METAPHYSICS
BOOK III

LESSON I

The Need of Questioning Everything in the 8earch for Universal Truth

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176. With a view to the science under investigation we must attack first those subjects which must first be investigated. These are all the subjects about which some men have entertained different opinions, and any other besides these which has been omitted.

177. Now for those who wish to investigate the truth it is worth the while to ponder these difficulties well. For the subsequent study of truth is nothing else than the solution of earlier problems. For it is impossible to untie a knot without knowing it. But a perplexity on the part of the mind makes this evident in regard to the matter at hand; for insofar as the mind is perplexed, to that extent it experiences something similar to men who are bound; for in both cases it is impossible to move forward. For this reason, then, it is first necessary to consider all the difficulties and the reasons for them.

178. [This is also necessary] for another reason, namely, that those who make investigations without first recognizing the problem are like those who do not know where they ought to go.

179. Again, one would not even know when he finds the thing which he is seeking [and when not]; for the goal is not evident to such a man, but it is evident to one who previously discussed the difficulties.

180. Furthermore, one who has heard all the arguments of the litigants, as it were, and of those who argue the question, is necessarily in a better position to pass judgment.

COMMENTARY

338. Having indicated in Book II (331) the method of considering the truth, the Philosopher now proceeds with his study of the truth. First he proceeds disputatively, indicating those points which are open to question so far as the truth of things is concerned. Second (529), he begins to establish what is true, and he does this in Book IV, which begins: “There is a certain science.”

The first part is divided into two sections. In the first, he states what he intends to do. In the second (346), he proceeds to do it (“The first problem”).

In regard to the first he does two things. First, he states what he intends to do. Second (339), he gives the reasons for this (“Now for those”).

He says first, then, that with a view to this science which we are seeking about first principles and what is universally true of things, we must attack, first of all, those subjects about which it is necessary to raise questions before the truth is established. Now there are disputed points of this kind for two reasons, either because the ancient philosophers entertained a different opinion about these things than is really true, or because they completely neglected to consider them.

339. Now for those (177).

Here he gives four arguments in support of this thesis:

First, he says that for those who wish to investigate the truth it is “worth the while,” i.e., worth the effort, “to ponder these difficulties well,” i.e., to examine carefully those matters which are open to question. This is necessary because the subsequent study of truth is nothing else than the solution of earlier difficulties. Now in loosening a physical knot it is evident that one who is unacquainted with this knot cannot loosen it. But a difficulty about some subject is related to the mind as a physical knot is to the body, and manifests the same effect. For insofar as the mind is puzzled about some subject, it experiences something similar to those who are tightly bound. For just as one whose feet are tied cannot move forward on an earthly road, in a similar way one who is puzzled, and whose mind is bound, as it were, cannot move forward on the road of speculative knowledge. Therefore, just as one who wishes to loosen a physical knot must first of all inspect the knot and the way in which it is tied, in a similar way one who wants to solve a problem must first survey all the difficulties and the reasons for them.

340. [This is also necessary] (178).

Here he gives the second argument. He says that those who wish to investigate the truth without first considering the problem are like those who do not know where they are going. This is true for this reason, that, just as the terminus of a journey is the goal intended by one who travels on foot, in a similar way the solution of a problem is the goal intended by one who is seeking the truth. But it is evident that one who does not know where he is going cannot go there directly, except perhaps by chance. Therefore, neither can one seek the truth directly unless he first sees the problem.

341. Again, one would (179).

Here he gives the third argument. He says that, just as one who is ignorant of where he is going does not know whether he should stop or go further when he reaches his appointed goal, in a similar way one who does not know beforehand the problem whose solution marks the terminus of his search cannot know when he finds the truth which he is seeking and when not. For he does not know what the goal of his investigations is, but this is evident to one who knew the problem beforehand.

342. Furthermore (180).

He gives the fourth argument, which is taken from the viewpoint of a judge. For a judge must pass judgment on the things which he hears. But just as one can pass judgment in a lawsuit only if he hears the arguments on both sides, in a similar way one who has to pass judgment on a philosophy is necessarily in a better position to do so if he will hear all the arguments, as it were, of the disputants.

343. Now it must be noted that it was for these reasons that Aristotle was accustomed, in nearly all his works, to set forth the problems which emerge before investigating and establishing what is true. But while in other works Aristotle sets down the problems one at a time in order to establish the truth about each one, in this work he sets forth all the problems at once, and afterwards in the proper order establishes the things that are true. The reason for this is that other sciences consider the truth in a particular way, and therefore it belongs to them to raise problems of a particular kind about individual truths. But just as it belongs to this science to make a universal study of truth, so also does it belong to it to discuss all the problems which pertain to the truth. Therefore it does not discuss its problems one at a time but all at once.

344. There can also be another reason [why Aristotle proceeds in this way], namely, that those problems on which he touches are chiefly those about which the philosophers have held different opinions. However, he does not proceed to investigate the truth in the same order as the other philosophers did. For he begins with things which are sensible and evident and proceeds to those which are separate from matter, as is evident below in Book VII (1566), whereas the other philosophers wanted to apply intelligible and abstract principles to sensible things. Hence, because he did not intend to establish the truth in the same order as that followed by the other philosophers, and from whose views these problems arise, he therefore decided to give first all the problems in a separate section, and afterwards to solve these problems in their proper order.

345. Averroes gives another reason [for Aristotle’s procedure]. He says that Aristotle proceeds in this way because of the relationship of this science to logic, which will be touched on below in Book IV (588); and therefore he made dialectical discussion a principal part of this science.

LESSON 2

Questions Concerning the Method of This Science

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181. The first problem concerns the things about which we raised questions in our introductory statements, i.e., whether it belongs to one science or to many to speculate about the causes.

182. And there is also the problem whether it belongs to this science to know only the principles of substance, or also the principles on which all sciences base their demonstrations, e.g., whether it is possible to affirm and deny one and the same thing at the same time or not; and other such principles. And if this science deals with substance, there is the question whether one science deals with all substances, or many sciences. And if many, whether all are cognate, or whether some should be called wisdom and others something else.

183. It is also necessary to inquire whether sensible substances alone must be said to exist, or whether there are other substances in addition to these; and whether they are unique, or whether there are many classes of substances, aswas claimed by those who created the Forms and made the objects of mathematics an intermediate class between these Forms and sensible substances. As we have said, then, it is necessary to examine these questions.

184. There is also the problem whether this speculation has to do with substances alone or also with the proper accidents of substances. And we must inquire about sameness and difference, likeness and unlikeness, contrariety, priority and posteriority, and all other such things which the dialecticians attempt to treat (basing their investigations only on probabilities); for to them too it belongs to theorize about all these things. Furthermore, we must investigate all those essential accidents of these same things; and not only what each one of them is, but also whether there is one contrary for each one.

COMMENTARY

Q. 1: Does this science make use of all four causes?

346. Following out his announced plan, the Philosopher begins to set down the problems which are encountered in establishing the truth; and he divides this into two parts. In the first, he gives these problems; and in the second (369), he gives the reasons for these problems, by indicating the arguments on either side of the question (“Therefore let us discuss”).

Now it was stated in Book II (335) that it is necessary to seek the method of a science before seeking the science itself. Therefore he gives, first, the problems which pertain to this science’s method of investigation. Second (355), he gives the problems which pertain to the first principles with which this science deals, as has been stated in Book I (36) (“And we must inquire”).

Now a science is concerned with two things, as was said in Book II (336), namely, a study of the causes by which it demonstrates and the things with which it deals. Hence in regard to the first point he does two things. First, he presents a problem concerning the investigation of causes. Second (347), he presents several problems concerning the things with which this science deals (“And there is also the problem”)

He says, then, that the first problem is one which we proposed in the issues raised at the end of Book II (336), which is, so to speak, the prologue to the whole of science, i.e., whether a study of the four causes in their four classes belongs to one science or to many different sciences And this is to ask whether it belongs to one science, and especially to this science, to demonstrate by means of all the causes, or rather whether some sciences demonstrate by one cause and some by another.

Q. 2: Does it consider both principles of substance and principles of knowledge?

347. And there is also the problem (182).

Here he raises problems about the things which this science considers. First, he inquires about the things which this science considers about substances; and second (350), about substances themselves (“It is also necessary”). In regard to the first he raises three questions. For if it is supposed, from what was said in Book I (35), that this science considers first principles, the first question here will be whether it belongs to this science to know only the first principles of substances, or also to consider the first principles of demonstration, by means of which all sciences demonstrate. For example, should this science consider whether it is possible to affirm and deny one and the same thing at the same time or not? And the same thing applies to the other first and self-evident principles of demonstration.

Q. 3: Is its subject all substances, or do different sciences consider different substances?

348. And if this science considers substance as the primary kind of being, the second question is whether there is one science which considers all substances, or whether there are many sciences which consider different substances. For it seems that there should be many sciences which consider many substances.

Q. 4: Is it distinct from other sciences?

349. And if there are many sciences which consider many substances, the third question is whether all are “cognate,” i.e., whether all belong to one class, as geometry and arithmetic belong to the class of mathematical science, or whether they do not, but some to the class of wisdom and some to another class, for example, to the class of natural philosophy or to that of mathematical science. For according to the first point of view it seems that they do not belong to one class, since material and immaterial substances are not known by the same method.

Q. 5. Are there immaterial substances, and of what kind?

350. It is also necessary (183).

Here he adds to the number of questions about substance; and he does this by raising two questions. The first question is whether sensible substances alone must be held to exist, as the philosophers of nature claimed, or whether there are in addition to sensible substances other immaterial and intelligible substances, as Plato claimed.

351. And if there are some substances separate from sensible things, the second question is whether “they are unique,” i.e., whether they belong only to one class, or whether there are many classes of such substances. For certain men, understanding that there is a twofold abstraction, namely, of the universal from the particular, and of the mathematical form from sensible matter, held that each class is self-subsistent. Thus they held that there are separate substances which are subsisting abstract universals, and between these and particular sensible substances they placed the objects of mathematics—numbers, continuous quantities, and figures—which they regarded as separate subsisting things. Concerning the questions which have now been raised, then, it is necessary to investigate them below. He does this, first, by arguing both sides of the question, and, second, by determining its truth.

Q. 6: Does this science consider accidents or properties of substance?

352. There is also the problem (184).

Here he asks whether this science’s investigations extend to accidents; and he raises three questions. The first is whether this science, seeing that it is called the philosophy of substance, speculates about substance alone, or whether it also speculates about the proper accidents of substance; for it seems to be the office of the same science to consider a subject and the proper accidents of that subject.

