.e., the squaring of a circle by dissecting the circumference, because this method supposes nothing contrary to the principles of the science of geometry. For somebody 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 figure, which was rectilinear, equal to some of the figures which were contained by the dissections of the circumference and the cords (either many or all), 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, for example, a square. And he divided in half the arcs by which the sides of the square were subtended. And from the points of dissection he led straight lines to all the angles of the square. And then there resulted in the circle a figure of eight angles, which 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, which 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 [L5]), 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 where he says, ‘At the same time ...’ (185 a 18), 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 a problem (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.

LECTURE 3 (185 a 20-b 27)
THE ASSERTION OF PARMENIDES AND MELISSUS THAT ALL THINGS ARE ONE BEING IS REFUTED

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. Secondly, where he says, ‘The physicists, on the other hand ...’ (187 a 11; L8 #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, and secondly against their arguments, where he says,’Further the arguments they use ...’ (186 a 5; L5 #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’which is the subject in this proposition. Secondly, where he says, ‘Again, “one” itself . ..’(185 b 5 #22), he uses an argument dealing with the ‘one’ which is the predicate.

21. He says first that that which should be taken primarily as a principle in arguing against the aforesaid position is the fact that that which is, i.e., 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, i.e., 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, it must either 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. For accident can in no way be without sub~tance. 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. For he held that being was infinite, whence 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 where he says, ‘Again “one” itself...’ (185 b 5) he sets forth his second argument which deals with the ‘one’.

Concerning this he makes two points. First he gives the argument. Secondly, where he says, ‘Even the more recent ...’ (185 b 25; L4 #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: either as the continuous is one, such as a line or a body, or as the indivisible is one, such as a point, or as those things are said to be one whose nature [ratio] or definition is one, as drink 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 which 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 this question, perhaps, 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 the same as one of the parts, then for the same reason it would be the same as another of the parts. But things which 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 having no diversity of parts.

23. Next where he says, ‘But to proceed ...’ (185 b 18), 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 which 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 is not finite. For the finite and the infinite are found in quantity.

24. Next where he says, ‘But if all things...’ (185 b 19), he shows how it cannot be said that all things are one in definition [ratio]. For if this were true, three absurdities would follow.

The first is that contraries would be one according to definition [ratio), so 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, IV:3.

The second absurdity is that the definitions [ratio] 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 that all beings would not only be one being, as they hold, but also they would be non-being or nothing. For things which are one in definition are so related that they may be used interchangeably as predicates. Whence 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 [ratio]. 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”’ (185 b 24).

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

LECTURE 4 (185 b 27-186 a 4)
THE LATER PHILOSOPHERS ALSO WERE INVOLVED IN THIS SAME ERROR, NAMELY, THAT THE ONE AND THE MANY COULD NOT IN ANY WAY CONCUR

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

Parmenides and Melissus erred because they did not know how to distinguish the uses of the term ‘one’. Thus, what is one in a certain respect, they said was one simply. But the later philosophers, also not knowing how to distinguish the uses of the term ‘one’, thought it absurd that one and 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 ‘disturbed’ (that is, fell into a difficulty similar to that of the ancients, i.e., 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 him who heard if names were spoken without the addition of any verb, some, wishing to correct this, changed the mode of speech. 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’ [albari] 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 (i.e., white man) to be many, as if one and being were used 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 definition [ratio]. Thus the white and the musical are the same in subject but many in definition [ratio]. 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. Whence 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 [#26], found some solution to the objection that things could be one in subject and many in definition [ratio], they failed altogether to answer the objection that a thing may be one as a whole but many in its parts. They still believed it to be something of an absurdity that the one should be many.

But it is not absurd 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, i.e., 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 which he had uppermost in mind, namely, that it is clear from the foregoing arguments that it is impossible for all beings to be one.

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. Secondly, where he says, ‘The fallacy of Melissus ...’ (186 a 10 #31), he answers the argument of Melissus. Thirdly, where he says,’The same kind of argument ...’ (186 a 23; L6 #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 does not cause any difficulty. 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 when he says, ‘The fallacy of Melissus ...’ (186 a 10), he answers the argument of Melissus, which 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 as a result 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, because 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 which some natural philosophers also used. Aristotle gives this argument below, near the end of Book I [L14 #120].

32. Aristotle disproves this argument of Melissus on four counts.

He argues first against the statement of Melissus that if what is made has a beginning, then what is not made has no beginning. This does not follow. Rather it is a fallacy of consequent. For he argues from the destruction of the antecedent to the destruction of the consequent, whereas the correct form of argumentation would be the converse. Whence it does not follow that if a thing which 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. Secondly, where he says, ‘Then this also is absurd ...’ (186 a 13), 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.

Whence 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, so that the beginning of time and of generation is not another meaning of the term.

However a simple and instantaneous generation (which is the induction of a form in matter) does not have a beginning. For of a simple generation there is no 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. Thirdly, where he says, ‘Again does it follow...’ (186 a 15), he disproves the above position with reference to its third inference, namely, that 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 with in water so 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. Fourthly, where he says,’But further...’(186 a 19), 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.

` 6 (186 a 23-b 35)
THE ARGUMENT OF PARMENIDES IS ANSWERED IN A NUMBER OF WAYS

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

First he disproves the argument. Secondly, where he says, ‘Some thinkers did...’(187 a 1; L7 #47ff.), 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. Secondly, where he says,’His assumption...’(186 a 24 #39), he resolves the argument in these ways.

