METAPHYSICS
BOOK IIIMETAPHYSICAL PROBLEMS
CONTENTS
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 are 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?
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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.388. Now it would be (199).
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?
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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 are 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 sensible and immaterial, depends on it.
444. For if there is nothing (236).
Here he advances an argument to show that universals are separate from singular things. For singular things are infinite in number, and what is infinite cannot be known. Hence all singular things can be known only insofar as they are reduced to some kind of unity which is universal. Therefore there is science of singular things only inasmuch as universals are known. But science is only about things which are true and which exist. Therefore universals are things which exist of themselves apart from singular things.
445. But if this is (237)
Then he argues the other side of the question in this way: if it is necessary that universals be something apart from singular things, it is necessary that genera exist apart from singular things, either the first genera or also the last, which are immediately prior to singular things. But this is impossible, as is clear from the preceding discussion. Therefore universals are not separate from singular things.
446. The Philosopher solves this problem in Book VII (659:C 1592) Of this work, where he shows in many ways that universals are not substances which subsist of themselves. Nor is it necessary, as has often been said, that a thing should have the same mode of being in reality that it has when understood by the intellect of a knower. For the intellect knows material things immaterially, and in a similar way it knows universally the natures of things which exist as singulars in reality, i.e., without considering the principles and accidents of individuals.
447. Further, if there is something (238).
Here he raises another question, namely, whether anything is separate from things composed of matter and form; and in regard to this he does two things. First, he raises the question. Second (239:C 448), he proceeds to deal with it (“If, then, there is”).
In regard to the first it should be observed that he first raises the question whether a universal is separate from singular things. Now it happens to be the case that some singular things are composed of matter and form. But not all singular things are so composed, either according to the real state of affairs, since separate substances are particular because existing and operating of themselves, or even according to the opinion of the Platonists, who held that even among separate mathematical entities there are particulars inasmuch as they held that there are many of them in a single species. And while it is open to dispute whether there is anything separate in the case of those things which are not composed of matter and form, as the universal is separate from the particular, the problem is chiefly whether there is anything separate in the case of things which are composed of matter and form. Hence he says that the point which causes most difficulty is whether there is something “apart from the concrete whole,” i.e., apart from the thing composed of matter and form. The reason why a composite thing is called a concrete whole he explains by adding “when something is predicated of matter.” For Plato held that sensible matter participates in separate universals, and that for this reason universals are predicated of singular things. These participations in universal forms by material sensible things constitute a concrete whole inasmuch as a universal form is predicated of matter through some kind of participation. Now in regard to these things he raises a question which has three parts, namely, whether there is anything that exists apart from all things of this kind, or apart from some and not from others, or apart from none.
448. If, then, there is (239)
Here he proceeds to deal with this problem; and concerning it he does two things. First, he argues against the position that nothing can be held to be separate from things composed of matter and form. Second (244:C 454), he argues the other side of the question (“But again if anyone holds this”).
In regard to the first (239) he advances two arguments. First, he argues from the principle that those things which are composed of matter and form are sensible things; and therefore he proposes that those things which are composed of matter and form are singulars. However, singular things are not intelligible but sensible. Therefore, if there is nothing apart from singular things which are composed of matter and form, nothing will be intelligible but all beings will be sensible. But there is science only of things which are intelligible. Therefore it follows that there will be no science of anything, unless one were to say that sensory perception and science are the same, as the ancient philosophers of nature held, as is stated in Book I of The Soul. But both of these conclusions are untenable, namely, that there is no science and that science is sensory perception. Therefore the first position is also untenable, namely, that nothing exists except singular things which are composed of matter and form.
449. Further, neither will anything (240).
Second, he argues on the grounds that things composed of matter and form are mobile. He gives the following argument. All sensible things composed of matter and form perish and are subject to motion. Therefore, if there is nothing apart from beings of this kind, it will follow that nothing is eternal or immobile.
450. But if there is (241).
Here he shows that this conclusion is untenable, namely, that nothing is eternal and immobile. He does this, first, with respect to matter; and second (242:C 451), with respect to form (“Further, since generation”).
Accordingly, he says first (241) that if nothing is eternal, it is impossible for anything to be generated. He proves this as follows. In every process of generation there must be something which comes to be and something from which it comes to be. Therefore, if that from which a thing comes to be is itself generated, it must be generated from something. Hence there must either be an infinite regress in material principles, or the process must stop with some first thing which is a first material principle that is ungenerated, unless it might be said, perhaps, that it is generated from non-being; but this is impossible. Now if the process were to go on to infinity, generation could never be completed, because what is infinite cannot be traversed. Therefore it is necessary to hold either that there is some material principle which is ungenerated, or that it is impossible for any generation to take place.
451. Further, since generation (242).
Here he proves the same thing with respect to the formal cause; and he gives two arguments, the first of which is as follows. Every process of generation and motion must have some terminus. He proves this on the grounds that no motion is infinite, but that each motion has some terminus. This is clear in the case of other motions which are completed in their termini. But it seems that a contrary instance is had in the case of circular motion, which can be perpetual and infinite, as is proved in Book VIII of the Physics. And even though motion is assumed to be eternal, so that the entire continuity of circular motion is infinite insofar as one circular motion follows another, still each circular motion is both complete in its species and finite. That one circular motion should follow another is accidental so far as the specific nature of circular motion is concerned.
452. The things which he said about motion in general he proves specially in regard to generation; for no process of generation can be infinite, because that thing cannot be generated whose process of generation cannot come to an end, since the end of generation is to have been made. That its being made is the terminus of generation is clear from the fact that what has been generated must exist “as soon as it has come to be,” i.e., as soon as its generation is first terminated. Therefore, since the form whereby something is, is the terminus of generation, it must be impossible to have an infinite regress in the case of forms, and there must be some last form of which there is no generation. For the end of every generation is a form, as we have said. Thus it seems that just as the matter from which a thing is generated must itself be ungenerated because it is impossible to have an infinite regress, in a similar way there must be some form which is ungenerated because it is impossible to have an infinite regress in the case of forms.
453. Further, if matter exists (143).
He gives the second argument, which runs thus. If there is some first matter which is ungenerated, it is much more reasonable that there should be some substance, i.e., some form, which is ungenerated, since a thing has being through its form, whereas matter is rather the subject of generation and transmutation. But if neither of these is ungenerated, then absolutely nothing will be ungenerated, since everything which exists has the character of matter or form or is composed of both. But it is impossible that nothing should be ungenerated, as has been proved (24-2:C 452). Therefore it follows that there must be something else “besides the synolon,” or concrete whole, i.e., besides the singular thing which is composed of matter and form. And by something else I mean the form or specifying principle. For matter in itself cannot be separated from singular things, because it has being only by reason of something else. But this seems to be true rather of form, by which things have being.
454. But again if anyone (244).
Here he argues the other side of the question. For if one holds that there is some form separate from singular things which are composed of matter and form, the problem arises in which cases this must be admitted and in which not. For obviously this must not be held to be true in the case of all things, especially in that of those made by art. For it is impossible that there should be a house apart from this sensible house, which is composed of matter and form.
455. Now Aristotle solves this problem partly in Book XII (2488) of this work, where he shows that there are certain substances separate from sensible things and intelligible in themselves; and partly in Book VII (1503), where he shows that the forms or specifying principles of sensible things are not separate from matter. However, it does not follow that no science of sensible things can be had or that science is sensory perception. For it is not necessary that things have in themselves the same mode of being which they have in the intellect of one who knows them. For those things which are material in themselves are known in an immaterial way by the intellect, as has also been stated above (446). And even though a form is not separate from matter, it is not therefore necessary that it should be generated; for it is not forms that are generated but composites, as will be shown in Book VII (1417) of this work. It is clear, then, in what cases it is necessary to posit separate forms and in what not. For the forms of all things which are sensible by nature are not separate from matter, whereas the forms of things which are intelligible by nature are separate from matter. For the separate substances do not have the nature of sensible things, but are of a higher nature and belong to another order of existing things.
LESSON 10
Do All Things Have a Single Substance? Do All Things Have the Same or Different Principles?
ARISTOTLE’S TEXT Chapter 4: 999b 20-1000a
245. Again, there is the problem whether all things, for example, all men, have a single substance.
246. But this is absurd; for not all things whose substance is one are themselves one, but are many and different. But this too is untenable.