Q. 7: How does it differ from logic in considering these things?

353. The second question is whether this science considers certain things which seem to be proper accidents of being and which belong to all beings, namely, sameness and difference, likeness and unlikeness, contrariety, priority, and posteriority, and all others of this kind which are treated by the dialecticians, who deal with all things. However, they do not examine such things according to necessary premises but according to probable ones. For from one point of view it seems that, since these accidents are common ones, they pertain to first-philosophy; but from another point of view it seems that, since they are considered by the dialecticians, whose office it is to argue from Probabilities, an examination of them does not belong to the consideration of the philosopher, whose office it is to demonstrate.

Q. 8: Does it consider how these accidents are inter-related?

354. And since certain proper attributes naturally flow from these common accidents of being, the third question is whether it is the function of the philosopher to consider in regard to the common accidents only their quiddity or also their properties; for example, whether there is one opposite for each one.

LESSON 3

Questions Concerning the Things with Which This Science Deals

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185. And we must inquire whether it is genera that constitute the principles and elements of things, or the parts into which each existing thing is divided. And if it is genera, whether it is those that are predicated of individuals first or last. And we must also inquire whether animal or man is a principle, and exists more truly than the singular.

186. But most of all it is necessary to investigate and treat the question whether besides matter there is any cause in the proper sense or not; and whether it is separable or not; and whether it is numerically one or many. And we must ask whether there is anything besides the synolon (and by synolon I mean matter when something is predicated of it), or nothing; or whether this is true of some things but not of others, [and what these things are].

187. Further, we must inquire whether the principles of things are limited in number or in kind, both those in the intelligible structures of things and those in the underlying subject; and whether the principles of corruptible and of incorruptible things are the same or different; and whether they are all incorruptible, or whether those of corruptible things are corruptible. And the most difficult question of all, and the most disputed one, is whether unity and being are not something different from the substances of existing things, as the Pythagoreans and Plato say, or whether this is not the case, but the underlying subject is something different,” as Empedocles holds of love, another thinker of fire, another of water, and another of air. And we must inquire whether the principles of things are universals or singular things.

188. Again, we must inquire whether they exist potentially or actually. And also whether they are principles of things in some other way or in reference to motion; for these questions present great difficulty.

189. And in addition to these questions we must inquire whether numbers or lengths and points are somehow substances or not. And if they are substances, whether they are separate from sensible things or are found in them. Concerning all these matters it is not only difficult to discover what is true, but it is not even easy to state the problems well.

COMMENTARY

Q. 9: How are substances to be analysed, into elements or into genera?

355. Having raised questions pertaining to the method of investigation which this science uses, the Philosopher now raises questions pertaining to the things which this science considers. And since this science considers first principles, as has been stated in Book I (35), he therefore raises here questions pertaining to the principles of things.

Now both the Forms and the objects of mathematics were held to be the first principles of things. Therefore, first, he raises questions concerning the Forms; and second (366), concerning the objects of mathematics (“And in addition to these”).

In regard to the first he does two things. First, he asks what things are principles; and second (361), what sort of beings they are (“Further, we must inquire”).

And since separate universals were held to be the principles of things, he asks, first, whether universals are the principles of things; and second (357), whether separate entities are the principles of things (“But most of all”).

Concerning the first he asks two questions. The first is whether genera constitute the principles and elements of things, or the ultimate parts into which each individual thing is dissolved. This question arises because an element is that of which a thing is first composed and into which it is ultimately dissolved. Now we find a twofold mode of composition and dissolution. One has to do with the intelligible constitution, in which species are resolved into genera, and according to this mode genera seem to be the principles and elements of things, as Plato claimed. The other mode of composition and dissolution has to do with the real order; for example, natural bodies are composed of fire, air, water and earth, and are dissolved into these. It was for this reason that the natural philosophers claimed that the elements constitute the first principles of things.

356. And assuming that genera are the principles of things, the second question is whether the principles of things are to be identified with the universals which are predicated of individual things, i.e., the lowest species, which he calls genera after the usage of the Platonists, because the lowest species contain under themselves many individuals just as genera contain many species; or whether it is rather the first and most common genera that constitute principles, for example, which of the two is more of a principle, animal or man; for man is a principle according to the Platonists, and is more real than any singular man. Now this problem arises because of two divisions which reason makes. One of these is that whereby we divide genera into species, and the other is that whereby we resolve species into genera. For it seems that whatever is the last term in a process of division is always the first principle and element in a process of composition.

Q. 10: Is there an immaterial principle? Is it one or many?

357. But most of all (186).

Here he inquires whether separate entities are the principles of things; and he raises four questions. For since the first philosophers of nature posited only a material cause, the first question is whether besides matter there is anything else that is a cause in the proper sense or not.

358. And granted that there is some other cause besides matter, the second question is whether it is separable from matter, as Plato held, or as Pythagoras held.

359. And if there is something separable from matter, the third question is whether it is a single thing, as Anaxagoras claimed, or many, as Plato and Aristotle himself claimed.

Q. 11: Is individuality distinct from the specific form?

360. The fourth question is whether there is anything “besides the synolon,” i.e., the concrete whole, or nothing; or whether there is something in certain cases and not in others; and what kind of things they are in those cases in which there is something else, and what kind of things they are in those in which there is not. And he explains what a synolon or concrete whole is; i.e., it is matter when something is predicated of it. Now in order to understand this we must note that Plato claimed that man and horse, and universals which are predicated in this way, are certain separate Forms; and that man is predicated of Socrates or Plato by reason of the fact that sensible matter participates in a separate Form. Hence Socrates or Plato is called a synolon or concrete whole, because each is constituted as a result of matter participating in a separate form. And each is, as it were, a kind of predicate of matter. Hence the Philosopher asks here whether the whatness of the individual thing is something else in addition to the individual thing itself, or not; or also whether it is something rise in the case of some things and not in that of others. The Philosopher will answer this question in Book VII (7356).

361. Further, we must inquire (187).

Here he raises questions about the way in which principles exist. And since being is divided by the one and many, and by act and potency, he asks, first, whether these principles are one or many; and second (365), whether they are actual or potential (“Again, we must inquire”). In regard to the first he asks four questions:

Q. 12 The first is whether the principles of things are limited in number or in kind; as we say, for example, that there are three principles of nature. Now the statement that they are limited in number can mean that the principle of nature is numerically a single form and a single matter and privation. And the statement that they are limited in kind can mean that there are many material principles which have in common the specific nature of material principle, and so on for the rest. And since some of the philosophers, such as the Platonists, attributed formal causes to things, while others, such as the ancient natural philosophers, attributed only material causes to things, he adds that this question is applicable both “in the intelligible structures,” i.e., in formal causes, “and in the underlying subject,” i.e., in material causes.

Q. 13: Are the principles of corruptible and incorruptible things the same or different?

362. (2) The second question is whether the principles of corruptible and of incorruptible things are the same or different. And if they are different, whether all are incorruptible, or whether the principles of corruptible things are corruptible and those of incorruptible things are incorruptible.

Q. 14: Are “one” and “being” the same as or distinct from specific natures?

363. (3) The third question is whether unity and being signify the very substance of things and not something added to the substance of things, as the Pythagoreans and Platonists claimed; or whether they do not signify the substance of things, but something else is the subject of unity and being, for example, fire or air or something else of this kind, as the ancient philosophers of nature held. Now he says that this question is the most difficult and most puzzling one, because on this question depends the entire thought of Plato and Pythagoras, who held that numbers are the substance of things.

364. The fourth question is whether the principles of things are “somehow universals or are in some sense singular things,” i.e., whether those things which are held to be principles have the character of a principle in the sense of a universal intelligible nature, or according as each is a particular and singular thing.

365. Again, we must inquire (188).

Here he asks whether these principles exist potentially or actually. This question seems to refer especially to material principles; for it can be a matter of dispute whether the first material principle is some actual body, such as fire or air, as the ancient philosophers of nature held, or something which is only potential, as Plato held. And since motion is the actualization of something in potency, and is, in a sense, midway between potentiality and actuality, he therefore adds another question: whether the principles of things are causes only in reference to motion, as the philosophers of nature posited only principles of motion, either material or efficient, or also whether they are principles which act in some other way than by motion, as Plato claimed that sensible things are caused by immaterial entities by a certain participation in these. Futhermore, he says that these questions have been raised because they present the greatest difficulty, as is clear from the manner in which the philosophers have disagreed about them.

366. And in addition to these (189).

Here he raises questions concerning the objects of mathematics, which are posited as the principles of things. He raises two questions. The first is whether numbers, lengths, figures and points are somehow substances, as the Pythagoreans or Platonists held, or whether they are not, as the philosophers of nature held.

367. And if they are substances, the second question is whether they are separate from sensible things, as the Platonists held, or exist in sensible things, as the Pythagoreans held.

368. Now these questions are raised as problems which must be debated and settled below, because in these matters it is not only difficult to discover the truth, but it is not even easy to debate the matter adequately by finding probable arguments for either side of the question.

LESSON 4

Are All the Classes of Causes Studied by One Science or by Many?

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190. Therefore let us discuss first the problem about which we first spoke (181): whether it is the office of one science or of many to study all the classes of causes.

191. For how will it be the office of one science to come to principles since they are not contrary?

192. Furthermore, in the case of many existing things not all the principles are present. For how can a principle of motion be present in all immobile things, or how can the nature of the good be found there? For everything which is a good in itself and by reason of its own nature is an end and thus a cause, because it is for its sake that other things come to be and exist. Further, the end and that for the sake of which something comes to be is the terminus of some action. But all actions involve motion. Therefore it would be impossible for this principle to be present in immobile things, nor could there be an autoagathon, i.e., a good in itself. Hence in mathematics too nothing is proved by means of this cause, nor is there any demonstration on the grounds that a thing is better or worse. Nor does anyone make any mention at all of anything of this kind. And for this reason some of the Sophists, for example, Aristippus, disregarded these. For in the other arts, even in the servile ones, such as building and cobbling, all things are to be explained on the grounds that they are better or worse; but the mathematical sciences give no account of things which are good or evil.

193. But on the other hand, if there are many sciences of the causes, and different sciences for different principles, which of these must be said to be the one that is being sought, or which one of those who have them is best informed about the subject under investigation?

194. For it is possible for the same thing to have all the classes of causes; for example, in the case of a house the source of motion is the art and the builder, the reason for which is its function, the matter is earth and stones, and the form is the plan.