37. Concerning the first part it must be known that the argument of Parmenides was as follows, as is clear from Metaphysics, I:5. 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 from this he concluded 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.

It is clear, moreover, from their very arguments that Parmenides considered being under the aspect [secundum rationem] of being, and so held it to be one and finite; whereas 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, 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 answerdd 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 which he assumed and which 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 which he assumed.

39. Next where he says, ‘His assumption ...’ (186 a 24), he follows the procedures just mentioned. First according to the first way, and secondly according to the second way, where he says, ‘His conclusion does not follow ...’ (186 a 25 #40).

He says, therefore, first that Parmenides assumed false propositions because he held that what is, i.e., being, is used simply, i.e., in one way. Whereas in fact it is used in many ways.

For being is used in one way for substance, in another way for accident; and the latter is used in many ways according to the different genera. Being also can 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, as it were, commonly for substance and accident. If, however, being is taken for accident alone or for substance alone, this is false, as will be shown below [#42-43].

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 where he says, ‘His conclusion does not follow ...’ (186 a 25), he follows the second method of answering the argument, i.e., that the argument of Parmenides does not draw its conclusion according to proper form.

He shows this first in an example. And secondly, where he says, ‘It is necessary for him ...’ (186 a 33 #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 of the fact that 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, i.e., from the fact that white is a continuum, it will not be one simply. For a continuum is in a certain respect many, as was said above [L3 #22].

And in like manner white will not be one in definition [ratio], for the white and that which is receptive of the white are different in definition [ratio]. Furthermore there will not be something other than white, as it were, separated from it. For the white is not other than that which is receptive of it because the white is separable from that which is receptive of it, but because the definitions [ratio] 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 [ratio].

41. Next where he says, ‘It is necessary for him ...’ (186 a 33), 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 [ratio]. Secondly, where he says, ‘In particular then...’ (186 b 13 #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. Secondly, where he says, ‘If, then, substance ...’ (186 b 4 #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 signify not some one being or what is predicated of some one thing. Rather it will signify what truly is, i.e., substance, and it will signify what is truly one, i.e., 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 (i.e., 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 nonbeing. 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, therefore, which is not win be’ (186 b 1), 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, IV:7. Whence he concludes that if anything is truly being, as is supposed in the proposition ‘whatever is other than being is nonbeing’, 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 nature [ratio] of being, unless being should signify many, so that each of the many would be a being. But it was assumed by Parmenides that being signifies one only.

43. Next where he says, ‘If, then, substance.. .’(186 b 4), 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. Whence 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 necesstuy that ‘what truly is’, i.e., substance, be signified by being rather than by non-being.

But this cannot stand. For let it be held that that which truly is, i.e., 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, i.e., what is not substance, is not that which is, i.e., is not being. But what is other than being, i.e., 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 nonbeing 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.

Whence it follows that being is non-being. And this indeed is impossible, because one contradictory is not predicated of another.

Whence, if 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 many according to nature [ratio].

44. Next where he says, ‘In particular then ...’ (189 b 13), 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 and secondly with reference to the parts of definition [ratio], where he says, ‘Substance is plainly divisible ...’ (186 b 14).1

He says, therefore, first 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 natures [ratio] of each of the parts are not the same, but different. Whence it follows that this one being is not a corporeal substance.

45. Secondly, where he says, ‘Substance is plainly divisible ...’ (186 b 14), he shows that this being cannot be a definable substance.

For in a definition it is clear that that which truly is, i.e., the substance, is divided into many, each one of which is what truly is, i.e. substance, and each one of which has a different nature [ratio]. Let us suppose that man is one thing which truly is. 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, i.e., 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 which 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 [i.e., from two-footed and animal] 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 which 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, VI: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 twofooted 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 twofooted 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. If, however, 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.

That it would follow that man would be an accident of another if animal and two-footed were accidents of another, he shows as follows. What is said of both animal and two-footed taken separately may be said of them taken together, i.e., two-footed animal. And what is said of two-footed animal may be said of that which is from them, i.e., man, ecause 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 in the passage beginning, ‘But we must assume ...’ (186 b 33), Aristotle sets forth the second argument of Parmenides to show that being is one. And this argument is as follows. A being which 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 this either proceeds to infinity, which is impossible in itself, or else 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.

LECTURE 7 (187 a 1-10)
HE DISPROVES THE POSITION OF THOSE WHO SAID THAT NON-BEING IS SOMETHING

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 inconsistencies.

Concerning this he makes two points. First he sets forth their position. Secondly, he disproves it where he says, ‘But obviously it is not...’ (187 a 3 #50).

48. It must be noted first that the Philosopher used two arguments above [L6 #36ff.] against the argument of Parmenides. 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 an is one does not follow because, if it were a magnitude, it would follow that this 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, VI:2 that Plato held that sophistry dealt with nonbeing, because it treated most of all those things which 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, III:1.

50. Next where he says, ‘But obviously ...’ (187 a 3), 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 [VI L1].

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. Secondly, he disproves Plato’s remark that unless we hold this (i.e., that the non-being which is accident is something), it will follow that all is one. He does this where he says, ‘To say that all things ...’ (187 a 7 #52).