247. And at the same time there is the problem how matter becomes each of the many things and a concrete whole.
248. And again one might also raise this problem about principles. For if they are specifically one, there will be nothing that is numerically one. Nor again will unity itself and being be one. And how will there be science unless there is some unity in all things?
249. But, on the other hand, if they are numerically one, each of the principles will also be one, and not as in the case of sensible things, different for different things; for example, if the syllable ba is taken as a species, its principles in every case are specifically the same, for they are numerically different. However, if this is not so, but the things which are the principles of beings are numerically one, there will be nothing else besides the elements. For it makes no difference whether we say “numerically one” or “singular,” because it is in this way that we say each thing is numerically one. But the universal is what exists in these. For example, if the elements of a word were limited in number, there would have to be as many letters as there are elements. Indeed, no two of them would be the same, nor would more than two.
COMMENTARY
Q. 11: Are there one or many forms and principles of things?
456. Having asked what the principles are, and whether some are separate from matter, the Philosopher now asks what the principles are like. First (245:C 456), he asks whether the principles are one or many; second (287:C 519), whether they exist potentially or actually (“And connected with these problems”); and third (290:C 523), whether they are universals or singular things (“And there is also the problem”).
In regard to the first he does two things. First (245:C 456), he inquires how the principles stand with respect to unity; and second (266:C 488), what relationship unity has to the notion of principle (“But the most difficult”).
In regard to the first he does three things. First, he inquires specially about the formal principle: whether all things that are specifically the same have a single form. Second (248:C 46o), he asks the same question of all principles in general (“And again one might”). Third (250:C 466), he asks whether corruptible and incorruptible things have the same principles or different ones (“Again there is the problem”).
In regard to the first he does two things. First, he introduces the problem. Second (246:C 457), he debates it (“But this is absurd”).
The problem (245), then, is whether all things that belong to the same species, for example, all men, have a single substance or form.
457. But this is absurd (246).
Then he advances arguments on one side of the question, to show that all things belonging to one species do not have a single form. He does this by means of two arguments, the first of which runs thus. Things that belong to one species are many and different. Therefore, if all things that belong to one species have a single substance, it follows that those which have a single substance are many and different. But this is unreasonable.
458. And at the same time (247)
Then he gives the second argument, which runs thus. That which is one and undivided in itself is not combined with something divided in order to constitute many things. But it is evident that matter is divided into different singular things. Hence, if substance in the sense of form is one and the same for all things, it will be impossible to explain how each of these singular things is a matter having a substance of the kind that is one and undivided, so that as a singular thing it is a concrete whole having two parts: a matter and a substantial form which is one and undivided.
459. Now he does not argue the other side of the question, because the very same arguments which were advanced above regarding the separateness of universals are applicable in the inquiry which follows it against the arguments just given. For if a separate universal exists, it must be held that things having the same species have a single substance numerically, because a universal is the substance of singular things. Now the truth of this question will be established in Book VII (588:C 1356) of this work, where it is shown that the whatness or essence of a thing is not other than the thing itself, except in an accidental way, as will be explained in that place.
460. And again one might (248).
Here he raises a difficulty concerning the unity of principles in general: whether the principles of things are numerically the same, or only specifically the same and numerically distinct. And in regard to this he does two things. First, he advances arguments to show that they are numerically the same. Second (249:C 464), he argues on the other side of the question (“But, on the other hand”).
In regard to the first (248) he gives three arguments; and he introduces the problem, saying that the same question which was raised about substance can be raised about principles in general, i.e., whether the principles of things are numerically the same.
461. He introduces the first argument to show that they are numerically the same. For things composed of principles merely contain what they receive from these principles. Therefore, if principles are not found to be one numerically but only specifically, the things composed of these principles will not be one numerically but only specifically.
462. The second argument runs thus: unity itself or being itself must be numerically one. And by unity itself or being itself he means unity or being in the abstract. Hence, if the principles of things are not one numerically but only specifically, it will follow that neither unity itself or being itself will subsist of themselves.
463. The third argument is this: science is had of things because there is found to be a one-in-many, as man in common is found in all men; for there is no science of singular things but of the unity [i.e., common attribute] found in them. Moreover, all science or cognition of things which are composed of principles depends on a knowledge of these principles. If, then, principles are not one numerically but only specifically, it will follow that there is no science of beings.
464. But, on the other hand (249).
Here he argues the opposite side of the question in the following fashion. If principles are numerically one so that each of the principles considered in itself is one, it will be impossible to say that the principles of beings exist in the same way as the principles of sensible things. For we see that the principles of different sensible things are numerically different but specifically the same, just as the things of which they are the principles are numerically different but specifically the same. We see, for example, that syllables which are numerically distinct but agree in species have as their principles letters which are the same specifically though not numerically. And if anyone were to say that this is not true of the principles of beings, but that the principles of all beings are the same numerically, it would follow that nothing exists in the world except the elements, because what is numerically one is a singular thing. For what is numerically one we call singular, just as we call universal what is in many. But what is singular is incapable of being multiplied, and is encountered only as a singular. Therefore, if it is held that numerically the same letters are the principles of all syllables, it will fd1low that those letters could never be multiplied so that there could be two of them or more than two. Thus a could not be found in these two different syllables ba or da. And the argument is the same in the case of other letters. Therefore, by the same reasoning, if the principles of all beings are numerically the same, it will follow that there is nothing besides these principles. But this seems to be untenable; because when a principle of anything exists it will not be a principle unless there is something else besides itself.
465. Now this question will be solved in Book XII (2464); for it will be shown there that the principles which things have, namely, matter and form or privation, are not numerically the same for all things but analogically or proportionally the same. But those principles which are separate, i.e., the intellectual substances, of which the highest is God, are each numerically one in themselves. Now that which is one in itself and being is God; and from Him is derived the numerical unity found in all things. And there is science of these, not because they are numerically one in all, but because in our conception there is a one in many. Moreover, the argument which is proposed in support of the opposite side of the question is true in the case of essential principles but not in that of separate ones, which is the class to which the agent and final cause belong. For many things can be produced by one agent or efficient cause, and can be directed to one end.
LESSON 11
Do Corruptible and Incorruptible Things Have the Same or Different Principles?
ARISTOTLE’S TEXT Chapter 4: 1000a 5-1001a 3
250. Again, there is a problem which has been neglected no less by the moderns than by their predecessors: whether the principles of corruptible and incorruptible things are the same or different.
251. For if they are the same, how is it that some things are incorruptible and others corruptible? And what is the cause?
252. The followers of Hesiod and all those who were called theologians paid attention only to what was plausible to themselves and have neglected us. For,’ making the principles of things to be gods or generated from the gods, they say that whatever has not tasted nectar and ambrosia became mortal.
253. And it is clear that they are using these terms in a way known to themselves, but what they have said about the application of these causes is beyond our understanding. For if it is for the sake of pleasure that the gods partake of these things, nectar and ambrosia are not the cause of their being. But if they partake of them to preserve their being, how will the gods be eternal in requiring food?
254. But with regard to those who have philosophized by using fables, it is not worth our while to pay any serious attention to them.
255. However, from those who make assertions by means of demonstration it is necessary to find out, by questioning them, why some of the things which are derived from the same principles are eternal in nature and others are corrupted. But since these philosophers mention no cause, and it is unreasonable that things should be as they say, it is clear that the principles and causes of these things will not be the same.
256. For the explanation which one will consider to say something most to the point is that of Empedocles, who has been subject to the same error. For he posits a certain principle, hate, which is the cause of corruption.
257. Yet even hate would seem to generate everything except the one. For all things except God are derived from this. Hence he says: “From which have blossomed forth all that was and is [and will be]: trees, and men and women, and beasts and flying things, and water-nourished fish, and the long-lived gods.” And apart from these things it is evident that, if hate did not exist in the world, all things would be one, as he says: “For when they have come together, then hate will stand last of all.”
258. For this reason too it turns out that God, who is most happy, is less wise than other beings. For he does not know all the elements, because hate he does not have, and knowledge is of like by like. “For one knows earth by earth, water by water, affection by affection, and hate by mournful hate.”
259. But it is also clear (and this is where our discussion began) that hate no more turns out to be the cause of corruption than of being.
260. Nor, similarly, is love the cause of existence; for in blending things together into a unity it corrupts other things.
261. Moreover, he does not speak of the cause of change itself, except to say that it was naturally disposed to be so.
262. [He says]: “But thus mighty hate was nourished among the members and rose to a position of honor when the time was fulfilled, which being changeable dissolved the bond.” Hence change is a necessity, but he gives no reason for its necessity.