195. Therefore, from the things which were established a little while ago (14-26:C 36-51) as to which of the sciences one should call wisdom, there is reason for calling every one of them such. For inasmuch as wisdom takes precedence and is a more authoritative science, and one which the others, like slaves, have no right to contradict, then the science which deals with the end and the good is such a science, because other things are for the sake of this.

196. But insofar as wisdom has been defined (24:C 49) as the science of first causes and of what is most knowable, such a science will be about substance. For while a subject may be known in many ways, we say that he who knows what a thing is in its being knows it better than he who knows it in its nonbeing. And in the former case one knows better than another, especially he who knows what a thing is, and not how great it is or of what sort it is or anything that it is naturally disposed to do or to undergo. Further, in the case of other things too we think that we know every single thing, and those of which there are demonstrations, when we know what each is, for example, what squaring is, because it is finding the middle term. The same thing is true in other cases.

197. But with regard to processes of generation and actions and every change, we think that we know these perfectly when we know the principle of motion. But this differs from and is opposite to the end of motion. And for this reason it seems to be the province of a different science to speculate about each one of these causes.

COMMENTARY

Q 1: Can one science consider many causes?

369. Having raised the questions which cause difficulty in this science, Aristotle begins here to treat them dialectically. This is divided into three parts. In the first part, he treats the questions which pertain to the method of investigation of this science. In the second (403), he treats the questions which pertain to substances (“Furthermore, there is”). In the third (423), he treats the questions which pertain to the principles of substances (“Concerning the principles”).

In regard to the first he does three things. First, he argues dialectically about this science’s method of investigation, with reference to the causes by means of which it demonstrates; second (387), with reference to the first principles of demonstration (“But insofar”); and third (393), with reference to substances themselves (“And there is the problem”).

In regard to the first he does two things. First, he takes up again the question about which he plans to argue dialectically, concluding from the order in which the questions have been listed that it is necessary first to debate those issues which were stated first in the list of questions, namely, whether it is the function of one science or of many to investigate all the classes of causes; so that in this way the order of argument corresponds to the order in which the questions have been raised.

370. For how will it be (191).

Second, he gives the arguments relating to this question; and in regard to this he does three things. First (191), he gives an argument for the purpose of showing that it is not the office of a single science to consider all the classes of causes. Second (193:C 376), assuming that it belongs to different sciences to consider the different classes of causes, he asks which class of cause it is that is investigated by first philosophy. He argues on both sides of this question (“But on the other hand”). Third (197:C 386), he draws from this second dispute the conclusion of the first arguments (“But-with regard to”).

In regard to the first (191) he gives two arguments. He says that since it belongs to one science to consider contraries, how will it belong to one science to consider principles since they are not contrary? This view, if it is considered superficially, seems to be of no importance; for it appears to follow from the destruction of the antecedent, as if one were to argue thus: if principles are contraries, they belong to one science; therefore, if they are not contraries, they do not belong to one science.

371. Therefore it can be said that in these disputes the Philosopher not only uses probable arguments but sometimes also uses sophistical ones when he gives arguments introduced by others. But it does not seem reasonable that in such an important matter so great a Philosopher would have introduced an argument which is both trifling and insignificant. Hence a different explanation must be given, namely, that if one rightly considers the nature of the various things which belong to the same science, some belong to a single science-insofar as they are different, but others insofar as they are reduced to some one thing. Hence many other different things are found to belong to one science insofar as they are reduced to one thing, for example, to one whole, one cause, or one subject. But contraries and all opposites belong essentially to one science by reason of the fact that one is the means of knowing the other. And from this comes this probable proposition that all different things which are contraries belong to one science. Therefore, if principles were different and were not contraries, it would follow that they would not belong to one science.

372. Furthermore, in the case of (192).

Here he gives the second argument, which runs thus. In the case of different things which belong to one science, whatever science considers one also considers another. This is evident in the case of contraries, which are different and belong essentially to one science without being reduced to some other unity. But not every science which considers one cause considers all causes. Therefore the study of all the causes does not belong to a single science.

373. He proves the minor premise thus: Different sciences deal with different beings, and there are many beings to which all the causes cannot be assigned. He makes this dear, first, with regard to that cause which is called the source of motion; for it does not seem that there can be a principle of motion in immobile things. Now certain immobile things are posited, especially by the Platonists, who claim that numbers and substances are separate entities. Hence, if any science considers these, it cannot consider the cause which is the source of motion.

374. Second, he shows that the same thing is true of the final cause, which has the character of good. For it does not seem that the character of goodness can be found in immobile things, if it is conceded that everything which is good in itself and by reason of its own nature is an end. And it is a cause in the sense that all things come to be and exist because of it and for its sake. However, he says “everything which is good in itself and by reason of its own nature” in order to exclude the useful good, which is not predicated of the end but of the means to the end. Hence those things which are said to be good only in the sense that they are useful for something else arc not good in themselves and by reason of their own nature. For example, a bitter potion is not good in itself but only insofar as it is directed to the end, health, which is a good in itself. But an end, or that for the sake of which something comes to be, seems to be the terminus of an action. But all actions seem to involve motion. Therefore it seems to follow that this principle, i.e., the final cause, which has the character of goodness, cannot exist in immobile things. Further, since those things which exist of themselves apart from matter must be immobile, it therefore does not seem possible that “an autoagathon,” i.e., a good-in-itself, exists, as Plato held. For he called all immaterial and unparticipated things entities which exist of themselves, just as he called the Idea of man, man-in-himself, as though not something participated in matter. Hence he also called the good-in-itself that which is its own goodness unparticipated, namely, the first principle of all things.

375. Moreover, with a view to strengthening this argument he introduces an example. For, from the fact that there cannot be an end in the case of immobile things, it seems to follow that in the mathematical sciences, which abstract from matter and motion, nothing is proved by means of this cause, as in the science of nature, which deals with mobile things, something is proved by means of the notion of good. For example, we may give as the reason why man has hands that by them he is more capable of executing the things which reason conceives. But in the mathematical sciences no demonstration is made in this way, that something is so because it is better for it to be so, or worse if it were not so; as if one were to say, for example, that the angle in a semi-circle is a right angle because it is better that it should be so than be acute or obtuse. And because there can be, perhaps, another way of demonstrating by means of the final cause (for example, if one were to say that, if an, end is to be, then what exists for the sake of an end must first be), he therefore adds that in the mathematical sciences no one makes any mention at all of any of those things which pertain to the good or to the final cause. And for this reason certain sophists, as Aristippus, who belonged to the Epicurean school, completely disregarded any demonstrations which employ final causes, considering them to be worthless in view of the fact that in the servile or mechanical arts, for example, in the “art of building,” i.e., in carpentry, and in that of “cobbling,” all things are explained on the grounds that something is better or worse; whereas in the mathematical sciences, which are the noblest and most certain of the sciences, no mention is made of things good and evil.

376. But on the other hand (193).

Here he interjects another question. First, he states this question, which has two parts. The first part of the question is this. If different causes are considered by many sciences, so that a different science considers a different cause, then which of these sciences should be called the one “that is being sought,” i.e., first philosophy? Is it the one which considers the formal cause, or the one which considers the final cause, or the one which considers one of the other causes? The second part of the question is this: If there are some things which have many causes, which one of those who consider those causes knows that subject best?

377. For it is possible (194).

He clarifies the second part of the question by the fact that one and the same thing is found to have every type of cause. For example, in the case of a house the source of motion is the art and the builder; the reason, for which, or the final cause of the house, “is its function,” i.e., its use, which is habitation; its material cause is the earth, from which the walls and floor are made; and its specifying or formal cause is the plan of the house, which the architect, after first conceiving it in his mind, gives to matter.

378. Therefore from the things (195)

Here he takes up again the question as to which of the aforesaid sciences we can call wisdom on the basis of the points previously established about wisdom at the beginning of this work (14:C 36), namely, whether it is the science which considers the formal cause, or the one which considers the final cause, or the one which considers one of the other causes. And he gives in order arguments relating to each of the three causes, saying that there seems to be some reason why “every oxie of the sciences,” i.e., any one which proceeds by means of any cause at all, should be called by the name of wisdom. First, he speaks of that science which proceeds by means of the final cause. For it was stated at the beginning of this work that this science, which is called wisdom, is the most authoritative one, and the one which directs others as subordinates. Therefore, inasmuch as wisdom “takes precedence,” i.e., is prior in the order of dignity and more influential in its authoritative direction of the other sciences (because it is not right that the others should contradict it but they should take their principles from it as its servants), it seems that that science “which deals with the end and the good,” i.e., the one which proceeds by means of the final cause, is worthy of the name of wisdom. And this is true because everything else exists for the sake of the end, so that in a sense the end is the cause of all the other causes. Thus the science which proceeds by means of the final cause is the most important one. This is indicated by the fact that those arts which are concerned with ends are more important than and prior to the other arts; for example, the art of navigation is more important than and prior to the art of ship-building. Hence, if wisdom is pre-eminent and regulative of the other sciences, it seems that it proceeds especially by means of the final cause.

379. But insofar as wisdom (196).

Here he introduces the arguments relating to the formal cause. For it was said in the prologue of this work (26:C 51) that wisdom is concerned with first causes and with whatever is most knowable and most certain. And according to this it seems to be concerned with “substance,” i.e., it proceeds by means of the formal cause. For among the different ways of knowing things, we say that he who knows that something exists, knows more perfectly than he who knows that it does not exist. Hence in the Posterior Analytics the Philosopher proves that an affirmative demonstration is preferable to a negative demonstration. And among those who know something affirmatively, we say that one knows more perfectly than another. But we say that he knows more perfectly than any of the others who knows what a thing is, and not he who knows how great it is, or what it is like, or what it can do or undergo. Therefore, to know a thing itself in the most perfect way absolutely is to know what it is, and this is to know its substance. But even in knowing other things, for example, a thing’s properties, we say that we know best every single thing about which there are demonstrations when we also know the whatness of their accidents and properties; because whatness is found not only in substance but also in accidents.

380. He gives the example of squaring, i.e., squaring a surface of equally distant sides which is not square but which we say we square when we find a square equal to it. But since every rectangular surface of equally distant sides is contained by the two lines which contain the right angle, so that the total surface is simply the product of the multiplication of one of these lines by the other, then we find a square equal to this surface when we find a line which is the proportional mean between these two lines. For example, if line A is to line B as line B is to line C, the square of line B is equal to the surface contained by C and A, as is proved in Book VI of Euclid’s Elements.

381. This becomes quite evident in the case of numbers. For 6 is the proportional mean between 9 and 4; for 9 is related to 6 in the ratio of 11/2 to 1, and so also is 6 to 4. Now the square of 6 is 36, which is also produced by multiplying 4 by 9; for 4 x 9 = 36. And it is similar in all other cases.