51. He says, therefore, first that the argument by which Plato concluded that being signifies one clearly does not follow. For he held that being is a genus and is predicated univocally of all things by a 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 the one, 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 the one, which is substance, it would follow that whatever is not substance is non-being. But there is something which 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, i.e., not substance, is absolute non-being. Hence, although accident is not being simply, it cannot, indeed, be called absolute nonbeing.

52. Next where he says, ‘To say that all things ...’ (187 a 7), he shows further that, if the non-being which 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 [L6 #45], even if magnitude and accident are removed. For the definition of substance is divided into the many things which 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 which he had uppermost in mind, namely, that all things are not one, as Parmenides and Melissus said.

LECTURE 8 (187 a 11-26)
THE OPINIONS OF THE PHYSICISTS WHO SPOKE OF THE PRINCIPLES AS NATURAL PHILOSOPHERS

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, i.e., natural philosophers.

Concerning this he makes two points. First he sets forth the diversity of their opinions. Secondly he examines one of these opinions, where he says, ‘The theory of Anaxagoras ...’ (187 a 28; L9 #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, i.e., fire, air, and water (for no one made earth alone the principle, as was said above [L2 #13]) or else some intermediate between them, for example, that which would be more dense than fire and more subtle than air. Theythen 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 which 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 which 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 contraries themselves and different things are drawn forth from one thing in which they already existed, as it were, mixed and confused.

But they differed as follows. Anaximander held that the principle is one confused state in which there are not many things mixed together. Thus he held one principle only. But Empedocles and Anaxagoras held rather that the principles are the very things which 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, so that all things never will be mixed into one.

They also differed in another way. Anaxagoras held that the principles are infinite parts which are alike and contrary. Thus there are infinite parts of flesh which are like each other and infinite parts of bone and other things which 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 which are commonly called elements, i.e., fire, air, water, and earth.

LECTURE 9 (187 a 27-188 a 18)
THE OPINION OF ANAXAGORAS THAT THE PRINCIPLES ARE INFINITE IS REFUTED

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, where he says, ‘Now the infinite ...’ (187 b 7 #64).

Concerning the first part he makes three points. First he sets forth those things which Anaxagoras supposed and from which he argues. Secondly, where he says, ‘The one, they reasoned ...’ (187 a 33 #62)2 he sets forth the order of his argument. Thirdly, where he says, ‘But things, as they say ...’ (187 b 2 #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 which 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 would be forced to hold that something new comes to be which 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 natural 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 pre-existed together as in one material principle said that to come to be is nothing other than to be 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 pre-existed 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 which come to be naturally do not come to be from nonbeing simply, but from being in potency, and not, indeed, from being in act, as they thought. Hence things which come to be did not necessarily pre-exist in act, as they said, but only in potency.

61. Next where he says, ‘Moreover the fact that ...’ (187 a 32), he mentions the second thing which Anaxagoras assumed.

Anaxagorai 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 pre-exists 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 ...’ (187 a 33), he sets forth the deductive order of the argument.

Anaxagoras proceeded as follows. If something comes to be, it is necessary that it should come to be either from being or from nonbeing. But he excluded one of these alternatives-namely, that something should come to be from non-being. He does this because of the common opinion of the philosophers mentioned above [#59]. Whence he concluded that the remaining member was correct, namely, that a thing comes to be from being. For example, if air comes to be from water, then air pre-existed. For it cannot be said that air comes to be from water unless air pre-existed in water. Hence he wished to say that everything which comes to be from something pre-existed 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 pre-exists in it), he forestalled this objection by holding that that which comes to be from something pre-exists in it as certain most minute parts which 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 which comes to be from something pre-exists in it, he further assumed that everything comes to be from everything. Whence 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 infinite minute parts were in each thing.

63. Next where he says, ‘But things, as they say ...’ (187 b 2), he excludes a certain tacit 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 where he says, ‘Now the infinite ...’ (187 b 7), Aristotle refutes the above mentioned position.

Concerning this he makes two points. First he disproves the position absolutely. Secondly, where he says, ‘... and it is better...’ (188 a 17), 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. Secondly, where he says, ‘The statement that...’ (188 a 5 #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, in that respect in which it is infinite, is unknown. He explains why he says ‘in that respect in which it is infinite’. If it is infinite in respect to multitude or magnitude, it will be unknown in respect to quantity. If, however, it is infinite in 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 in respect to quantity or in respect to species.

But if the principles are unknown, those things which 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 [principles] it is composed, i.e., 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 in respect to quantity or in respect to species.

65. At the point where he says, ‘Further if the parts ...’ (187 b 14), 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 not necessarythat the whole 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 into which a whole can be divided and which are actually present in it’ (187 b 15). And by this he excludes the parts of a continuous whole which 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 which 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, considered mathematically, is divisible to infinity, 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 determin.ate quantity and also other accidents. Whence 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 where he says, ‘Again according to the theory ...’ (187 b 23).

Concerning this he makes two points. First he sets forth certain things which are the basis of the argument. Secondly, where he says, ‘For let flesh ...’ (187 b 28 #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 [#62], all things are together. And from this Aristotle wishes to reduce Anaxigoras’ argument to absurdity. For Anaxagoras said, as was pointed out [#62ff], that all things which are of a certain kind, i.e., all things which 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 pre-exist. And each thing is named from that which abounds in it, i.e., 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 in the same way flesh comes to be from water.