263. Yet he alone speaks expressly to this extent. For he does not make some beings corruptible and others incorruptible, but makes all things corruptible ex. cept the elements. But the problem that has been stated is why some things are corruptible and others are not, supposing that they come from the same principles. To this extent, then, it has been said that the principles of things will not be the same.
264. But if the principles are different, one problem is whether they will be incorruptible or corruptible. For supposing that they are corruptible, it is evident that they must also come from certain things, because all things that are corrupted are dissolved into those elements from which they come. Hence it follows that there are other principles prior to these principles. But this is also unreasonable, whether the process stops or goes on to infinity. Further, how will corruptible things exist if their principles are destroyed? But if they are incorruptible, why will corruptible things come from incorruptible principles, and incorruptible things from others? For this is unreasonable, and is either impossible or requires a great deal of reasoning.
265. Further, no one has attempted to say that these things have different principles, but [all thinkers] say that all things have the same principles. But they admit the first problem, considering it a trifling matter.
COMMENTARY
466. Having investigated in a general way whether all principles belonging to one species are numerically the same, the Philosopher inquires here whether the principles of corruptible and incorruptible things are numerically the same. In regard to this he does three things. First (250:C 466), he raises the question. Second (25I:C 467), he introduces an argument to show that the principles of corruptible and those of incorruptible things are not the same (“For if they are the same”). Third (264:C 483), he introduces arguments to show that they are not different (“But if the principles”).
He says first (250), then, that there is a problem which has been neglected no less by the modern philosophers, who followed Plato, than by the ancient philosophers of nature, who also were puzzled whether the principles of corruptible and incorruptible things are the same or different.
467. For, if they are the same (251).
Here he advances an argument to show that the principles of corruptible and of incorruptible things are not the same. In regard to this he does three things. First (251:C 467), he gives the argument. Second (252:C 468), he criticizes the solution of the proposed argument which the theological poets gave (“The followers of Hesiod”). Third (255:C 472), he criticizes the solution which some philosophers of nature gave (“However, from those who”).
He says first (251), then, that if the principles of corruptible and of incorruptible things are held to be the same, since from the same principles there follow the same effects, it seems that either all things are corruptible or all are incorruptible. Therefore the question arises how some things are corruptible and others incorruptible, and what the reason is.
468. The followers of Hesiod (252)
He criticizes the solution given by the theological poets. First (252:C 468), he gives their solution. Second (253:C 470), he argues against it (“And it is clear that”). Third (254:C 471), he gives the reason why he does not criticize this position with more care (“But with regard to those”).
Concerning the first (252) it Must be noted that there were among the Greeks, or philosophers of nature, certain students of wisdom, such as Orpheus, Hesiod and certain others, who were concerned with the gods and hid the truth about the gods under a cloak of fables, just as Plato hid philosophical truth under mathematics, as Simplicius says in his Commentary on the Categories.’ Therefore he says that the followers of Hesiod, and all those who were called theologians, paid attention to what was convincing to themselves and have neglected us, because the truth which they understood was treated by them in such a way that it could be known only to themselves. For if the truth is obscured by fables, then the truth which underlies these fables can be known only to the one who devised them. Therefore the followers of Hesiod called the first principles of things gods, and said that those among the gods who have not tasted a certain delectable food called nectar or manna became mortal, whereas those who had tasted it became immortal.
469. But some part of the truth could lie hidden under this fable, provided that by nectar or manna is understood the supreme goodness itself of the first principle. For all the sweetness of love and affection is referred to goodness. But every good is derived from a first good. Therefore the meaning of these words could be that some things are incorruptible by reason of an intimate participation in the highest good, as those which participate perfectly in the divine being. But certain things because of their remoteness from the first principle, which is the meaning of not to taste manna and nectar, cannot remain perpetually the same in number but only in species, as the Philosopher says in Book II of Generation. But whether they intended to treat this obscurely or something else, cannot be perceived any more fully from this statement.
470. And it is clear (253).
He argues against the aforesaid position. He says that the meaning which these followers of Hesiod wished to convey by the terms nectar or manna was known to them but not to us. Therefore their explanation of the way in which these causes are meant to solve this question and preserve things from corruption is beyond our understanding. For if these terms are understood in their literal sense, they appear to be inadequate, because the gods who tasted nectar or manna did so either for the sake of pleasure or because these things were necessary for their existence, since these are the reasons why men partake of food. Now if they partook of them for the sake of pleasure, nectar and manna could not be the cause of their existence so as to make them incorruptible, because pleasure is something that follows on being. But if they partook of the aforesaid nourishment because they needed it to exist, they would not be eternal, having repeated need of food. Therefore it seems that gods who are first corruptible, as it were, standing as they do in need of food, are’made incorruptible by means of food. This also seems to be unreasonable, because food does not nourish a thing according to its species unless it is corrupted and passes over into the species of the one nourished. But nothing that is corruptible can be responsible for the incorruptibility of something else.
471. But with regard to those (254).
Here he gives his reason for not investigating this opinion with more care, He says that it is not worth our while to pay any attention to those who have philosophized “by using fables,” i.e., by hiding philosophical truth under fables. For if anyone argues against their statements insofar as they are taken in a literal sense, these statements are ridiculous. But if one wishes to inquire into the truth hidden by these fables, it is not evident. Hence it is understood that Aristotle, in arguing against Plato and other thinkers of this kind who have treated their own doctrines by hiding them under something else, does not argue about the truth which is hidden but about those things which are outwardly expressed.
472. However, from those who make assertions (255).
Then he argues against the answer given by some of the philosophers of nature; and in regard to this he does three things. First (255:C 472), he gives the argument. Second (256:C 473), he gives the answer (“For the explanation”). Third (257:C 474), he criticizes it (“Yet even hate”).
Accordingly, he says, first (255), that, having dismissed those who treated the truth by using fables, it is necessary to seek information about the aforesaid question from those who have treated the truth in a demonstrative way, by asking them why it is that, if all beings are derived from the same principles, some beings are eternal by nature and others are corrupted. And since these men give no reason why this is so, and since it is unreasonable that things should be as they say (that in the case of beings having the same principles some should be corruptible and others eternal), it seems clearly to follow that corruptible and eternal things do not have the same principles or the same causes.
473. For the explanation (256).
Then he gives one solution. He says that the explanation given to the aforesaid question which seems to fit it best is the one which Empedocles gave, although he was subject to the same error as the others, because the explanation which he gave is no more adequate than theirs, as is about to be shown. For he maintained that corruptible and incorruptible things have certain common principles, but that a special principle, hate, causes the corruption of the elements in such a way that the coming together of this cause and another principle produces corruption in the world.
474. Yet even hate (257).
Here he criticizes Empedocles’ argument, and he does this in three ways. First (257:C 474), he does this by showing that the argument which Empedocles gave is not in keeping with his position; second (261:C 478), by showing that it is not adequate (“Moreover, he does not”); third (263:C 481), by showing that it is not to the point (“Yet he alone speaks”).
In regard to the first he does three things. First, he shows that Empedocles’ argument does not agree with his other views about hate; second (258:C 476), that it does not agree with his view about God himself (“For this reason”); and third (26o:C 477), that it does not agree with his view about love (“Nor, similarly”).
Accordingly, he says, first (257), that Empedocles’ position that hate is the cause of corruption is untenable, because according to his position hate also seems to be the cause of the generation of all things except one. For he held that everything else is composed essentially of hate along with the other principles, with the exception of God alone, whom he claimed to be composed of the other principles without hate. Moreover, he called the heavens God, as was stated above in Book I (49:C 101), because Xenophanes, after reflecting upon the whole heaven, said that the one itself is God. And Empedocles, considering the indestructibleness of the heavens, held that the heavens are composed of the four elements and love, but not of strife or hatred. But in the case of other things he said that all those which are or were or will be, come, from hate, such as sprouting trees, and men and women, and beasts (which are terrestial animals), and vultures (which are flying and long-lived animals), and fish (which are nourished in the water), and the long-lived gods. And by the gods he seems to mean either the stars, which he held are sometimes corrupted, although after a long period of time, or the demons, which the Platonists held to be ethereal animals. Or by the gods he also means those beings whom the Epicureans held to be of human form, as was stated above (210:C 408). Therefore, from the fact that all living things except one are generated from hate, it can be said that hate is the cause of generation.