382. But with regard to processes (197)

Here he gives an argument pertaining to the cause of motion. For in processes of generation and actions and in every change we see that we may say that we know a thing when we know its principle of motion, and that motion is nothing else than the actuality of something mobile produced by a mover, as is stated in the Physics, Book III. He omits the material cause, however, because that cause is a principle of knowing in the most imperfect way; for the act of knowing is not caused by what is potential but by what is actual, as is stated below in Book IX (805:C 1894)

383. Then after having given those arguments which pertain to the second question, he introduces an argument which is based on the same reasons as were given above (191:C 370 ff.) in reference to the first question, namely, that it is the office of a different science to consider all these causes by reason of the fact that in different subject-matters different causes seem to have the principal role, for example, the source of motion in mobile things, the quiddity in demonstrable things, and the end in things which are directed to an end.

384. However, we do not find that Aristotle explicitly solves this question later on, though his solution can be ascertained from the things which he establishes below in different places. For in Book IV (533) he establishes that this science considers being as being, and therefore that it also belongs to it, and not to the philosophy of nature, to consider first substances; for there are other substances besides mobile ones.

But every substance is either a being of itself, granted that it is only a form; or it is a being by its form, granted that it is composed of matter and form. Hence inasmuch as this science considers being, it considers the formal cause before all the rest. But the first substances are not known by us in such a way that we know what they are, as can be understood in some way from the things established in Book IX (1904); and thus in our knowledge of them the formal cause has no place.

But even though they are immobile in themselves, they are nevertheless the cause of motion in other things after the manner of an end. Hence inasmuch as this science considers first substances, it belongs to it especially to consider the final cause and also in a way the efficient cause.

But to consider the material cause in itself does not belong to it in any way, because matter is not properly a cause of being but of some definite kind of being, namely, mobile substance. However, such causes belong to the consideration of the particular sciences, unless perhaps they are considered by this science inasmuch as they are contained under being; for it extends its analysis to all things in this way.

385. Now when these things are seen it is easy to answer the arguments which have been raised. For, first, nothing prevents the different causes in this science from belonging to a single existing thing, even though they are not contraries, because they are reducible to one thing—being in general—as has been stated (384).

And in a similar way, even though not every science considers all of the causes, still nothing prevents one science from being able to consider all of the causes or several of them insofar as they are reducible to some one thing. But to be more specific, it must be said that in the case of immobile things nothing prevents the source of motion and the end or good from being investigated. By immobile things I mean here those which are still causes of motion, as the first substances. However, in the case of those things which are neither moved cause motion there is no investigation of the source of motion, or of the end in the sense of the end of motion, although an end can be considered as the goal of some operation which does not involve motion. For if there are held to be intellectual substances which do not cause motion, as the Platonists claimed, still insofar as they have an intellect and will it is necessary to hold that they have an end and a good which is the object of their will. However, the objects of mathematics neither are moved nor cause motion nor have a will. Hence in their case the good is not considered under the name of good and end, although in them we do consider what is good, namely, their being and what they are. Hence the statement that the good is not found in the objects of mathematics is false, as he proves below in Book IX (1888) .

386. The reply to the second question is already clear; for a study of the three causes, about which he argued dialectically, belongs to this science.

LESSON 5

Are the Principles of Demonstration and Substance Considered by One Science or by Many?

ARISTOTLE’S TEXT Chapter 2: 996b 26-997a 15

198. But with respect to the principles of demonstration there is also the problem whether they are studied by one science or by many. By principles of demonstration I mean the common axioms from which fall] demonstrations proceed, e.g., “everything must either be affirmed or denied,” and “it is impossible both to be and not to be at the same time,” and all other such propositions. Is there one science which deals with these principles and with substance or are there different sciences? And, if not one, which of the two must be called the one that is now being sought?

199. Now it would be unreasonable that these things should be studied by one science; for why should the study of these be proper to geometry rather than to any other science? In a similar way, then, if this study pertains to any science but cannot pertain to all, an understanding of these principles is no more proper to the science which studies substance than it is to any other science.

200. But at the same time how will there be a science of these principles? For we already know what each one of them is; and therefore the other arts use them as something known. However, if there is demonstration of them, there will have to be some subject-genus, and some of the principles will have to be properties and others axioms. For there cannot be demonstration of all things, since demonstration must proceed from something, and be about something, and [be demonstration] of certain things. It follows, then, that there is a single genus of demonstrable things; for all demonstrative sciences use axioms.

201. But on the other hand, if the science which considers substance differs from the one which considers axioms, which of these sciences is the more important and prior one? For axioms are most universal and are the principles of all things. And if it does not belong to the philosopher to establish the truth and falsity [of these principles], to what other person will it belong?

COMMENTARY

Q. 2: Is the science of substance also that of first principles?

387. Having debated the first question which had to do with the study of causes, Aristotle’s intention here is to argue dialectically about the science which is concerned with the study of the first principles of demonstration; and in regard to this he does three things. First, he raises the question. Second (388), he argues one side of the question. Third (391), he argues on the other side of the question.

Accordingly, he states, first, the problem relating to the first principles of demonstration, namely, whether the study of these principles belongs to one science or to many. Further, he explains what the principles of demonstration are, saying that they are the common conceptions of all men on which all demonstrations are based, i.e., inasmuch as the particular principles of the proper demonstrated conclusions derive their stability from these common principles. And he gives an example of first principles, especially this one, that everything must either be affirmed or denied [of some subject]. Another principle which he mentions is that it is impossible for the same thing both to be and not to be at the same time. Hence the question arises whether these principles and similar ones pertain to one science or to many. And if they pertain to one science, whether they pertain to the science which investigates substance or to another science. And if to another science, then which of these must be called wisdom, or first philosophy, which we now seek.

Here he argues one side of the question with a view to showing that it is not the office of one science to consider all first principles, i.e. the first principles of demonstration and substance. He gives two arguments, of which the first runs thus: since all sciences employ these principles of demonstration, there seems to be no reason why the study of them should pertain to one science rather than to another; nor again does it seem reasonable that they should be studied by all sciences, because then it would follow that the same thing would be treated in different sciences; but that would be superfluous. Hence it seems to follow that no science considers these principles. Therefore, for the very same reason that it does not belong to any of the other sciences to give us a knowledge of such principles, for this reason too it follows that it does not belong to the science whose function it is to consider substance.

389. But at the same time (200).

Here he gives the second argument, which runs thus. In the sciences there are two methods by which knowledge is acquired. One is that by which the whatness of each thing is known, and the other is that by which knowledge is acquired through demonstration. But it does not belong to any science to give us a knowledge of the principles of demonstration by means of the first method, because such knowledge of principles is assumed to be prior to all the sciences. For "we already know" what each one of them is, i.e., we know from the very beginning what these principles signify, and by knowing this the principles themselves are immediately known. And since such knowledge of principles belongs to us immediately, he concludes that all the arts and sciences which are concerned with other kinds of cognitions make use of these pinciples as things naturally known by us.

390. But it is proved in the same way that a knowledge of these principles is not presented to us in any science by means of demonstration, because if there were demonstration of them, then three principles would have to be considered, namely, some subjectgenus, its properties and the axioms. In order to clarify this he adds that there cannot be demonstration of all things; for subjects are not demonstrated but properties are demonstrated of subjects. Concerning subjects, however, it is necessary to know beforehand whether they exist and what they are, as is stated in Book I of the Posterior Analytics. The reason is that demonstration must proceed from certain things as principles, which are the axioms, and be about something, which is the subject, and [be demonstration] of certain things, which are properties. Now according to this it is immediately evident of one of these three, i.e., the axioms, that they are not demonstrated, otherwise there would have to be certain axioms prior to the axioms; but this is impossible. Therefore, having dismissed this method of procedure as obvious, he proceeds to consider the subject-genus. For since one science has one subject-genus, then that science which would demonstrate axioms would have one subject-genus. Thus there would have to be one subjectgenus for all demonstrative sciences, because all demonstrative sciences use axioms of this kind.

391. But on the other hand (201).

Here he argues the other side of the question. For if it is said that there is one science which deals with sucn principles, and another which deals with substance, the problem will remain as to which of these sciences is the more important and prior one. For, on the one hand, since the axioms are most universal and are the principles of everything that is treated in any of the sciences, it seems that the science which deals with such principles is the most important one. Yet, on the other hand, since substance is the first and principal kind of being, it is evident that first-philosophy is the science of substance. And if it is not the same science which deals with substance and with the axioms, it will not be easy to state to which of the other sciences it belongs to consider the truth and falsity of these axioms, i.e., if it does not belong to first philosophy, which considers substance.

392. The Philosopher answers this question in Book IV (590) of this work. He says that the study of the axioms belongs chiefly to the [first] philosopher inasmuch as it pertains to him to consider being in general, to which first principles of this kind essentially belong, as is most evident in the case of the very first principle: it is impossible for the same thing both to be and not to be [at the same time]. Hence all the particular sciences use principles of this kind just as they use being itself, although it is the first philosopher who is chiefly concerned with this. And the first argument is solved in this way.

But the second argument is solved thus: the [first] philosopher does not consider principles of this kind in such a way as to make them known by defining them or by demonstrating them in an absolute sense, but by refutation, i.e., by arguing disputatively against those who deny them, as is stated in Book IV (608).

LESSON 6

Are All Substances Considered by One Science or by Many? Does the Science of Substance Consider the Essential Accidents of Substance?

ARISTOTLE’S TEXT Chapter 2: 997a 15-997a 34

202. And there is the problem whether there is one science which deals with all substances, or many sciences.

203. If there is not one science, then with what substances must this science deal?

204. But it is unreasonable that there should be one science of all substances; for then one science would demonstrate all essential accidents, i.e., if it is true that every demonstrative science speculates about the essential accidents of some subject by proceeding from common opinions. Hence it is the office of the same science to study the essential accidents of the same subject-genus by proceeding from the same opinions. For it belongs to one science to consider that something is so, and it belongs to one science to consider the principles from which demonstrations proceed, whether to the same science or to a different one. Hence it belongs to one science to consider accidents, whether they are studied by these sciences or by one derived from them.

205. Further, there is the problem whether this science is concerned only with substances or also with accidents. I mean, for example, that if a solid is a kind of substance, and also lines and surfaces, the question arises whether it is the function of the same science to know these and also the accidents of each class of things about which the mathematical sciences make demonstrations, or whether it is the concern of a different science.