And the third point is that every finite body is reduced by a finite body. That is, 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 primiarily intended, namely, that each thing is not in each thing. And this is contrary to the first of these three points. For in arguments which lead to absurdity the denial of one of the premises is the final conclusion.

68. Next where he says, ‘For let flesh...’(187 b 28), 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 is not less than a certain smallness, i.e., 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 small particle of flesh than which there is no smaller, he proceeds as follows.

If from water flesh is separated, and again other flesh, the process of separation will either 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, e.g., water, there are certain things which are finite in respect to quantity, and equal to each other, and 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 nature 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, for example, 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 nature [ratio] of quantity which is found in a mathematical body.

70. He gives his fourth argument where he says, ‘Another proof may be added ...’ (187 b 35). 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 from this nothing can be separated, because the remainingfiesh would be smaller than this smallest piece of flesh. Therefore it is impossible that everything comes to be from everything by separation.

71. At the point where he says, ‘Lastly in each ...’ (188 a 3), 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 where he says, ‘The statement that ...’ (188 a 5), 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. Secondly, where he says, ‘Nor is Anaxagoras...’(188 a 13),1 he shows that Anaxagoras did not have sufficient evidence for holding this position.

He says, therefore, 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 froin the previously existing mixture. If then colours and other accidents of this sort are mixed together, as he said, and if someone on this supposition says all things that are mixed can be separated, it would follow that there would be white and healthy, and yet there would be 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 absurdity results from the following. Anaxagoras held that all things were mixed from the very beginning, but intellect began to separate them. Now any intellect which attempts to do what cannot be done is not worthy of the name intellect. Hence that intellect will be inconsistent, intending the impossible, if it truly wishes this, i.e., 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, for from any small quantity something can be subtracted, and from the point of view of quality, because accidents are not separable from their subjects.

73. Next where he says, ‘Nor is Anaxagoras ...’ (188 a 13), 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 which 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, i.e., he did not understand that a thing is not always generated by things which 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 bricks; in other instances, however, 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; whereas 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, i.e., 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, i.e., through composition, as the house is made of sides, and by resolution, as the sides come to be from the house.

74. Next where he says, ‘... and it is better ...’ (188 a 17), 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.

LECTURE 10 (188 a 19-189 a 10)
THE OPINIONS OF THE ANCIENTS CONCERNING THE CONTRARIETY OF THE FIRST PRINCIPLES

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. Secondly, where he says, ‘We will now give ...’ (189 b 30; L12 #98), he determines the truth demonstratively. The Oxford English translation seems to be based upon this variant reading. Lecture 12, 98.

Concerning the first part he makes two points. First he investigates the contrariety of the principles, secondly, where he says, ‘The next question is ...’ (189 a 11; L11 #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. Secondly, where he says, ‘And with good reason ...’ (188 a 27 #77) he gives an argument in favour of this position. Thirdly he shows how the philosophers are related to each other in saying that the principles are contraries. He does this where he says, ‘Up to this point...’ (188 b 27 #79).

76. He says, therefore, first 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, e.g., the hot and the cold. He attributed the hot to fire and the cold to earth.

Secondly 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 which 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, I:8. Therefore he held that all bodies are composed of the fixed and the empty, that is, composed of the plenum and the void. Hence he said that the plenum and the void are principles of nature. But he assdeiated the plenum with being and the void 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, i.e., above and below, before and behind, and also contraries in the genus of figure, i.e., the straight, the angular, and the circular. The principles also are contraries in the genus of order, i.e., prior and posterior. (These last contraries 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 [L8 #56-57]. 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 where he says, ‘And with good reason’ (188 a 27), 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 nature of principles. First, they are not from other things. Secondly, they are not from each other. Thirdly, all other things are from them. But these three notes 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, e.g., 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, which 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 which are first are manifestly not from others. Moreover things which 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 [L11 #90]. 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 which are contingent in the sense of merely happening to be together, or between things which 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 which is black or some mean colour. And in like manner, the musical comes to be from the non-musical, and again not from just any nonmusical, but from its opposite, which is called the unmusical, i.e., 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 (e.g., the white into the musical) except accidentally. Rather white is corruptedper se into the non-white, and not into just any non-white, but into black or some mean colour. 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. Whence it is necessary that that which a thing comes to beper se and that intowhich a thing is corruptedper se be such that it includes in its nature [ratio] 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 with simple things, but 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 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, e.g., an army; and other wholes consist of a harmony of composition, e.g., a house. And the nature [ratio] of each of these is the same. It is also clear that all composites come to be from the noncomposed, 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 everything which comes to be or is corrupted comes to be from contraries or from some intermediate between them, or is corrupted into them. Moreover, intermediates between contraries come to be from the contraries, as the intermediate colours come to be from black and white. Hence he concludes that whatever comes to be according to nature is either a contrary, such as white and black, or comes to be from the contraries, such as the intermediates between the contraries.

This, then, is th e principal conclusion which he intended to draw, namely, thafall things come to be from contraries, w hich was the third characteristic of principles.

79. Next where he says, ‘Up to this point ...’ (188 b 27), Aristotle shows how the philosophers are related in holding that the principles are contraries. First he shows how they are related with reference to being moved toward this position. Secondly, where he says, ‘They differ, however...’(188 b 30 #80), he shows howthey are related itirespect to the position itself.