475. And in addition to this there is another reason [why hate can be said to be the cause of generation]; for according to Empedocles’ position it is evident that, if hate did not exist in the world, all things would be one, since hate is the reason why things are distinct, according to Empedocles. Hence he quotes Empedocles’ words to the effect that, when all things come together into a unity, for example, when chaos comes into being, hate will stand last of all, separating and dissolving things. Hence the text of Boethius says: “When it comes together, then chaos knows the ultimate discord.” Thus it is clear that, since the being of the world consists in the distinction of things, hate is the cause of the world’s generation.
476. For this reason (258).
Here he gives a second argument, which pertains to the deity. He says that, since Empedocles would hold that hate is not a constituent of the divine composition, it follows, according to his arguments, that God, who is said by all men to be most happy, and consequently most knowing, is less prudent than all other beings who have knowledge. For according to Empedodes’ position it follows that God does not know the elements because He does not contain hate. Hence He does not know himself. And like knows like according to the opinion of Empedodes, who said that by earth we know earth, by water water, “and by affection,” i.e., love or concord, we know affection, or love or concord. And in a similar way we know “hate by hate,” which is sadness, whether unpleasant or evil, according to the text of Boethius, who says that “by evil discord we know discord.” It is evident, then, that Aristotle thought this untenable and contrary to the position that God is most happy because He himself would not know some of the things that we know. And since this argument seemed to be beside the point, therefore, returning to his principal theme, he says (259) that, in returning to the point from which the first argument began, it is evident, so far as Empedocles is concerned, that hate is no more a cause of corruption than of being.
477. Nor, similarly, is love (260).
Here he gives the third argument, which pertains to love. He says that in like manner love is noe the cause of generation or being, as Empedocles claimed, if another position of his is considered. For he said that, when all the elements are combined into a unity, the corruption of the world will then take place; and thus love corrupts all things. Therefore, with respect to the world in general, love is the cause of corruption, whereas hate is the cause of generation. But with respect to singular things, hate is the cause of corruption and love of generation.
478. Moreover, he does (261).
Here he shows that Empedocles’ argument is not adequate. For Empedodes said that there exists in the world a certain alternation of hate and friendship, in such a way that at one time love unites all things and afterwards hate separates them. But as to the reason why this alternation takes place, so that at one time hate predominates and at another time love, he said nothing more than that it was naturally disposed to be so.
479. And next he gives Empedocles’ words, which, because they are written in Greek verse, are difficult and differ from the common way of speaking. These words are (262): “But thus mighty hate was nourished among the members and rose to a position of honor when the time was fulfilled, which being changeable dissolved the bond.” But the text of Boethius runs thus: “But when mighty discord in the members was promoted to a place of honor, because it marched forward in a completed year, which, when these things have been changed, returns to a full bond.” Now in order to understand this it must be noted that he speaks poetically of the whole world as though it were a single living thing in whose members and parts there is found at first the greatest harmony, which he calls love or concord, and afterwards there begins to exist little by little a certain dissonance, which he calls discord. And, similarly, in the parts of the universe at first there was maximum concord, and afterwards hate was nourished little by little until it acquired “the place of honor,” i.e., it acquired dominion over the elements. This comes about when a completed time is reached or a year is completed, as Empedocles held, “which” (hate or discord, or the year), being changeable, dissolves “the bond,” i.e., the former union of the elements; or the year or hate returns to a full bond, because by a certain ability and hidden power it returns to predominate over things.
480. After these words of Empedodes, Aristotle, in giving the meaning of the word “changeable” which he used, adds the explanation as though change were necessary; for he says that Empedocles made the foregoing statements as though it were necessary that there should be an alternation of hate and love, but he gives no reason for this necessity. For in the case of this one living thing it is evident that what causes the alternation of hate and love is the motion of the heavens which causes generation and corruption in the world. But no such cause can be assigned why the whole should be changed in this way by love and hate. Hence it is clear that his argument was inadequate.
481. Yet he alone (263).
Here he shows that this argument of Empedocles is not to the point. He says that Empedocles seems to say 11 expressly,” i.e., clearly, only that he does not hold that some of the things derived from these principles are corruptible and others incorruptible, but he holds that all things are corruptible with the exception of the elements alone. Thus he seems to avoid the foregoing problem inasmuch as the question remains why some things are corruptible and some not, if they come from the same principles. Hence it is also clear that his argument is not to the point, because he neglects the very point that requires explanation.
482. But it can be asked how he can say here that Empedocles held all things to be corruptible except the elements, since Empedocles has said above that the one is God, i.e., what is composed of the other principles except hate. It must be noted, however, that Empedocles posited two processes of corruption in the world, as is clear from what was said above. He posited one with respect to the blending of the whole universe, which was brought about by love; and from this process he did not make even God immune, because in God he placed love, which caused other things to be mixed with God. And he posited another process of corruption for singular things, and the principle of this process is hate. But he excluded this kind of corruption from God, seeing that he did not posit hate in God. In summing up, then, Aristotle concludes that this much has been said for the purpose of showing that corruptible and incorruptible things do not have the same principles.
483. But if the principles (264)
Here he argues the other side of the question, with two arguments. The first is this: if the principles of corrup4le and incorruptible things are not the same, the question arises whether the principles of corruptible things are corruptible or incorruptible. If one says that they are corruptible, he proves that this is false by two arguments. The first runs thus: every corruptible thing is dissolved into the principles of which it is composed. If, then, the principles of corruptible things are corruptible, it will be necessary to hold also that there are other principles from which they are derived. But this is untenable, unless an infinite regress is posited. Now it was shown in Book II (152:C 299) that it is impossible to have an infinite regress in principles in any class of cause. And it would be just as untenable for someone to say that this condition applies in the case of corruptible principles, since corruption seems to come about as a result of something being dissolved into prior principles.
484. The second argument runs thus. If the principles of corruptible things are corruptible, they must be corrupted, because every corruptible thing will be corrupted. But after they have been corrupted they cannot be principles, for what is corrupted or has been corrupted cannot cause anything. Therefore, since corruptible things are always caused in succession, the principles of corruptible things cannot be said to be corruptible.
485. Again, if it is said that the principles of corruptible things are incorruptible, evidently the principles of incorruptible things are incorruptible. Therefore the question remains why it is that from certain incorruptible principles corruptible effects are produced, and from certain others incorruptible effects are produced; for this seems to be unreasonable and is either impossible or requires considerable explanation.
486. Further, no one (265).
Then relative to his main thesis he gives his second argument, which is drawn from the common opinions of all men. For no one has attempted to say that corruptible and incorruptible things have different principles, but all say that all things have the, same principles. Yet the first argument, given in favor of the first part of the question, all pass over lightly, as though it were of little importance; but this is to acknowledge its truth. Hence the text of Boethius says: “But they swallow the first argument as though they considered it a minor matter.”
Q. 13: Are the principles of corruptible and incorruptible things the same?
487. Now the solution to this problem is given in Book XII (2553), where the Philosopher shows that the first active or motive principles of all things are the same but in a certain sequence. For the first principles of things are unqualifiedly incorruptible and immobile, whereas the second are incorruptible and mobile, i.e., the celestial bodies, which cause generation and corruption in the world as a result of their motion. Now the intrinsic principles of corruptible and of incorruptible things are the same, not numerically but analogically. Still the intrinsic principles of corruptible things, which are matter and form, are not corruptible in themselves but only in reference to something else. For it is in this way that the matter and form of corruptible things are corrupted, as is stated in Book I of the Physics.
LESSON 12
Are Unity and Being the Substance and Principle of All Things?
ARISTOTLE’S TEXT Chapter 4: 1001a 4-1001b 25
266. But the most difficult problem which has to be considered, and the one which is most necessary for a knowledge of the truth, is whether unity and being are the substance of existing things, and whether each of them is nothing else than unity and being. Or whether it is necessary to investigate what being and unity themselves are, as though there were some other nature which underlies them.
267. For some think that reality is of the former sort, and some of the latter. For Plato and the Pythagoreans thought that being and unity were nothing else [than themselves], and that this is their nature, their substance being simply unity and being. But among the other philosophers [there are different opinions] about the nature of unity. Empedocles, for example, as though reducing it to something better known, says that unity is being; for he would seem to say that this is love, since this is the cause why unity belongs to all things. Others say that this unity and being of which existing things consist and have been made is fire, and others say it is air. And those who hold that there are many elements say the same thing; for they must also speak of unity and being in as many ways as they say there are principles.