206. For if it is the concern of the same science, a particular one will undertake these demonstrations and this will be the one which deals with substance. However, there does not seem to be any demonstration of the quiddity.

207. But if it is the concern of a different science, which science will it be that studies the accidents of substances? For to solve this is very difficult.

COMMENTARY

Qq. 3 & 6: Does the science of substance consider all substances as well as accidents?

393. Having debated the questions the third question, which pertains to which pertain to the scope of investigation of this science, he now treats the study of substances and accidents. This is divided into two parts inasmuch as he discusses two questions on this point. The second (403) begins where he says, “Furthermore, there is.”

In regard to the first he does three things. First, he raises the question whether there is one science that considers all substances, or whether there are many sciences that consider different substances.

394. If there is not (203).

Second, he argues the first side of the question with a view to showing that there is one science of all substances. For if there were not one science of all substances, then apparently it would be impossible to designate the substance which this science considers, because substance as substance is the primary kind of being. Hence it does not seem that one substance rather than another belongs to the consideration of the basic science.

395. but it is unreasonable (204).

Third, he argues the other side of the question, saying that it is unreasonable to hold that there is one science of all substances. For it would follow that there would be one demonstrative science of all essential accidents. And this is true because every science which demonstrates certain accidents speculates about the essential accidents of some particular subject, and it does this from certain common conceptions. Therefore, since a demonstrative science considers the accidents only of some particular subject, it follows that the study of some subject-genus belongs to the same science that is concerned with the study of the essential accidents of that genus and vice versa, so long as demonstrations proceed from the same principles.

396. But sometimes it happens to be the function of some science to demonstrate from certain principles that a thing is so, and sometimes it happens to be the function of some science to demonstrate the principles from which it was demonstrated that a thing is so, sometimes to the same science and sometimes to a different one.

An example of its being the function of the same science is seen in the case of geometry, which demonstrates that a triangle has three angles equal to two right angles in virtue of the principle that the exterior angle of a triangle is equal to the two interior angles opposite to it; for to demonstrate this belongs to geometry alone. And an example of its being the function of a different science is seen in the case of music, which proves that a tone is not divided into two equal semitones by reason of the fact that a ratio of 9 to 8, which is superparticular, cannot be divided into two equal parts. But to prove this does not pertain to the musician but to the arithmetician. It is evident, then, that sometimes sciences differ because their principles differ, so long as one science demonstrates the principles of another science by means of certain higher principles.

397. But if it is assumed that the principles are identical, sciences could not differ so long as the accidents are the same and the subject-genus is the same, as if one science considered the subject and another its accidents. Hence it follows that that science which considers a substance will also consider its accidents, so that if there are many sciences which consider substances, there will be many sciences which consider accidents. But if there is only one science which considers substances, there will be only one science which considers accidents. But this is impossible, because it would then follow that there would be only one science, since there is no science which does not demonstrate the accidents of some subject. Therefore it is not the function of one science to consider all substances.

398. This is treated in Book IV (546) of this work, where it is shown that the examination of substance as substance belongs to the first science, whose province it is to consider being as being; and thus it considers all substances according to the common aspect of substance. Therefore it belongs to this science to consider the common accidents of substance. But it belongs to the particular sciences, which deal with particular substances, to consider the particular accidents of substances, just as it belongs to the science of nature to consider the accidents of mobile substance. However, among substances there is also a hierarchy, for the first substances are immaterial ones. Hence the study of them belongs properly to first-philosophy, just as the philosophy of nature would be first philosophy if there were no other substances prior to mobile corporeal substances, as is stated below in Book VI (1170).

399. Further, there is the problem (205).

Here he raises another question regarding the study of substance and accidents. Concerning this he does three things. First, he raises the question whether the investigation of this science is concerned with substance alone or also with the attributes that are accidents of substances. For example, if we say that lines, surfaces and solids are substances of some sort, as some held, the question arises whether it belongs to the same science to consider such things and also their proper accidents, which are demonstrated in the mathematical sciences, or whether it belongs to another science.

400. For if it is the concern (206).

Second, he argues one side of the question. For if it belongs to the same science to consider accidents and substances, then, since a science which considers accidents demonstrates accidents, it follows that a science which considers substance demonstrates substances. But this is impossible; for the definition of a substance, which expresses the quiddity’ is indemonstrable. Hence it will belong to the same science to consider substances and accidents.

401. But if it is the concern (207).

Third, he argues the other side of the question: if different sciences consider substance and accident, it will not be possible to state which science it is that speculates about the accidents of substance; because the science which would do this would consider both, although this would seem to pertain to all sciences; for every science considers the essential accidents of its subject, as has been explained.

402. The Philosopher answers this question in Book IV (570) of this work, saying that it is also the office of that science which is concerned with the study of substance and being to consider the proper accidents of substance and being. Yet it does not follow that it would consider each in the same way, i.e., by demonstrating substance as it demonstrates accidents, but by defining substance and by demonstrating that accidents either belong to or do not belong to it, as is explained more fully at the end of Book IX (1895) of this work.

LESSON 7

Are There Certain Other Substances Separate from Sensible Things? Criticism of the Different Opinions Regarding the Objects of Mathematics

ARISTOTLE’S TEXT Chapters 2 & 3: 997a 34-998a 21

208. Furthermore, there is the problem whether sensible substances alone must be said to exist, or others besides these. And whether there is one genus or many genera of substances, as is held by those who speak of the Forms and the intermediate entities with which they say the mathematical sciences deal.

209. Now the way in which we say that the Forms are both causes and substances in themselves has been treated in our first discussions concerning all of these things (69).

210. But while they involve difficulty in many respects, it is no less absurd to say that there are certain other natures besides those which exist in the heavens, and that these are the same as sensible things, except that the former are eternal whereas the latter are corruptible. For they [i.e., the Platonists] say nothing more or less than that there is a man-in-himself and horse-in-itself and health-in-itself, which differ in no respect [from their sensible counterparts]; in which they act like those who say that there are gods and that they are of human form. For just as the latter made nothing else than eternal men, in a similar way the former make the Forms nothing else than eternal sensible things.

211. Furthermore, if anyone holds that there are intermediate entities in addition to the Forms and sensible substances, he will face many problems. For evidently there will be, in like manner, lines in addition to ordinary sensible lines, and the same will be true of other classes of things. Therefore, since astronomy is one of these [mathematical sciences], there will be a heaven in addition to the one we perceive, and a sun and moon, and the same will be true of the other celestial bodies. And how are we to accept these things? For it is unreasonable that a heaven should be immobile, but that it should be mobile is altogether impossible. The same thing is true of the things with which the science of perspective is concerned, and of harmonics in mathematics, because for the same reasons it is also impossible that these should exist apart from sensible things. For if there are intermediate sensible objects and senses, evidently there will be intermediate animals between animals-in-themselves and those which are corruptible.

212. Again, one might also raise the question as to what things these sciences must investigate. For if geometry, which is the art of measuring the earth, differs from geodesy, which is the art of dividing the earth, only in this respect that the latter deals with things which are perceptible by the senses, whereas the former deals with those which are imperceptible, evidently there will be, in addition to the science of medicine, another science midway between the science of medicine itself and this particular science of medicine; and this will be true of the other sciences. But how is this possible? For then there will be certain healthy things besides those which are sensible and besides health-in-itself.

213. Similarly, neither does it seem that geodesy is concerned with continuous quantities which are sensible and corruptible. For in this case it would be destroyed when they are destroyed.

214. Nor again will astronomy deal with sensible continuous quantities, or with this heaven. For the lines we perceive by the senses are not such as those of which geometry speaks, since none of the things perceived by the senses are straight or round in this way. For the circle does not touch the rule at a point, but in the way in which Protagoras spoke in arguing against the geometricians. Neither are the motions or revolutions of the heavens similar to the things of which geometry speaks, nor do points have the same nature as the stars.

215. However, there are also some who say that these intermediate entities, which are below the Forms and above sensible things, do not exist outside of sensible things but in them. But to enumerate all the impossible consequences which follow from this theory would require too long a discussion. It will be sufficient to propose the following consideration.

216. It is unreasonable that this should be so only in the case of such things, but evidently it is also possible for the Forms to exist in sensible things, because both of these views depend on the same argument.

217. Furthermore, it would be necessary for two solids to occupy the same place.

218. And [the objects of mathematics] would not be immobile since they exist in sensible things, which are moved.

219. Moreover, on the whole, to what end would anyone hold that they exist but exist in sensible things? For the same absurdities as those described will apply to these suppositions. For there will be a heaven in addition to the one which we perceive, although it will not be separate but in the same place; but this is quite impossible.

Chapter 3

In these matters, then, it is difficult to see how it is possible to have any positive truth.

COMMENTARY

Q. 5: Are there substances besides sensible ones?

403. Having debated the questions which pertain to the scope of this science, the Philosopher now treats dialectically the questions which pertain to the substances themselves with which this science is chiefly concerned. In regard to this he does three things. First, he raises the questions. Second (406), he indicates the source from which arguments can be drawn in support of one side of the question (“Now the way”). Third (407), he argues on the other side of the question (“But while they involve”).

In regard to the first part of this division he raises two questions. The first question is whether sensible substances alone are found in the universe, as certain of the ancient philosophers of nature claimed, or whether besides sensible substances there are certain others, as the Platonists claimed.

404. And assuming that besides sensible substances there are certain others, the second question is whether these substances belong to one genus, or whether there are many genera of substances. For he considers both opinions. For some thinkers held, that in addition to sensible substances there are only separate Forms, i.e., an immaterial man-in-himself and horse-in itself and so on for the other classes of things, whereas others held that there are certain other substances midway between the Forms and sensible things, namely, the objects of mathematics, with which they said the mathematical sciences deal.

405. The reason for this view is that they posited on the part of the intellect a twofold process of abstracting things: one whereby the intellect is said to abstract the universal from the particular, and according to this mode of abstraction they posited separate Forms, which subsist of themselves; and another [whereby the intellect is said to abstract] from sensible matter certain forms in whose definition sensible matter is not given, for example, the abstraction of circle from brass. And according to this mode of abstraction they posited separate objects of mathematics, which they said are midway between the Forms and sensible substances, because they have something in common with both: with the Forms inasmuch as they are separate from sensible matter, and with sensible substances inasmuch as many of them are found in one class, as many circles and many lines.

406. Now the way in which (209).

Then he shows how it is possible to argue one side of the question, saying that it has been stated “in our first discussions,” i.e., in Book I (69:C 151), how the Forms are held to be both the causes of sensible things and substances which subsist of themselves. Hence, from the things which have been said there in presenting the views of Plato, arguments can be drawn in support of the affirmative side of the question.