He says, therefore, as was pointed out above [#76] 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 reason, but rather as forced to it by the truth itself. For truth is the good of the intellect, toward which the intellect is naturally ordered. Hence as things which lack knowledge are moved to their ends without reason [ratio], so, at times, the intellect of man, by a sort of natural inclination, tends toward the truth, though it does not perceive the reason [ratio] for the truth.

80. Next where he says, ‘They differ, however, ...’ (188 b 30), he shows how the aforesaid 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. Secondly, where he says, ‘Hence their principles...’ (188 b 37 #81), he shows how they both differ and agree.

He says, therefore, 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 [derived] contraries.

And of those who appealed to the primary contraries, some considered those contraries which were better known to reason, others those contraries which were better known to sense.

Or it could be said that this second difference explains the first. For those things which are better known to reason are prior simply, whereas those things which are better known to sense are posterior simply, and

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 which 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 which 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.

Others, however, held principles which 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. Whereas 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. Whence it is clear that the diversity mentioned above appears in these positions.

81. Next where he says, ‘Hence their principles ...’ (188 b 37), 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 #80); yet they are the same insofar as their principles were alike according to analogy, i.e., proportion. For the principles taken by an of them have the same proportion.

And this is true in three respects. First, all the principles which they assumed are related as contraries. And thus Aristotle says that they all took their principles from the same columns, i.e., 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 are containers, as the prior and more common; and others axe 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, or the plenum, or the hot, are better; but strife, or the void, or 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 habit, as is said in Metaphysics, X:4.

Thixdly they agree according to analogy by reason of the fact that they all took principles which are better known. But some took principles which are better known to reason, others those which are 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, whereas singulars (such as the rare and the dense, which are less common) are better known to sense.

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

LECTURE 11 (189 a 11-b 29)
THERE ARE THREE PRINCIPLES OF NATURAL THINGS, NO MORE, NO LESS

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. Secondly, where he says, ‘One they cannot be ...’ (189 a 12 #83), he excludes certain things which are not pertinent to this question. Thirdly, he takes up the question, where he says, ‘Granted, then, that...’ (189 a 21 #89).

He says, therefore, first that after an investigation into the contrariety of the principles, an inquiry about their number should follow, i.e., whether they are two, or three, or more.

83. Next where he says, ‘One they cannot be ...’ (189 a 12), he excludes those things which are not pertinent to this question. He shows first that there is not just one principle, and secondly, where he says, ‘Nor can they be ...’ (189 a 12 #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 [L 10] 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 where he says, ‘Nor can they be ...’ (189 a 12), 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 which are from the principles are unknown. It follows, therefore, that nothing in the world could be known.

85. He gives the second argument where he says, ‘... and in any one genus...’ (189 a 13). The argument is as follows. The principles must be primary contraries, as was shown above [L10 #77]. 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 where he says, also a finite number ...’ (189 a 15). The argument is as follows. It is better to say that what can come to be from finite principles comes from finite principles rather than from infinite principles. But all things which come to be according to nature are explained by Empedocles through finite principles,just as they are explained byAnaxagoras through infinite principles. Hence an infinite number of principles should not be posited.

87. He gives the fourth argument where he says, ‘Lastly, some con traries ...’ (189 a 17). The argument is as follows. Principles are contraries. If, therefore, the principles are infinite, it is necessary that all the contraries be principles. But all of the contraries are not 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. Secondly, the principles ought not to be from each other, as was said above [L10 #77]. 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 which are seen in many instances, and which cannot be false taken as a whole, 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 [L10 #78], 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 where he says,’Granted then...’(189 a 21), he takes up the question under discussion, namely, what is the number of the principles. ‘Concerning this he makes two points. First he shows that there are not just two principles, but three. Secondly, where he says, ‘On the other hand ...’ (189 b 18 #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. Secondly, where he says, ‘If, then, we accept ...’ (189 a 34 #93), he shows that even the ancient philosophers agreed on this point.

90. Concerning the first part 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 abovei that the principles are contraries, it seems that there are only two principles, because contrariety exists between two extremes.

But one might question this. For it is necessary that other things come to befrom the principles, as was said above [L10 #77]. 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 friendship does not move strife and make something out of it, nor does the converse happen. Rather each of the contraries changes some third thing which 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 which 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 II [L2].

91. He gives the second argument where he says, ‘Other objections ...’(189 a 28). He says that, unless there is something other than the contraries which are given as principles, then there arises an even greater difficulty. For a first principle cannot be an accident which is predicated of a subject. For since a subject is a principle of the accident which 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 what is ‘of’ a principle would be a 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 something else. 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 which were well known among the ancients.

92. He gives the third argument where he says, ‘Again we hold...’ (189 a 33). The argument is as follows. Everything which is not a principle must be from principles. If, therefore, 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 certain things is posterior to them. 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 where he says, ‘If, then, we accept ...’ (189 a 34), 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. Secondly, where he says, ‘All, however agree...’ (189 b 9 #94), he shows how they posited two contrary principles besides this one material principle.

However, we must first note that the Philosopher in the preceding arguments seemed to be opposed, in the manner of those who dispute, to both sides of the question. For first he 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 some kind of 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 vapour, or some other thing of this sort.