268. But if anyone holds that unity and being are not substances, it will follow that no other universals are such; for these are the most universal of all. But if there is no one-in-itself or being-in-itself, there will hardly be any other things that exist apart from what are called singular things. Further, if unity is not a substance, evidently number will not exist as another reality separate from existing things; for number is units, and a unit is truly something one. But if there is a one-in-itself and being-in-itself, the substance of these must be unity itself and being itself. For nothing else is predicated universally of all things but these two.
269. But, on the other hand, if there is to be a one-in-itself and being-in-itself, there is great difficulty in seeing how there will be anything else besides these. I mean, how will there be more beings than one? For that which differs from being does not exist, Hence according to Parmenides’ argument it must follow that all beings are one, and that this is being.
270. But there is a difficulty in either case; for whether unity itself is not a substance, or whether there is a unity itself, it is impossible for number to be a substance. Now it has already been stated why this follows if unity is not a substance; but if it is, the same difficulty will arise with regard to being. For from something outside of being something else will be one; for it must be not one. But all beings are either one or many, each of which is a one.
271. Further, if unity itself is indivisible, according to Zeno’s axiom it will be nothing. For that which when added does not make a thing greater or when subtracted does not make it smaller, this, he says, does not belong to the realm of existing things, as though it were evident that whatever has being is a continuous quantity.’ And if it is a continuous quantity, it is corporeal; for this in every respect is a being. But other quantities, for example, a surface and a line, when added in one way will make a thing greater, but in another way they will not; and a point and a unit will do so in no way.
272. But this philosopher speculates clumsily, and it is possible for a thing to be indivisible in such a way that some answer may be made against him; for when something of this kind is added it will not make a thing greater but more.
273. Yet how will continuous quantity come from such a unity or from many of them? For this would be like saying that a line is made up of points.
274. But even if someone were to think that the situation is such that number has come, as some say, from unity itself and from something else that is not one, none the less it would be necessary to inquire why and how the thing which has come to be would sometimes be a number and sometimes a continuous quantity, if that not-one were inequality and the same nature in either case. For it is not clear how continuous quantities would be produced from unity and this principle, or from some number and this principle.
COMMENTARY
Q. 14a: Are “one” and “being” substances or principles of things?
488. Having asked whether the principles of things are the same or different, the Philosopher now asks how unity itself could have the nature of a principle; and in regard to this he does three things. First, he asks whether unity itself is a principle; second (502), he asks whether numbers, which arise or follow from unity, are the principles of things; and third (515), whether the Forms, which are certain separate unities, are the principles of things.
In regard to the first he does three things. First, he raises the question. Second (489), he gives the opinions on both sides (“For some think”). Third (490), he advances arguments on both sides (“But if anyone”).
He says, first (266), that of all the different questions which have been raised, one is more difficult to consider because of the weight of the arguments on both sides, and that this question is also one about which it is necessary to know the truth, because our decision about the substances of things depends on it. Now this question is whether unity and being are the substances of things, not so that either of them must be attributed to some other nature which would be informed, as it were, by unity and being, but rather so that the unity and being of a thing are its substance; or, in an opposite way, whether it is necessary to ask what that thing is to which unity and being properly belong, as though there were some other nature which is their subject.
489. For some think (267)
Here he gives the opinions on each side of the question. He says that some philosophers thought that reality was of one kind, and some of another. For Plato and the Pythagoreans did not hold that unity and being are the attributes of some nature, but that they constitute the nature of things, as though being itself and unity itself were the substance of things. But some philosophers, in speaking about the natural world, attributed unity and being to certain other natures, as Empedocles reduced the one to something better known, which he- said is unity and being; and this seems to be love, which is the cause of unity in the world. But other philosophers of nature attributed these to certain elementary causes, whether they posited one first principle, as fire or air, or more than one. For since they would hold that the material principles of things are the substances of things, it was necessary that each of these should constitute the unity and being of things; so that whichever one of these anyone might hold to be a principle, he would logically think that through it being and unity would be attributed to A things, whether he posited one principle or more than one.
490. But if anyone (268).
Here he gives arguments on both sides of the question. First, he gives arguments in support of the view of Plato and Pythagoras. Second (269:C 493), he gives arguments on the other side of the question, in support of the view of the philosophers of nature (“But, on the other hand”).
In regard to the first (268), he makes use of elimination as follows. It is necessary to hold either that unity and being, separate and existing apart, are a substance, or not. Now if it is said that unity and being are not a substance, two untenable consequences will follow. The first of these is this: unity and being are said to be the most universal of all, and therefore, if unity and being are not separate in such a way that unity itself or being itself is a certain substance, it will then follow that no universal is separate. Thus it will follow that there is nothing in the world except singular things, which seems to be inappropriate, as has been stated in earlier questions (C 443).
491. The other untenable consequence is this. Number is nothing else than units, because number is composed of units; for a unit is nothing else than unity itself. Therefore, if unity itself is not separate as a substance existing of itself, it will follow that number will not be a reality separate from those things which are found in matter. This can be shown to be inappropriate in view of what has already been stated above. Hence it cannot be said that unity and being are not a substance which exists by itself.
492. Therefore, if the other part of the division is conceded, that there is something which is unity itself and being itself, and that this exists separately, it must be the substance of all those things of which unity and being are predicated. For everything that is separate and is predicated of many things is the substance of those things of which it is predicated. But nothing else is predicated of all things in as universal a way as unity and being. Therefore unity and being will be the substance of all things.
493. But, on the other hand (269).
Then he argues the other side of the question; and he gives two arguments. The second (271:C 496) of use these begins where he says, “Further, if unity itself.”
In regard to the first he does two things. First, he gives the argument. Second (270:C 494), he shows how the question is made difficult as a result of the argument given (“But there is a difficulty in either case”).
The first (269) argument, then, is as follows: if there is something which is itself being and unity as something,existing separately, it will be necessary to say that unity is the very same thing as being. But that which differs from being is non-being. Therefore it follows, according to the argument of Parmenides, that besides the one there is only non-being. Thus all things will have to be one, because it could not be held that that which differs from the one, which is essentially separate, is a being.
494. But there is a difficulty (270).
Here he shows how this argument creates a difficulty in the case of the position of Plato, who held that number is the substance of things. He says that Plato faces a difficulty in either case, whether it is said that this separate one is a substance or not. For whichever view is held, it seems impossible that number should be the substance of things. For if it is held that unity is not a substance, it has already been stated (269:C 493) why number cannot be held to be a substance.
495. But if unity itself is a substance, the same problem will arise with respect to both unity and being. For either there is some other unity besides this unity which exists separately of itself, or there is not. And if there is no other, a multitude of things will not exist now, as Parmenides said. But if there is another unity, then that other unity, since it is not unity itself, must have as a material element something that is other than unity itself, and, consequently, other than being. And that material element from which this second unity comes to be, will have not to be a being. Thus a multitude of beings cannot be constituted from this unity which exists apart from unity itself, because all beings are either one or many, each of which is a one. But this one has as its material element something that is neither unity nor being.
496. Further, if unity (271).
Here he gives the second argument; and in regard to this he does three things. First (271:C 496), he gives the argument. Second (272:C 498), he criticizes it (“But this”). Third (273:C 499), he shows that the difficulty remains (“Yet how will continuous quantity”).
He says first (271), then, that if this separate unity is indivisible, there follows from this the other position, which Zeno assumed, that nothing exists. For Zeno supposed that that which when added does not make a thing greater and when taken away does not make it smaller, is nothing in the real order. But he makes this assumption on the grounds that continuous quantity is the same as being. For it is evident that this is not a continuous quantity—I mean that which when added does not make a thing greater and when subtracted does not make it smaller. Therefore, if every being were a continuous quantity, it would follow that that which when added does not make a thing greater and when subtracted does not make it smaller, is non-being.
497. And better still, if any particular thing were to bear this out, every being would have to be a corporeal continuous quantity. For anything added to or subtracted from a body in any one of its dimensions, makes the body greater or less. But other continuous quantities, such as lines and surfaces, become greater insofar as one dimension is added, whereas others do not. For line added to line in length causes increase in length but not in width; and surface added to surface causes increase in width and in length but not in depth. But a point and a unit do not become greater or less in any way. Hence according to Zeno’s axiom it would follow that a point and a unit are non-beings in an absolute sense, whereas a body is a being in every respect, and surfaces and lines are beings in one respect and non-beings in another respect.