407. But while they involve (210).

Here he advances reasons for the negative side. He does this, first (210), for the purpose of showing that the Forms are not separate from sensible things; and, second (211:C 410), for the purpose of showing that the objects of mathematics are not separate (“Furthermore, if anyone”). Now above in Book I (103:C 208) he gave many arguments against those who posited separate Forms; and, therefore, passing over those arguments, he gives the line of reasoning which seems most effective. He says (210) that while the position of those who posit separate Forms contains many difficulties, the position of those which is now given is no less absurd than any of the others, i.e., that someone should say that there are certain natures in addition to the sensible ones which are contained beneath the heavens. For the heavens constitute the limit of sensible bodies, as is proved in Book I of The Heavens and the World. But those who posited the Forms did not place them below the heavens or outside of it, as is stated in Book III of the Physics. Hence, in accordance with this he says that they posited certain other natures in addition to those which exist in the heavens. And they said that these opposite natures are the same as these sensible things both in kind and in their intelligible constitution, and that they exist in these sensible things; or rather they said that those natures are the Forms of these sensible things. For example, they said that a separate man constitutes the humanity of this particular man who is perceived by the senses, and that a man who is perceived by the senses is a man by participating in that separate man. Yet they held that these differ in this respect, that those immaterial natures are eternal, whereas these sensible natures are corruptible.

408. That they hold those natures to be the same as these sensible things is clear from the fact that, just as man, horse, and health are found among sensible things, in a similar way they posited among these natures “a man-inhimself,” i.e., one lacking sensible matter; and they did the same with regard to horse and health. Moreover, they claimed that nothing else existed in the class of separate substances except [the counterpart of] what existed materially in the sensible world. This position seems to be similar to that of those who held that the gods are of human form, which was the position of the Epicureans, as Tully states in The Nature of the Gods. For just as those who held that the gods are of human form did nothing else than make men eternal in nature, in a similar way those who claimed that there are Forms do nothing else than hold that there are eternal sensible things, such as horse, ox, and the like.

409. But it is altogether absurd that what is naturally corruptible should be specifically the same as what is naturally incorruptible; for it is rather the opposite that is true, namely, that corruptible and incorruptible things differ in kind to the greatest degree, as is said below in Book X (895:C 2137) Of this work. Yet it can happen that what is naturally corruptible is kept in being perpetually by Divine power.

410. Furthermore, if anyone (211).

Then he argues against those who claimed that the objects of mathematics are midway between the Forms and sensible things. First (211:C 410), he argues against those who held that the objects of mathematics are intermediate entities and are separate from sensible things; and, second (215:C 417), against those who held that the objects of mathematics exist but exist in sensible things (“However, there are”).

In regard to the first he does two things. First, he introduces arguments against the first position. Second (214:C 416), he argues in support of this position (“Nor again”).

He brings up three arguments against the first position. The first argument is this: just as there is a mathematical science about the line, in a similar way there are certain mathematical sciences about other subjects. If, then, there are certain lines in addition to the sensible ones with which geometry deals, by the same token there will be, in all other classes of things with which the other mathematical sciences deal, certain things in addition to those perceived by the senses. But he shows that it is impossible to hold this with regard to two of the mathematical sciences.

411. He does this, first, in the case of astronomy, which is one of the mathematical sciences and which has as its subject the heavens and the celestial bodies. Hence, according to what has been said, it follows that there is another heaven besides the one perceived by the senses, and similarly another sun and another moon, and so on for the other celestial bodies. But this is incredible, because that other heaven would be either mobile or immobile. If it were immobile, this would seem to be unreasonable, since we see that it is natural for the heavens to be always in motion. Hence the astronomer also makes some study of the motions of the heavens. But to say that a heaven should be both separate and mobile is impossible, because nothing separate from matter can be mobile.

412. Then he shows that the same view is unacceptable in the case of other mathematical sciences, for example, in that of perspective, which considers visible lines, and “in the case of harmonics,” i.e., in that of music, which studies the ratios of audible sounds. Now it is impossible that there should be intermediate entities between the Forms and sensible things; because, if these sensible things—sounds and visible lines—were intermediate entities, it would also follow that there are intermediate senses. And since senses exist only in an animal, it would follow that there are also intermediate animals between the Form animal, and corruptible animals; but this is altogether absurd.

413. Again, one might (212).

The second argument [which he uses against the possibility of the objects of mathematics being an intermediate class of entities separate from sensible things] is as follows. If in those classes of things with which the mathematical sciences deal there are three classes of things—sensible substances, Forms and intermediate entities, then since the intelligible structure of all sensible things and of all Forms seems to be the same, it appears to follow that there are intermediate entities between any sensible things at all and their Forms. Hence there remains the problem as to what classes of things are included in the scope of the mathematical sciences. For if a mathematical science such as geometry differs from geodesy, which is the science of sensible measurements, only in this respect that geodesy deals with sensible measurements, whereas geometry deals with intermediate things which are not sensible, there will be in addition to all the sciences which consider sensible things certain [other] mathematical sciences which deal with these intermediate entities. For example, if the science of medicine deals with certain sensible bodies, there will be in addition to the science of medicine, and any like science, some other science which will be intermediate between the science of medicine which deals with sensible bodies and the science of medicine which deals with the Forms. But this is impossible; for since medicine is about “healthy things,” i.e., things which are conducive to health, then it will also follow, if there is an intermediate science of medicine, that there will be intermediate health-giving things in addition to the health-giving things perceived by the senses and absolute health, i.e., health-in-itself, which is the Form of health separate from matter. But this is clearly false. Hence it follows that these mathematical sciences do not deal with certain things which are intermediate between sensible things and the separate Forms.

414. Similarly, neither (213).

Then he gives the third argument [against the possibility of the objects of mathematics being an intermediate class]; and in this argument one of the points in the foregoing position is destroyed, namely, that there would be a science of continuous quantities which are perceptible; and thus, if there were another science of continuous quantities, it would follow from this that there would be intermediate continuous quantities. Hence he says that it is not true that geodesy is a science of perceptible continuous quantities, because such continuous quantities are corruptible. It would follow, then, that geodesy is concerned with corruptible continuous quantities. But it seems that a science is destroyed when the things with which it deals are destroyed; for when Socrates is not sitting, our present knowledge that he is sitting will not be true. Therefore it would follow that geodesy, or geosophics as other readings say, is destroyed when sensible continuous quantities are destroyed; but this is contrary to the character of science, which is necessary and incorruptible.

415. Yet this argument can be brought in on the opposite side of the question inasmuch as one may say that he intends to prove by this argument that there are no sciences of sensible things, so that all sciences must be concerned with either the intermediate entities or the Forms.

416. Nor again will (214)

Here he argues in support of this position, as follows: it belongs to the very notion of science that it should be concerned with what is true. But this would not be the case unless it were about things as they are. Therefore the things about which there are sciences must be the same in themselves as they are shown to be in the sciences. But perceptible lines are not such as geometry says they are. He proves this on the grounds that geometry demonstrates that a circle touches “the rule,” i.e., a straight line, only at a point, as is shown in Book III of Euclid’s Elements. But this is found to be true of a circle and a line in the case of sensible things. Protagoras used this argument when he destroyed the certainties of the sciences against the geometricians. Similarly, the movements and revolutions of the heavens are not such as the astronomers describe them; for it seems to be contrary to nature to explain the movements of the celestial bodies by means of eccentrics and epicycles and other different movements which the astronomers describe in the heavens. Similarly, neither are the quantities of the celestial bodies such as the astronomers describe them to be, for they use stars as points even though they are still bodies having extension. It seems, then, that geometry does not deal with perceptible continuous quantities, and that astronomy does not deal with the heaven which we perceive. Hence it remains that these sciences are concerned with certain other things, which arc intermediate.

417. However, there are (215)

Here he argues against another position. First, he states the point at issue. Second (216:C 418), he brings in arguments germane to his purpose (“It is unreasonable”).

Accordingly, he says, first (215), that some thinkers posit natures midway between the Forms and sensible things, yet they do not say that these natures are separate from sensible things but exist in sensible things themselves. This is clear regarding the opinion of those who held that there are certain self-subsistent dimensions which penetrate all sensible bodies, which some thinkers identify with the place of sensible bodies, as is stated in Book IV of the Physics and is disproved there. Hence he says here that to pursue all the absurd consequences of this position is a major undertaking, but that it is now sufficient to touch on some points briefly.

418. It is unreasonable (216).

Then he brings four arguments against this position. The first runs as follows. It seems to be for the same reason that in addition to sensible things the Forms and objects of mathematics are posited, because both are held by reason of abstraction on the part of the intellect. If, then, the objects of mathematics are held to exist in sensible things, it is fitting that not only they but also the Forms themselves should exist there. But this is contrary to the opinion of those who posit [the existence of] the Forms. For they hold that these are separate, and not that they exist anywhere in particular.

419. Furthermore, it would be (217)

Here he gives the second argument, which runs thus: if the objects of mathematics differ from sensible things yet exist in them, since a body is an object of mathematics, it follows that a mathematical body exists simultaneously with a sensible body in the same subject. Therefore “two solids,” i.e., two bodies, will exist in the same place. This is impossible not only for two sensible bodies but also for a sensible body and a mathematical one, because each has dimensions, by reason of which two bodies are prevented from being in the same place.

420. Furthermore, if anyone (211).

Then he argues against those who claimed that the objects of mathematics are midway between the Forms and sensible things. First (211:C 410), he argues against those who held that the objects of mathematics are intermediate entities and are separate from sensible things; and, second (215:C 417), against those who held that the objects of mathematics exist but exist in sensible things (“However, there are”).

In regard to the first he does two things. First, he introduces arguments against the first position. Second (214:C 416), he argues in support of this position (“Nor again”).

He brings up three arguments against the first position. The first argument is this: just as there is a mathematical science about the line, in a similar way there are certain mathematical sciences about other subjects. If, then, there are certain lines in addition to the sensible ones with which geometry deals, by the same token there will be, in all other classes of things with which the other mathematical sciences deal, certain things in addition to those perceived by the senses. But he shows that it is impossible to hold this with regard to two of the mathematical sciences.