This seems especially true in regard to an intermediate. For this third thing ietaken 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, e.g., the hot and the cold, 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 which is most sensible and which is very active. For in fire there is an excellence of heat. If, however, the elements are compared with reference to their subtlety, those who made fire the principle seem to have spoken better, as is said elsewhere,’ 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 where he says, ‘All, however, agree ...’ (189 b 9), 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 which he had uppermost in mind, 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 where he says, ‘On the other hand ...’ (189 b 18), he shows that there are no more than three principles. He uses two arguments, the first of which 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 where he says, ‘Moreover it is impossible ...’ (189 b 23). 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 which 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, namely, 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: namely, 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.

LECTURE 12 (189 b 30-190 b 15)
IN EVERY COMING TO BE THREE PRINCIPLES ARE TO BE FOUND: THE SUBJECT, THE TERMINUS OF THE PRODUCTION, AND ITS OPPOSITE

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. Secondly, where he says, ‘We will not proceed...’ (191 a 23; L14 #120ff), he excludes from the truth already deterrained 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. Secondly, where he says, ‘Plainly, then ...’ (190 b 16; L13 #110), he shows from this that these three things are principles.

Concerning the first part he makes two points. First he states his intention, and secondly he pursues his intention, where he says, ‘We say that ...’ (189 b 33 #100).

99. Because he had said above [L11 #97] 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 mutation. For in any mutation 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 mutations. He also points out the reason for this order of procedure. It is necessary to speak first of those things which are common, and afterwards to think of those things which are proper to each thing, as was said in the beginning of the Book [L1 #6].

100. Next where he says, ‘We say that one thing ...’ (189 b 33), he develops his position. Concerning this he makes two points. First he sets forth certain things which are necessary to prove his position. Secondly, where he says, ‘These distinctions drawn ...’ (190 a 13 #103),he proves his point.

Concerning the first part he makes two points. First he sets up a cerr tain division, secondly, where he says, ‘As regards one ...’ (190 a 5 #102), he points out the differences among the parts of the division.

101. He says, therefore, first 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 [esse], or one comes to be from another with reference to coming to be in regard to accidental being [esse]. Hence every change has two termini. The word ‘termini’, however, is used in two ways, for the termini of a production or mutation 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. Yet when coming to be is attributed to man or to the nonmusical, each is simple. And thus, that which becomes, i.e., that to which coming to be is attributed, is said to come to be simply. Moreover, that in which the very coming to be is terminated, which is also said 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 (i.e., both what becomes, i.e., that to which the coming to be is attributed, and what is made, i.e., 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 nonmusical man becomes a musical man, then there is composition on the part of each.

102. Next where he says, ‘As regards one ...’ (190 a 5), he points out two differences in what was said above.

The first is that in some of the cases mentioned above we use a twofold mode of speech, i.e., 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 where he says, ‘When a “simple”...’ (190 a 8). He says that when coming to be is attributed to two simple things, i.e., 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 the negative opposite, as the non-musical, or the privation or 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, and the non-musical becomes musical, and the non-musical man becomes musical. Of these three, only the first remains complete in a production, the other two do not remain.

103. Next where he says, ‘These distinctions drawn ...’ (190 a 13), having assumed the foregoing, he proves his position, namely that three t . ngs are found in any natural production.

Concerning this he makes three points. First he enumerates two things which are found in any natural production. Secondly, where he says, ‘One part survives ...’ (190 a 17 #105), he proves what he had supposed. Thirdly, where he says, ‘Thus, clearly, ...’ (190 b 10 #109), he draws his conclusion.

104. He says, therefore, first that, if anyone, taking for granted what was said above, wishes to consider [coming-to-be] in all the things which 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 [ratio]. For when it is said of a man that he becomes musical, the man is indeed one in subject, but two in nature [ratio]. For man and the non-musical are not the same according to nature [ratio]. Aristotle does not, however, mention here the third point, namely, that in every generation there must be something generated, for this is obvious.

105. Next where he says, ‘One part survives...’ (190 a 17), he proves the two things which he had assumed. He shows first that the subject to which the coming to be is attributed is two in nature [ratio]. Secondly, where he says, ‘But there are different ...’ (190 a 32 #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 he points out that in the subject to which the coming to be is attributed there is something which is permanent and something which 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 nature [ratio], since the one remains, whereas the other does not.

106. Secondly, where he says, ‘We speak of ...’(190 a 2 1), 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 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 nonmusical. 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 which is understood.

From this very fact, then, 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 nature [ratio].

107. Next where he says, ‘But there are different ...’ (190 a 32), he proves the other point which he had assumed, namely, that 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, VII:7. He proves it here only by induction. He does this first in regard to the things which come to be; secondly in regard to the modes of coming to be, where he says, ‘Generally things ...’ (190 b 5 #108).

He says, therefore, first 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 it previously will not have been simply, which happens in those things which comer to be substantially. For when a man comes to be, he not only previously was not a man, but it is true to say that he simply was not. When, however, a man becomes white, it is not true to say that he previously was not, but that he previously was not such.

Those things, however, which 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 where he says, ‘Generally things ...’ (190 b 5), he shows the same thing by induction from the modes of coming to be.

He says that of things which 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 the image of Mercury comes to be from stone by sculpture. Still other things come to be by composition, e.g., a house; and other things 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. Whence it is clear that everything which comes to be comes to be from a subject.

But it must be noted that artificial things are here enumerated along with those things which 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 II [L2 #149].