498. But this (272).
Here he criticizes the argument which has been given. He says that Zeno, by proposing such an axiom, speculated “clumsily,” i.e., in an unskilled and rude manner, so that according to him there cannot be anything indivisible. And for this reason some answer must be given to the foregoing argument; and if not to the point at issue, at least to the man. Now we say that even though a unity when added to something else does not make it larger, it does cause it to be more. And it is sufficient for the notion of being that in the case of what is continuous it should make a thing larger, and that in the case of what is discrete it should make it more.
499. Yet how will (273).
Then he states the difficulty which still faces the Platonists after the above solution. And he advances two difficulties. The Ifirst of these is that the Platonists held that the one which is indivisible is the cause not only of number, which is a plurality, but also of continuous quantity. Therefore, if it is granted that when a one is added it makes a thing more, as would seem to suffice for the one which is the cause of number, how will it be possible for continuous quantity to come from an indivisible one of this kind, or from many such ones, as the Platonists held? For this would seem to be the same thing as to hold that a line is composed of points. For unity is indivisible just as a point is.
500. But even if someone (274)
Here he gives the second difficulty. He says that if anyone were to think that the situation is such that number is the result of the indivisible one and of something else which is not one, but participates in the one as a kind of inaterial nature, as some say, the question would still remain why and how that which comrs from the one as form and from another material nature, which is called the not-one, is sometimes a number and sometimes a continuous quantity. The difficulty would be most acute if that material not-one were inequality, as is implied in the continuously extended, and were to be the same reality. For it is not clear how numbers come from this inequality as matter and from the one as form; nor again is it clear how continuous quantities come from some number as form and from this inequality as matter. For the Platonists held that number comes from a primary one and a primary two, and that from this number and material inequality continuous quantity is produced.
501. The solution of this problem is treated by Aristotle in the following books. For the fact that there is something separate, which is itself one and being, he will prove below in Book XII (2553), when he establishes the oneness of the first principle which is separate in an absolute sense, although it is not the substance of all things which are one, as the Platonists thought, but is the cause and principle of the unity of all things. And insofar as unity is predicated of other things it is used in two ways. In one way it is interchangeable with being, and in this way each thing is one by its very essence, as is proved below in Book IV (548); and unity in this sense adds nothing to being except merely the notion of undividedness. Unity is used in another way insofar as it has the character of a first measure, either in an absolute sense or with respect to some genus. And this unity if it is both a minimum in the absolute sense and indivisible, is the one which is the principle and measure of number. But if it is not both a minimum in an absolute sense and indivisible, it will not be a unit and measure in an absolute sense, as a pound in the case of weights and a half-tone in the case of melodies, and a foot in the case of lengths. And nothing prevents continuous quantities from being composed of this kind of unity. He will establish this in Book X (1940) of this work. But because the Platonists thought that the one which is the principle of number and the one which is interchangeable with being are the same, they therefore held that the one which is the principle of number is the substance of each thing, and consequently that number, inasmuch as it is composed of many substantial principles, makes up or comprises the substance of composite things. But he will treat this question at greater length in Books XIII and XIV of this work.
LESSON 13
Are Numbers and Continuous Quantities the Substances and Principles of Sensible Things?
ARISTOTLE’S TEXT Chapter 5: 1001b 26-1002b 11
275. And connected with these is the question whether numbers and bodies and surfaces and points are substances, or not.
276. For if they are not, we are in a quandary as to what being is, and what the substances of things are. For affections and motions and relations and dispositions and their complex conceptions do not seem to signify substance; because all are predicated of some subject, and no one of them is a particular thing. And those things which seem to signify substance most of all, as fire, water, earth [and air], of which composite bodies are constituted, their heat and cold and similar affections, are not substances. And it is only the body which undergoes these that remains as a being and is a substance.
277. Yet a body is a substance to a lesser degree than a surface, and this than a line, and this in turn than a unit and a point; for a body is defined by means of these, and these seem to be capable of existing without a body, but that a body should exist without these is impossible.
278. For this reason many of the natural philosophers, including the first, thought that substance and being are bodies, and that other things are attributes of this kind of thing; and hence too that the principles of bodies are the principles of beings. But the later philosophers, who were wiser than these, thought that the principles-of things are numbers. Therefore, as we have said, if these are not substance, there is no substance or being at all; for the accidents of these things are not worthy to be called beings.
279. But if it is admitted that lengths and points are substances to a greater degree than bodies, and we do not see to what sort of bodies these belong (because it is impossible for them to exist in sensible bodies), there will then be no substance at all.
280. Further, all of these seem to be dimensions of bodies, one according to width, another according to depth, and another according to length.
281. And, similarly, any figure whatever already exists in a solid. Hence if neither Mercury is in the stone, nor one half of a cube in a cube as something segregated, neither will surface exist in a solid; for if this were true of anything whatever, it would also be true of that which divides a thing in half. And the same argument would apply in the case of a line, a point and a unit. If, then, a body is substance in the highest degree, and these things are such to a greater degree than it is, and these do not exist and are not substances, it escapes our understanding as to what being itself is and what the substance of beings is.
282. For along with what has been said there happen to be certain unreasonable views about generation and corruption. For if substance, not existing before, exists now, or existing before, does not exist afterwards, it seems to suffer these changes through generation and corruption. But it is impossible for points and lines and surfaces either to come to be or to be destroyed, even though they sometimes exist and sometimes do not. For when bodies are joined or divided, at one time, when they are joined, they [i.e., the two surfaces] simultaneously become one, and at another time, when they are divided, two surfaces are produced; because it [i.e., one of the two surfaces in question] is not in the bodies which have been joined but has perished. And when bodies are divided surfaces exist which did not exist before. For the indivisible point is not divided into two, and if things are generated and corrupted, they are generated from something.
283. And it is similar with regard to the now in time, for this cannot be generated and corrupted. Yet it seems always to exist, although it is not a substance. It is also clear that this is true of points, lines and surfaces, because the argument is the same; for they are all similarly either limits or divisions.
COMMENTARY
Q 14b: Are numbers and continuous quantities the substances or principles of sensible things?
502. Having inquired whether unity and being are the substances of sensible things, the Philosopher now asks whether numbers and continuous quantities are the substances of sensible things; and in regard to this he does three things. First (502), he presents the question. Second (503), he argues in support of one side of the question (“For if they are not”). Third (507), he argues on the other side (“But if it is admitted”).
Accordingly he says, first, that “connected with these,” i.e., following from the foregoing problem, there is the question whether numbers and continuous quantities, i.e., bodies, surfaces, and their extremities, such as points, are either substances that are separate from sensible things, or are the substances of sensible things themselves, or not. He says that this problem is a result of the foregoing one, because in the foregoing problem it was asked whether unity is the substance of things. Now unity is the principle of number. But number seems to be the substance of continuous quantity inasmuch as a point, which is a principle of continuous quantity, seems to be merely the number one having position, and a line to be the number two having position, and the primary kind of surface to be the number three having position, and a body the number four having position.
503. For if they are not (276).
Then he advances an argument to show that these are the substances of sensible things; and in regard to this he does two things. First (276:C 503), he introduces an argument to show that these are the substances of sensible things. Second (278:C 506), he shows how the early philosophers followed out the first arguments (“For this reason”).
In regard to the first he does two things. For, first, he advances an argument to show that body is the substance of things; and second (277:C 504), to show that many other things are substances to an even greater degree (“Yet a body”).
He says, first (276), that if these things are not substances, we are in a quandary as to what being is essentially, and what the substances of beings are. For it is evident that affections and motions and relations and dispositions or arrangements, and their complex conceptions ‘ according as they are put into words, do not seem to signify the substance of anything; because all things of this kind seem to be predicated of a subject as something belonging to the genus of quantity, and no one of them seems to signify “this particular thing,” i.e., something that is complete and subsists of itself. This is especially evident in regard to the foregoing things, which are not said to be complete things but things whose nature consists in a kind of relation. But of all things those which especially seem to signify substance are fire, earth, and water, of which many bodies are composed. But he omits air, because it is less perceptible; and this is the reason why some thought air to be nothing. But in these bodies there are found certain dispositions, namely, hot and cold and other affections and passible qualities of this kind, which are not substances according to what has been said. It follows, then, that body alone is substance.