421. He does this, first, in the case of astronomy, which is one of the mathematical sciences and which has as its subject the heavens and the celestial bodies. Hence, according to what has been said, it follows that there is another heaven besides the one perceived by the senses, and similarly another sun and another moon, and so on for the other celestial bodies. But this is incredible, because that other heaven would be either mobile or immobile. If it were immobile, this would seem to be unreasonable, since we see that it is natural for the heavens to be always in motion. Hence the astronomer also makes some study of the motions of the heavens. But to say that a

422. Now the Philosopher treats these questions below in Books XII, XIII and XIV of this work, where he shows that there are neither separate mathematical substances nor Forms. The reasoning which moved those who posited the objects of mathematics and the Forms, which are derived from an abstraction of the intellect, is given at the beginning of Book XIII. For nothing prevents a thing which has some particular attribute from being considered by the intellect without its being viewed under this aspect and yet be considered truly, just as a white man can be considered without white being considered. Thus the intellect can consider sensible things not inasmuch as they are mobile and material but inasmuch as they are substances or continuous quantities; and this is to abstract the thing known from matter and motion. However, so far as the thing known is concerned, the intellect does not abstract in such a way that it understands continuous quantities and forms to exist without matter and motion. For then it would follow either that the intellect of the one abstracting is false, or that the things which the intellect abstracts are separate in reality.

LESSON 8

Are Genera Principles of Things? And If So, Does This Apply to The Most Universal Genera or to Those Nearest to Individuals?

ARISTOTLE’S TEXT Chapter 3: 998a 20-999a 23

220. Concerning the principles of things there is the problem whether genera must be regarded as the elements and principles of things, or rather the first things of which each thing is composed inasmuch as they are intrinsic.

221. just as the elements and principles of a word seem to be those things of which all words are first composed, but not word in common. And just as we say that the elements of diagrams are those things whose demonstrations are found in the demonstrations of others, either of all or of most of them.

222. Furthermore, those who say that the elements of bodies are many, and those who say that they are one, call the things of which bodies are composed and constituted their principles, as Empedocles says that fire and water and those things which are included with these are the elements from which existing things derive their being; but he does not speak of them as the genera of existing things.

223. And again if anyone wished to speculate about the nature of other things, in finding out in regard to each (a bed, for example) of what parts it is made and how it is put together, he will come to know its nature. And according to these arguments genera are not the principles of existing things.

224. But if we know each thing through definitions, and genera are the principles of definitions, genera must be the principles of the things defined.

225. And if in order to acquire scientific knowledge of existing things it is necessary to acquire scientific knowledge of their species, according to which they are said to be beings, then genera are the principles of species.

226. Moreover, some of those who say that the elements of existing things are the one or being or the great and small, seem to use these as genera.

227. But it is not possible to speak of principles in both ways; for the meaning of substance is one. Therefore a definition by means of genera will differ from one which gives the intrinsic constituents.

228. Again, if genera are the principles of things in the fullest sense, there is the question whether the first genera must be thought to be principles, or those which are lowest and are predicated of individual things. For this also raises a problem.

229. For if universals are the principles of things to a greater degree, evidently these must be the highest genera, because it is most properly these which are predicated of all existing things. Therefore there will be as many principles of existing things as there are first genera. Hence being and unity will be principles and substances, for it is these especially which are predicated of all existing things.

It is impossible, however, that unity or being should be a single genus of existing things; for it is necessary both that the differences of each genus exist and that each be one. But it is impossible either that species be predicated of the differences of their own genera, or that a genus be so predicated independently of its species. If, then, unity or being is a genus, no difference will be one and a being. But if unity and being are not genera, neither will they be principles, supposing that genera are principles.

230. Further, those things which are intermediate and are taken along with differences will be genera down to individuals. But some seem to be such, whereas others do not. Again, differences are principles to a greater degree than genera; and if they are principles, principles will be infinite in number, so to speak. And [this will appear] in another way also if one holds that the first genus is a principle.

231. But, on the other hand, if unity is a specific principle to a greater degree, and unity is indivisible, and everything indivisible is such either in quantity or in species, and what is indivisible in species is prior, and genera are divisible into species, then it will be rather the lowest predicate which is one. For man is not the genus of particular men.

232. Further, in the case of those things to which prior and subsequent apply, it is not possible in their case that there should be something which exists apart from them. For example, if the number two is the first of numbers, there will not be any number apart from the species of numbers; nor, likewise, any figure apart from the species of figures. But if the genera of these things do not [exist apart from the species], then in the case of other things the teaching will be that there are genera apart from the species; for of these things there seem especially to be genera. But among individual things one is not prior and another subsequent.

233. Further, where one thing is better and another worse, that which is better is always prior; so that there will be no genus of these things. From these considerations, then, it seems that it is the terms predicated of individuals, rather than genera, which are principles.

234. But again it is not easy to state how one must conceive these to be the principles of things..For a principle or cause must be distinct from the things of which it is the principle or cause, and must be able to exist apart from them. But why should one think that anything such as this exists apart from singular things, except that it is predicated universally and of all things? But if this is the reason, then the more universal things are, the more they must be held to be principles. Hence the first genera will be principles of things.

COMMENTARY

Q. 9: What is the difference between genera and elements?

423. Having debated the questions which were raised about substances, the Philosopher now treats dialectically the questions which were raised about principles. This is divided into two parts. In the first he discusses the questions which asked what the principles of things are; and in the second (456), the questions which asked what kind of things the principles are (“Again, there is the problem”).

In the first part of this division he discusses two questions: first, whether universals are the principles of things; and second (443), whether any principles are separate from matter (“But there is a problem”).

In regard to the first he discusses two questions, of which the first is whether genera are the principles of things. The second (431) asks which genera these are, whether the first genera or the others (“Again, if genera”).

In regard to the first he does two things: first, he raises the question; and second (424), he treats it dialectically (“Just as the elements”).

The first question has to do with the principles of things: whether it is necessary to accept or believe that those genera which are predicated of many things are the elements and principles of things, or rather that those parts of which every single thing is composed must be called the elements and principles of things. But he adds two conditions, one of which is “inasmuch as they are intrinsic,” which is given in order to distinguish these parts from a contrary and a privation. For white is said to come from black, or the non-white, although these are not intrinsic to white. Hence they are not its elements. The other condition is what he calls “the first things,” which is given in order to distinguish them from secondary components. For the bodies of animals are composed of flesh and nerves, which exist within the animal; yet these are not called the elements of animals, because they are not the first things of which an animal is composed, but rather fire, air, water and earth, from which flesh and nerves derive their being.

424. Just as the elements (221).

Here he treats this question dialectically; and in regard to this he does three things. First, he shows that the first things of which anything is composed are its principles and elements. Second (224:C 427), he argues the opposite side of the question (“But if we know”). Third (227:C 430), he rejects one answer by which it could be said that both of these [i.e., genera and constituent parts] are the principles and elements of things (“But it is not”).

In regard to the first he gives three arguments. The first of these proceeds from natural phenomena, in which he makes his thesis evident by two examples. The first example which he gives if that of a word, whose principle and element is not said to be the common term word but rather the first constituents of which all words are composed, which are called letters. He gives as a second example, diagrams, i.e., the demonstrative descriptions of geometrical figures. For the elements of these diagrams are not said to be the common term diagram but rather those theorems whose demonstrations are found in the demonstrations of other geometrical theorems, either of all or of most of them, because the other demonstrations proceed from the supposition of the first demonstrations. Hence the book of Euclid is called The Book of Elements, because the first theorems of geometry, from which the other demonstrations proceed, are demonstrated therein.

425. Furthermore, those who (222).

Here he gives the second argument which also employs certain examples drawn from nature. He says that those who hold that the elements of bodies are either one or many, say that the principles and elements of bodies are those things of which bodies are composed and made up as intrinsic constituents. Thus Empedocles says~ that the elements of natural bodies are fire and water and other things of this kind, which along with these he calls the elements of things; and natural bodies are constituted of these first things inasmuch as they are intrinsic. Moreover, they [i.e., the philosophers of nature] held that in addition to these two principles there are four others—air, earth, strife and friendship—as was stated in Book I (50:C 104). But neither Empedocles nor the other philosophers of nature said that the genera of things are the principles and elements of these natural bodies.

426. And again if anyone (223).

Here he gives the third argument, which involves things made by art. He says that if someone wished to “speculate about their nature,” i.e., about the definition which indicates the essence of other bodies than natural ones, namely, of bodies made by human art, for example, if one wished to know a bed, it would be necessary to consider of what parts it is made and how they are put together; and in this way he would know the nature of a bed. And after this he concludes that genera are not the principles of existing things.

427. But if we know (224).

Here he argues the other side of the question. He gives three arguments, the first of which is as follows. Each thing is known through its definition. Therefore, if a principle of being is the same as a principle of knowing, it seems that anything which is a principle of definition is also a principle of the thing defined. But genera are principles of definitions, because definitions are first composed of them. Hence genera are the principles of the things defined.

428. And if in order to (225)

Here he gives the second argument, which runs thus. Scientific knowledge of each thing is acquired by knowing the species from which it gets its being, for Socrates can be known only by understanding that he is man. But genera are principles of species, because the species of things are composed of genera and differences. Therefore genera are the principles of existing things.

429. Moreover, some of those (226).

Here he gives a third argument, which is based on the authority of the Platonists, who held that the one and being are the principles of things, and also the great and small, which are used as genera. Therefore genera are the principles of things.

430. But it is not possible (227)

Here he excludes one answer which would say that both of these are principles. He says that it is impossible to say that both of these are “principles,” i.e., both the elements, or the parts of which something is composed, and genera. He proves this by the following argument. Of each thing there is one definite concept which exposes its substance, just as there is also one substance of each thing. But the definitive concept which involves genera is not the same as the one which involves the parts of which a thing is composed. Hence it cannot be true that each definition indicates a thing’s substance. But the definitive concept which indicates a thing’s substance cannot be taken from its principles. Therefore it is impossible that both genera and the parts of which things are composed should be simultaneously and being cannot be genera of all the principles of things.

431. Again, if genera (228).

Then he treats the second question dialectically. First, he raises the question; and second (432), he brings up arguments relative to this question (“For if universals”).

Accordingly, he says that if we hold that genera are the principles of things in the fullest sense which of these genera should be considered to be the principles of things to a greater degree? Must we consider those “genera” which are first in number, namely, the most common, or also the lowest genera, which are proximately predicated of the individual, i.e., the lowest species. For this is open to question, as is clear from what follows.

432. For if universals (229).

Here he argues about the question which was proposed; and in regard to this he does three things. First, he introduces arguments to show that the first genera cannot be principles. Second (231:C 436), he introduces arguments to show that the last species should rather be called the principles of things (“But, on the other hand”). Third (234:C 441), he debates the proposed question (“But again it is”).