109. Next where he says, ‘Thus clearly ...’ (190 b 10), 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 is twofold, i.e., the subject and the opposite, it is then clear that there are three things in any coming to be, namely, 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.

LECTURE 13 (190 b 16-191 a 22)
THERE ARE TWO per se PRINCIPLES OF THE BEING AND OF THE BECOMING OF NATURAL THINGS, NAMELY, MATTER AND FORM, AND ONE PER ACCIDENS PRINCIPLE, NAMELY, PRIVATION

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. Secondly, where he says, ‘Briefly, we explained ...’ (191 a 15 #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. Secondly he names them, where he says, ‘The underlying nature ...’ (191 a 8 #118).

Concerning the first part he makes three points. First he explains the truth about the first principles of nature. Secondly, where he says, ‘There is a sense ...’ (190 b 28 #114) from this disclosure of the truth he answers the problems about the principles which were raised above. Thirdly, since the ancients had said that the principles are contraries, he shows whether or not contraries are always required, where he says, ‘We have now stated ...’ (191 a 3 #115).

Concerning the first part he makes two points. First he shows that there are two per se principles of nature. Secondly, where he says, ‘Now the subject ...’ (190 b 23 #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. 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 which comes to be according to nature.

That that which comes to be according to nature comes to be from subject and form he proves as follows. 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 [ratio] of that which comes to be according to nature is resolved into subject and form. For the definition [ratio] of musical man is resolved into the definition [ratio] of man and the definition [ratio] 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 both are and 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 which comes to be according to nature are subject and form.

112. Next where he says, ‘Now the subject ...’ (190 b 23), he adds the third per accidens principle. He says that although the subject is one in number, it is nevertheless two in species and nature [ratio], as was said above [L12 #104]. 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, i.e., contrariety and privation, such as to be unmusical and unshaped. The third principle, then, is a species or form, as order is the form of a house, or musical is the form of a musical man, or as any of the other things which 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. Thus 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 nagter has one form, it is in privation of some other form. And so while it is coming to be that which it becomes (e.g., 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 posited 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, which occurs in the subject.

114, Next where he says, ‘There is a sense...’ (190 b 28), 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 in another respect that there are three, if we accept along with the per se principles 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, the harmonious and the inharmonious. Yet in another respect the principles, if they are taken without the subject, 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 [esse] is other, for the subject according to nature [ratio] is two, as was said [L12 #104ff]. And thus there are three principles, because man and the non-musical, and bronze and the unshaped, differ according to nature [ratio].

Therefore it is clear that the early opinions which argued for a part of the truth were in a certain respect true, but not altogether true.

115. Next where he says, ‘We have now stated ...’ (191 a 3), 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 it is clear how many principles of the generation of natural things there are, 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 V [L2 #649ff], there are three species of mutation, namely, generation and 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 mutation subject and form and privation are required. However, the nature [ratio] 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 priv ‘ ation are found in every mutation, but not a subject and two contraries.

117. This opposition is also found in substances, which are the first genus. This, however, is not the opposition of contrariety. 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 where he says, ‘The underlying nature ...’ (191 a 8), he clarifies the above-mentioned principles.

He says that the nature which is first subject to mutation, i.e., primary matter, cannot be known of itself, since everything which is known is known through its form. Primary 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, at other times the other. When, therefore, we see that air at times becomes water, it is necessary to say that there is something which 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 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 primary matter.

This, then, is one principle of nature. It is not one as a ‘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 nature [ratio) 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 where he says, ‘Briefly, we explained ...’ (191 a 15), he gives a r6sum6 of 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 nature [ratio]. Then it was pointed out what the subject is insofar as this could be made clear. But it has n ‘ ot yet been decided which is the greater substance, form or matter, for this will be explained at the beginning of Book II [L2 #153]. 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 had uppermost in mind, namely, that it is clear how many principles there are and what they are.

LECTURE 14 (191 a 23-b 34)
THE PROBLEMS AND THE ERRORS OF THE ANCIENTS WHICH SPRING FROM AN IGNORANCE OF MATTER ARE RESOLVED BY THE TRUTH ABOUT THE PRINCIPLES ALREADY DETERMINED

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 which stem from an ignorance of matter, and secondly, where he says, ‘Others indeed ...’ (191 b 35; L15 #129), the problems or errors which stem from an ignorance of privation. Thirdly, where he says, ‘The accurate determination ...’ (192 a 34; L15 #140), he reserves for another science the problems which 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. Secondly, where he says, ‘Our explanation ...’ (191 a 33 #122) he answers their difficulty by means of those things which have already been determined.

121. He says, therefore, first that, after determining the truth about the principles, it must be pointed out that only in this way is every difficulty 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 given a position which is in some way false, 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, i.e., 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 [L12 #107]. 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 where he says, ‘Our explanation...’ (191 a 33), he answers the objection just mentioned. Concerning this he makes two points. First, he answers the aforesaid objection in two ways. Secondly, where he says,’So as we said ...’ (191 b 30 #128), he draws the conclusion which he has uppermost in mind.

The first point is divided into two parts according to the two solutions given, the second of which is found where he says, ‘Another consists in ...’ (191 b 28 #127).

123. He says, therefore, first that as far as the mode 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 which are used; e.g., 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 doctor, and in like manner that the doctor becomes a nondoctor 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, i.e., per se and per accidens.

Whence 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 same argument applies to being.