504. Yet a body (277)
Here he proceeds to examine those things which appear to be substance to an even greater degree than a body. He says that a body seems to be a substance to a lesser degree than a surface, and a surface than a line, and a line than a point or a unit. He proves this in two ways, of which the first is as follows. That by which a thing is defined seems to be its substance, for a definition signifies substance. But a body is defined by a surface, a surface by a line, a line by a point, and a point by a unit, because they say that a point is a unit having position. Therefore surface is the substance of body, and so on for the others.
505. The second argument runs as follows. Since substance is the primary kind of being, whatever is prior seems to be substance to a greater degree. But a surface is naturally prior to a body, because a surface can exist without a body but not a body without a surface. Therefore a surface is substance to a greater degree than a body. The same reasoning can be applied to all the others in turn.
506. For this reason (278).
Then he shows how the earlier philosophers followed out the foregoing arguments. He says that it was because of the foregoing arguments that many of the ancient philosophers, especially the first, thought that body alone was being and substance, and that all other things were accidents of bodies. Hence when they wanted to study the principles of beings, they studied the principles of bodies, as was stated above in Book I (36:C 74) with regard to the positions of the ancient natural philosophers. But the other philosophers who came later, and were reputed to be wiser than the aforesaid philosophers inasmuch as they dealt more profoundly with the principles of things, i.e., the Pythagoreans and Platonists, were of the opinion that numbers are the substances of sensible things inasmuch as numbers are composed of units. And the unit seems to be one substance of things. Hence, according to the foregoing arguments and opinions of the philosophers, it seems that if these things—numbers, lines, surfaces, and bodies—are not the substances of things, there will be no being at all. For if these are not beings, it is unfitting that their accidents should be called beings.
507. But if it is (279).
Then he argues in support of the other side of the question; and he gives four arguments, the first of which is as follows. If anyone were to admit that lengths and points are substances to a greater degree than bodies, then supposing that things of this sort are not substances, it also follows that bodies are not substances. Consequently, no substance will exist, because the accidents of bodies are not substances, as has been stated above (C 503). But points,’lines and surfaces are not substances. For these must be the limits of some bodies, because a point is the limit of a line, a line the limit of a surface, and a surface the limit of a body. But it is not evident to what sort of bodies these surfaces, lines and points, which are substances, belong. For it is evident that the lines and surfaces of sensible bodies are not substances, because they are altered in the same way as the other accidents in reference to the same subject. Therefore it follows that there will be no substance whatever.
508. Further, all of these (280).
Here he gives the second argument, which is as follows. All of the abovementioned things seem to be certain dimensions of bodies, either according to width, as a surface, or according to depth, as a solid, or according to length, as a line. But the dimensions of a body are not substances. Therefore things of this kind are not substances.
509. And, similarly (281).
Here he gives a third argument, which is as follows. Any figure which can be educed from a solid body according to some dimension is present in that body in the same way, i.e., potentially. But in the case of a large piece of stone which has not yet been cut, it is evident that “Mercury,” i.e., the figure of Mercury, is not present in it actually but only potentially. Therefore, in like manner, “in a cube,” i.e., in a body having six square surfaces, one half of the cube, which is another figure, is not present actually; but it becomes actual in this way when a cube has already been divided into two halves. And since every eduction of a new figure in a solid which has been cut is made according to some surface which limits a figure, it is also evident that such a surface will not be present in a body actually but only potentially. For if each surface besides the external one were actually present in a solid body, then for the same reason the surface which limits one half of the figure would also be actually present in it. But what has been said of a surface must also be understood of a line, a point, and a unit; for these are actually present in the continuum only insofar as they limit the continuum, and it is evident that these are not the substance of a body. But the other surfaces and lines cannot be the substance of a body, because they are not actually present in it; for a substance is actually present in the thing whose substance it is. Hence he concludes that of all of these body especially seems to be substance, and that surfaces and lines seem to be substance to a great degree than bodies. Now if these are not actual beings or substances, it seems to escape our comprehension as to what being is and what the substances of things are.
510. For along with (282).
Here he gives the fourth argument. First, he states it, and second (283:C 513), he clarifies it by using a similar case (“And it is similar”).
Accordingly, he says, first (282), that along with the other untenable consequences mentioned there also happen to be certain unreasonable views about generation and corruption on the part of those who hold that lines and surfaces are the substances of sensible things. For every substance which at first did not exist and later does exist, or which first was and afterwards is not, seems to suffer this change by way of generation and corruption. This is most evident in the case of all those things which are caused by way of motion. But points and lines and surfaces sometimes are and sometimes are not. Yet they are not generated or corrupted. Neither, then, are they substances.
511. He then proves each assumption. The first of these, is that they sometimes are and sometimes are not. For it happens that bodies which were at first distinct are afterwards united, and that those which were at first united are afterwards divided. For when bodies which were initially separated are united, one surface is produced for the two of them, because the parts of a continuous body are united in having one common boundary, which is one surface. But when one body is divided into two, two surfaces are produced, because it cannot be said that when two bodies are brought together their surfaces remain intact, but that both “perish,” i.e., cease to be. In like manner, when bodies are divided there begin to exist for the first time two surfaces which previously did not exist. For it cannot be said that a surface, which is indivisible according to depth, is divided into two surfaces according to depth; or that a line, which is indivisible according to width, is divided according to width; or that a point, which is indivisible in every respect, is divided in any respect whatsoever. Thus it is clear that two things cannot be produced from one thing by way of division, and that one thing cannot be produced from two of these things by way of combination. Hence it follows that points, lines and surfaces sometimes begin to be and sometimes cease to be.
512. After having proved this, he proves the second assumption, namely, that these things are neither generated nor corrupted. For everything that is generated is generated from something, and everything that is corrupted is dissolved into something as its matter. But it is impossible to assign any matter whatever from which these things are generated and into which they are dissolved, because they are simple. Therefore they are neither generated nor corrupted.
513. And it is similar (283).
Then he makes the foregoing argument clear by using a similar case. For the now in time stands to time as a point to a line. But the now in time does not seem to be generated and corrupted, because if it were its generation and corruption would have to be measured by some particular time or instant. Thus the measure of this now either would be another now and so on to infinity, or would be time itself. But this is impossible. And even though the now is not generated or corrupted, still each now always seems to differ, not substantially but existentially, because the substance of the now corresponds to the mobile subject. But the difference of the now in terms of existence corresponds to the variation in motion, as is shown in Book IV of the Physics. Therefore the same thing seems to be true of a point in relation to a line, and of a line in relation to a surface, and of a surface in relation to a body, namely, that they are neither corrupted nor generated, although some variation is observable in things of this kind. For the same holds true of all of these, because all things of this kind are, in like manner, limits if regarded as at the extremities, or divisions if they are found in between. Hence, just as the now varies existentially as motion flows by, although it remains substantially the same because the mobile subject remains the same, so also does the point vary. And it does not become different because of the division of a line, even though it is not corrupted or generated in an absolute sense. The same holds true of the others.
514. But the Philosopher will treat this question in Books XIII and XIV. And the truth of the matter is that mathematical entities of this kind are not the substances of things, but are accidents which accrue to substances. But this mistake about continuous quantities is due to the fact that no distinction is made between the sort of body which/belongs to the genus of substance and the sort which belongs to the genus of quantity. For body belongs to the genus of substance according as it is composed of matter and form; and dimensions are a natural consequence of these in corporeal matter. But dimensions themselves belong to the genus of quantity, and are not substances but accidents whose subject is a body composed of matter and form. The same thing too was said above (500) about those who held that numbers are the substances of things; for their mistake came from not distinguishing between the one which is the principle of number and that which is interchangeable with being.
LESSON 14
Are There Separate Forms in Addition to the Objects of Mathematics and Sensible Things?
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284. But in general one will wonder why, in addition to sensible things and those which are intermediate, it is necessary to look for certain other things which we posit as the specific essences (or Forms) of sensible things.
285. For if it is because the objects of mathematics differ in one respect from the things which are at hand, they do not differ in being many things that are specifically the same. Hence the principles of sensible things will not be limited in number but only in species; unless one were to consider the principles of this particular syllable or word, for these are limited in number. And this is likewise true of the intermediate entities; for in their case too there are an infinite number of things that are specifically the same. Hence, if in addition to sensible substances and the objects of mathematics there are not certain other things, such as some call the Forms, there will be no substance which is one both numerically and specifically. Nor will the principles of beings be limited in number, but only in species. Therefore, if this is necessary, it will also be necessary on this account that there should be Forms. And even if those who speak of the Forms do not express themselves clearly, although this is what they wanted to say, they must affirm that each of the Forms is a substance, and that nothing accidental pertains to them.