In regard to the first (229) he gives three arguments, of which the first runs thus: if genera are principles to the extent that they are more universal, then those which are most universal, i.e., those which are predicated of all things, must be the first genera and the principles of things in the highest degree. Hence there will be as many principles of things as there are most common genera of this kind. But the most common of all genera are unity and being, which are predicated of all things. Therefore unity and being will be the principles and substances of all things. But this is impossible, because unity and being cannot be genera of all things. For, since unity and being are most universal, if they were principles of genera, it would follow that genera would not be the principles of things. Hence the position which maintains that the most common genera are principles is an impossible one, because from it there follows the opposite of what was held, namely, that genera are not principles.

433. That being and unity cannot be genera he proves by this argument: since a difference added to a genus constitutes a species, a species cannot be predicated of a difference without a genus, or a genus without a species. That it is impossible to predicate a species of a difference is clear for two reasons. First, because a difference applies to more things than a species, as Porphyry says; ‘ and second, because, since a difference is given in the definition of a species, a species can be predicated essentially of a difference only if a difference is understood to be the subject of a species, as number is the subject of evenness in whose definition it is given. This, however, is not the case; but a difference is rather a formal principle of a species. Therefore a species cannot be predicated of a difference except, perhaps, in an incidental way. Similarly too neither can a genus, taken in itself, be predicated of a difference by essential predication. For a genus is not given in the definition of a difference, because a difference does not share in a genus, as is stated in Book IV of The Topics; nor again is a difference given in the definition of a genus. Therefore a genus is not predicated essentially of a difference in any way. Yet it is predicated of that which “has a difference,” i.e., of a species, which actually contains a difference. Hence he says that a species is not predicated of the proper differences of a genus, nor is a genus independently of its species, because a genus is predicated of its differences inasmuch as they inhere in a species. But no difference can be conceived of which unity and being are not predicated, because any difference of any genus is a one and a being, otherwise it could not constitute any one species of being. It is impossible, then, that unity and being should be genera.

434. Further, those things (230)

Then he gives the second argument, which runs thus: if genera are called principles because they are common and predicated of many things, then for a like reason all those things which are principles because they are common and predicated of many will have to be genera. But all things which are intermediate between the first genera and individuals, namely, those which are considered together with some differences, are common predicates of many things. Hence they are both principles and genera. But this is evidently false. For some of them are genera, as subaltern species, whereas others are not, as the lowest species. It is not true, then, that the first or common genera are the principles of things.

435. Further, if the first genera are principles, because they are the principles by which we know species, then differences will be principles to a greater degree, because differences are the formal principles of species; and form or actuality is chiefly the principle of knowing. But it is unfitting that differences should be the principles of things, because in that case there would be an infinite number of principles, so to speak; for the differences of things are infinite, so to speak; not infinite in reality but to us. That they are infinite in number is revealed in two ways: in one way if we consider the multitude of differences in themselves; in another way if we consider the first genus as a first principle, for evidently innumerable differences are contained under it. The first genera, then, are not the principles of things.

436. But on the other hand (231).

Then he shows that the lowest species are principles to a greater degree than genera. He gives three arguments, of which the first runs thus: according to the Platonists it is the one which seems to have “the nature,” 3 or character, of a principle to the greatest degree. Indeed, unity has the character of indivisibility, because a one is merely an undivided being. But a thing is indivisible in two ways, namely, in quantity and in species: in quantity, as the point and unit, and this is a sort of indivisibility opposed to the division of quantity; and in species, as what is not divided into many species. But of these two types of indivisibility the first and more important one is indivisibility in species, just as the species of a thing is prior to its quantity. Therefore that which is indivisible in species is more of a principle because it is indivisible in quantity. And in the division of quantity the genus seems to be more indivisible, because there is one genus of many species; but in the division of species one species is more indivisible. Hence the last term which is predicated of many, which is not a genus of many species, namely, the lowest species, is one to a greater degree in species than a genus; for example, man or any other lowest species is not the genus of particular men. Therefore a species is a principle to a greater degree than a genus.

437. Further, in the case of (232).

Then he gives the second argument, which is based on a certain position of Plato; for at one time Plato held that there is some one thing which is predicated of many things without priority and posteriority, and that this is a separate unity, as man is separate from all men; and at another time he held that there is some one thing which is predicated of many things according to priority and posteriority, and that this is not a separate unity. This is what Aristotle means when he says “in the case of those things to which prior and subsequent apply,” i.e., that when one of the things of which a common term is predicated is prior to another, it is impossible in such cases that there should be anything separate from the many things of which this common term is predicated. For example, if numbers stand in such a sequence that two is the first species of number, no separate Idea of number will be found to exist apart from all species of numbers. And on the same grounds no separate figure will be found to exist apart from all species of figures.

438. The reason for this can be that a common attribute is held to be separate so as to be some first entity in which all other things participate. If, then, this first entity is a one applicable to many in which all other things participate, it is not necessary to hold that there is some separate entity in which all things participate. But all genera seem to be things of this kind, because all types of genera are found to differ insofar as they are more or less perfect, and thus insofar as they are prior and subsequent in nature. Hence, if in those cases in which one thing is prior to another it is impossible to regard anything common as a separate entity, on the supposition that there is a genus apart from species, then “in the case of other things the teaching” will [differ], i.e., there will be another doctrine and rule concerning them, and the foregoing rule will not apply to them. But considering the individuals of one species, it is evident that one of these is not prior and another subsequent in nature but only in time. And thus according to Plato’s teaching a species is separate. Since, then, these common things are principles inasmuch as they are separate, it follows that a species is a principle to a greater degree than a genus.

439. Further, where one thing (233)

Here he gives the third argument, which makes use of the notions “better or worse.” For in all those cases where one thing is better than another, that which is better is always prior in nature. But there cannot be held to be one common genus of those things which exist in this way. Hence there cannot be held to be one separate genus in the case of those things in which one is better and another worse; and thus the conclusion is the same as the above. For this argument is introduced to strengthen the preceding one, so to speak, i.e., with a view to showing that there is priority and posteriority among the species of any genus.

440. And from these three arguments he draws the conclusion in which he is chiefly interested, namely, that the lowest species, which are predicated immediately of individuals, seem to be the principles of things to a greater degree than genera.

441. But again it is not (234).

Here he argues the opposite side of the question, as follows: a principle and a cause are distinct from the things of which they are the principle and cause, and are capable of existing apart from them. And this is true, because nothing is its own cause. He is speaking here of extrinsic principles and causes, which are causes of a thing in its entirety. But the only thing that is held to exist apart from singular things is what is commonly and universally predicated of all things. Therefore the more universal a thing is, the more separate it is, and the more it should be held to be a principle. But the first genera are most universal. Therefore the first genera are the principles of things in the highest degree.

442. Now the solution to these questions is implied in this last argument. For according to this argument genera or species are held to be universal principles inasmuch as they are held to be separate. But the fact that they are not separate and self-subsistent is shown in Book VII (1592) of this work. Hence the Commentator also shows, in Book VIII, that the principles of things are matter and form, to which genus and species bear some likeness. For a genus is derived from matter and difference from form, as will be shown in the same book (720). Hence, since form is more of a principle than matter, species will consequently be principles more than genera. But the objection which is raised against this, on the grounds that genera are the principles of knowing a species and its definitions, is answered in the same way the objection raised about their separateness. For, since a genus is understood separately by the mind without understanding its species, it is a principle of knowing. And in the same way it would be a principle of being, supposing that it had a separate being.

LESSON 9

Do Any Universals Exist Apart from the Singular Things Perceived by the Senses and from Those Which Are Composed of Matter and Form?

ARISTOTLE’S TEXT Chapter 4: 999a 24-999b 20

235. But there is a problem connected with these things, which is the most difficult of all and the most necessary to consider, with which our analysis is now concerned.

236. For if there is nothing apart from singular things, and singular things are infinite in number, how is it possible to acquire scientific knowledge of them? For insofar as there is something that is one and the same, and insofar as there is something universal [which relates to singular things], to that extent we acquire knowledge of them.

237. But if this is necessary, and there must be something apart from singular things, it will be necessary that genera exist apart from singular things, and they will be either the last or the first. But the impossibility of this has already appeared from our discussion.

238. Further, if there is something apart from the concrete whole (which is most disputable), as when something is predicated of matter, if there is such a thing, the problem arises whether it must exist apart from all concrete wholes, or apart from some and not from others, or apart from none.

239. If, then, there is nothing apart from singular things, nothing will be intelligible, but all things will be sensible, and there will be no science of anything, unless one might say that sensory perception is science.

240. Further, neither will anything be eternal or immobile; for all sensible things perish and are subject to motion.

241. But if there is nothing eternal, neither can there be generation; for there must be something which has come to be and something from which it comes to be; and the last of these must be ungenerated, since the process of generation must have a limit, and since it is impossible for anything to come to be from non-being.

242. Further, since generation and motion exist, there must be a terminus; for no motion is infinite but every motion has a terminus. And that which is incapable of coming to be cannot be generated. But that which has come to be must exist as soon as it has come to be.

243. Further, if matter exists because it is ungenerated, it is much more reasonable that substance should exist, since that is what it (matter) eventually comes to be. For if neither the one nor the other exists, nothing at all will exist. But if this is impossible, there must be something besides the synolon, and this is the form or specifying principle.

COMMENTARY

Q. 10: Is there anything separate from sensible things, which is their principle?

443. Having debated the question whether universals are the principles of things, the Philosopher now raises a question about their separability, namely, whether there is anything separate from sensible things as their principle. In regard to this he considers two questions. The first (443) Of these is whether universals are separate from singular things. The second (447) is whether there is any formal [principle] separate from things which are composed of matter and form (“Further, if there is something”).

In regard to the first he does three things. First, he describes the problem. Second (444), he argues one side of the question (“For if there is nothing”). Third (445), he argues the other side of the question (“But if this is”).

Accordingly, this problem arises with regard to a point mentioned in the last argument of the preceding question, namely, whether a universal is separate from singular things, as the aforesaid argument supposed. He describes this problem as “the one with which our analysis is now concerned (235),” i.e., the one which immediately preceded the foregoing argument. And he speaks of it in this way: first, that “it is connected with,” i.e., is a consequence of, the foregoing one, because, as has already been stated, the consideration of the preceding question depends on this. For if universals are not separate, they are not principles; but if they are separate, they are principles. Second, he speaks of this problem as the most difficult of all the problems in this science. This is shown by the fact that the most eminent philosophers have held different opinions about it. For the Platonists held that universals are separate, whereas the other philosophers held the contrary. Third, he says that this problem is one which it is most necessary to consider, because the entire knowledge of substances, both sensi