But the ancients, failing to perceive this distinction, effed insofar as they thought that nothing comes to be. And they did not think that anything other than their first material principle had 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 that which is,i.e., being, is not from privationper 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, because 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 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 which 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-b,eing, as was said [#123]. 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 nonanimal, nor all body or non-body, is removed from that from which the thing comes to be. And likewise not all being [esse] nor all non-being [non-esse] 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 every thing which 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 where he says, ‘Another consists...’ (191 b 28).

He says that the same thing can be explained in terms of potency and act, as is clearly indicated in another place, i.e., in Metaphysics, IX: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 which 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, where he says, ‘So as we said ...’ (191 b 30), he draws the conclusion which he had uppermost in mind. He says that we can truly say that all the difficulties are answered by what has been said above. Driven on by certain difficulties, some of the ancients denied some of the things mentioned above, i.e., generation and corruption, and a plurality of substantially different things. But once matter is understood, all of their ignorance is removed.

LECTURE 15 (191 b 35-192 b 5)
MATTER IS DISTINGUISHED FROM PRIVATION. MATTER IS NEITHER GENERABLE NOR CORRUPTIBLE PER SE

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

Concerning this he makes three points. First, he sets forth the errors of those who wandered from the truth. Secondly, where he says, ‘Now we distinguish ...’ (192 a 2 #132), he shows how this position differs from the truth determined by him above. Thirdly, where he says, ‘For the one which persists ...’ (192 a 13 #134), he proves that his own opinion is true.

130. He says, therefore, first 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. Secondly, it seemed to them that that which is one in number or subject is also one in nature [ratio]. And Aristotle calls this a state of being one in potency, because things which are one in nature [ratio] are such that each has the same power. But things which are one in subject but not one in nature [ratio] 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, as for example, the bronze and the unshaped. Hence it seemed to them that they would be the same in nature [ratio] 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, IX:1, and in Book III [L3] of this work. 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 nature [ratio] there are many potencies according to its relation to different forms. Hence in Book Ills it will be said that to be able to be healed and to be able to be ill differ according to nature [ratio].

132. Next where he says, ‘Now we distinguish...’ (192 a 2), he explains the difference between his own opinion and the opinion just given.

Concerning this he makes two points. First he widens our understanding of his own opinion. Secondly, where he says, ‘They, on the other hand ...’ (192 a 6 #133), he shows what the other opinion holds.

He says, therefore, first that there is a great difference between a thing’s being one in number or subject and its being one in potency or nature [ratio]. For we say, as is clear from the above [L12 #104], that matter and privation although one in subject, are other in nature [ratio]. 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. Secondly, 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 where he says, ‘They, on the other hand ...’(192 a 6), 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 nature [ratio]. But the Platonists did not hold that one of these is privation and the other matter, but theyjoined privation to both, i.e., 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 separately. Whence it is clear that the Platonists, who posited form and the great and the small, held three completely different principles than 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 an natural forms, which nature is primary matter. But they made it one both in subject and in nature [ratio], 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 where he says, ‘For the one which persists ...’ (192 a 13), he proves that his opinion is true. Concerning this he makes two points. First he states his position, i.e., that it is necessary to distinguish privation from matter. Secondly, where he says, ‘The matter comes to be ...’ (192 a 25),1 he shows how matter is corrupted or generated.

He treats the first point in two ways, first by explanation, and secondly by reducing [the opposite opinion] to the impossible, where he says, ‘...the other such ...’ (192 a 18).

135. He says, therefore, first that this nature which is the subject, i.e., matter, together with form is a cause of the things which 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, insofar as it is in act, has form. Form is very good because act is the perfection of potency and is its good; and 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. Whence it follows that privation is not the same as matter, which is the cause of a thing as a mother.

136. Next where he says, the other such...’ (192 a 18), he proves the same thing by an argument which reduces [the opposite position] to the impossible.

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 absurdity 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. (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 nature [ratio] from 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 nature [ratio], 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 nature [ratio].

Nevertheless, matter is ‘a this’, i.e., 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, namely, matter, seeks to be form.

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

First, 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, as for example, the heavy naturally seeks the lowest place insofar as it is inclined by its heaviness to such a place.

Secondly, 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 which are impossible, or because it dislikes the form which 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, i.e., as a poet, not as a philosopher.

138. But it is easy to resolve objections of this sort. For we must note that everything which seeks something either knows that which it seeks and orders itself to it, or else it 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 not only ordered to its end 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 which 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 above [L13 #118] that primary 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 primary 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 which is of the nature [ratio] 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 where he says, ‘The matter comes to be ... (192 a 25), 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 from the following. If matter should come to be, there would have to be something which is the subject from which it comes to be, as is clear from what was said above [L12 #7,10ff]. 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 that which 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 which is corrupted is resolved into primary matter.. Therefore, at the very time when primary matter already is, it would be corrupted; and thus if primary matter is corrupted, it will have been corrupted before it is corrupted, which is impossible. Therefore, it is impossible for primary matter to be generated and corrupted. But by this we do not deny that it comes into existence through creation.

140. Next where he says, ‘The accurate determination...’ (192 a 34), he indicates that since the errors about matter and privation have been eliminated, then the errors and problems about form should also be eliminated. For some have posited separated forms, i.e., ideas, which they reduced to one first idea.

And so he says that first philosophy treats such questions 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, that is, into the principles of the science.