286. But if we hold that the Forms exist, and that principles are one numerically but not specifically, we have stated the untenable conclusions that follow from this view.
COMMENTARY
Q14c: Are forms substances or principles of things?
515. Having inquired whether the objects of mathematics are the principles of sensible substances, the Philosopher now inquires whether in addition to the objects of mathematics there are certain other principles, such as those which we call Forms, which are the substances and principles of sensible things. In regard to this he does three things. First, he presents the question. Second (516), he argues one side of the question (“For if it is because”). Third (518), he argues the other side (“But if we hold”).
Accordingly, he says, first, that if one assumes that the objects of mathematics are not the principles of sensible things and their substances, one will next have the problem why, in addition to both sensible things and the objects of mathematics (which are an intermediate class between sensible things and the Forms), it is necessary to posit a third class of entities, namely, the specific essences, i.e., the Ideas or separate Forms.
516. For if it is because (285)
Here he argues one side of the question. The reason why it is necessary to posit separate Forms over and above sensible substances and the objects of mathematics seems to be that the objects of mathematics differ in one respect “from the things at hand,” i.e., from sensible things, which exist in the universe; for the objects of mathematics abstract from sensible matter. Yet they do not differ but rather agree in another respect. For just as we find many sensible things which are specifically the same but numerically different, as many men or many horses, in a similar way we find many objects of mathematics which are specifically the same but numerically different, such as many equilateral triangles and many equal lines. And if this is true, it follows that, just as the principles of sensible things are not limited in number but in species, the same thing is true “of the intermediate entities”—the objects of mathematics. For since in the case of sensible things there are many individuals of one sensible. species, it is evident that the principles of sensible things are not limited in number but in species, unless of course we can consider the proper principles of a particular individual thing, which are also limited in number and are individual. He gives as an example words; for in the case of a word expressed in letters it is clear that the letters are its principles, yet there are not a limited number of individual letters taken numerically, but only a limited number taken specifically, some of which are vowels and some consonants. But this limitation is according to species and not according to number. For a is not only one but many, and the same applies to other letters. But if we take those letters which are the principles of a particular syllable, whether written or spoken, then they are limited in number. And for the same reason, since there are many objects of mathematics which are numerically different in one species, the mathematical principles of mathematical science could not be limited in number but only in species. We might say, for example, that the principles of triangles are three sides and three angles; but this limitation is according to species, for any of them can be multiplied to infinity. Therefore, if there were nothing besides sensible things and the objects of mathematics, it would follow that the substance of a Form would be numerically one, and that the principles of beings would not be limited in number but only in species. Therefore, if it is necessary that they be limited in number (otherwise it would happen that the principles of things are infinite in number), it follows that there must be Forms in addition to the objects of mathematics and sensible things.
517. This is what the Platonists wanted to say, because it necessarily follows from the things which they held that in the case of the substance of sensible things there is a single Form to which nothing accidental belongs. For something accidental, such as whiteness or blackness, pertains to an individual man, but to this separate man, who is a Form, according to the Platonists, there pertains nothing accidental but only what belongs to the definition of the species. And although they wanted to say this, they did not “express themselves” clearly; i.e., they did not clearly distinguish things.
518. But if wehold that (286).
Then he counters with an argument for the other side of the question. He says that, if we hold that there are separate Forms and that the principles of things are limited not only in species but also in number, certain impossible consequences will follow, which are touched on above in one of the questions (464).
But the Philosopher will deal with this problem in Book XII (2450) and Book XIV of this work. And the truth of the matter is that, just as the objects of mathematics do not exist apart from sensible things, neither do Forms exist apart from the objects of mathematics and from sensible substances. And while the efficient and moving principles of things are limited in number, the formal principles of things, of which there are many individuals in one species, are not limited in number but only in species.
LESSON 15
Do First Principles Exist Actually or Potentially, and Are They Universal or Singular?
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287. And connected with these problems there is the question whether the elements of things exist potentially or in some other way.
288. If they exist in some other way, then there will be something else prior to [first] principles. For potentiality is prior to that cause, but the potential need not exist in that way.
289. But if the elements exist potentially, it is possible for nothing to exist; for even that which does not yet exist is capable of existing, because that which does not exist may come to be. But nothing that is incapable of existing may come to be. It is necessary, then, to investigate these problems.
290. And there is also the problem whether [first] principles are universals or singular things, as we maintain.
291. For if they are universals, they will not be substances, because a common term signifies not a particular thing but what sort of thing; and a substance is a particular thing.
292. But if it is a particular thing, and is held to be the common whatness which is predicated of things, Socrates himself will be many animals: [himself] and man and animal; i.e., if each of these signifies a particular thing and a one. If, then, the first principles of things are universals, these consequences will follow.
293. However, if they are not universals but have the nature of singular things, they will not be knowable; for all scientific knowledge is universal. Hence, if there is to be any scientific knowledge of [first] principles, there will have to be different principles which are predicated universally and are prior to [first] principles.
COMMENTARY
Q 14d: Are principles of substances actual or potential?
519. Having inquired what the principles are, the Philosopher now asks how they exist. First, he asks whether they exist potentially or actually; and second (523), whether they are universals or singulars (“And there is also the problem”). In regard to the first he does three things. First, he raises the question. Second (520), he argues one side (“If they exist”). Third (501), he argues the opposite side (“But if the elements”).
His first question (287), then, is whether first principles exist potentially or “in some other way,” i.e., actually. This problem is introduced because of the ancient philosophers of nature, who held that there are only material principles, which are in potency. But the Platonists, who posited separate Forms as formal principles, claimed that they exist actually.
520. If they exist (288).
He proves that principles exist potentially. For if they were to exist “in some other way,” i.e., actually, it would follow that there would be something prior to principles; for potentiality is prior to actuality. This is clear from the fact that one thing is prior to another when the sequence of their being cannot be reversed; for if a thing exists, it follows that it can be, but it does not necessarily follow that, if a thing is possible, it will exist actually. But it is impossible for anything to be prior to a first principle. Therefore it is impossible for a first principle to exist in any other way than potentially.
521. But if the elements (289).
Here he argues the other side of the question. If the principles of things exist potentially, it follows that no beings exist actually; for that which exists potentially does not yet exist actually. He proves this on the grounds that that which is coming to be is not a being. For that which exists is not coming to be; but only that comes to be which exists potentially. Therefore everything that exists potentially is nonbeing. Hence if principles exist only potentially, beings will not exist. But if principles do not exist, neither will their effects. It follows, then, that it is possible for nothing to exist in the order of being. And in summing this tip he concludes that according to what has been said it is necessary to inquire about the principles of things for the reasons given.
522. This question will be answered in Book IX (1844) of this work, where it is shown that actuality is prior to potentiality in an unqualified sense, but that in anything moved from potentiality to actuality, potentiality is prior to actuality in time. Hence it is necessary that the first principle exist actually and not potentially, as is shown in Book XII (2500) of this work.
Q 14e: Are principles of substances universal or singular?
523. And here is also the problem (290).
Here he asks whether the principles of things exist as universals or as singular things; and in regard to this he does three things. First, he presents the question. Second (524), he argues one side (“For if they are universals”). Third (527), he argues the other side (“However, if they are not universals”). The problem (290), then, is whether principles are universals or exist in the manner of singular things.
524. For if they are (291).
Then he proves that principles are not universals, by the following argument. No predicate common to many things signifies a particular thing, but signifies such and such a thing or of what sort a thing is; and it does this not according to accidental quality but according to substantial quality, as is stated below in Book V (487:C 987) of this work. The reason for this is that a particular thing is said to be such insofar as it subsists of itself. But that which subsists of itself cannot be something that exists in many, as belongs to the notion of common. For that which exists in many will not subsist of itself unless it is itself many. But this is contrary to the notion of common, because what is common is what is onein-many. Hence it is clear that a particular thing does not signify anything common, but signifies a form existing in many things.
525. Further, he adds the minor premise, namely, that substance signifies a particular thing. And this is true of first substances, which are said to be substances in the full and proper sense, as is stated in the Categories; “ for substances of this kind are things which subsist of themselves. Thus it follows that, if principles are universals, they are not substances. Hence either there will be no principles of substances, or it will be necessary to say that the principles of substances are not substances.
526. But since it is possible for someone to affirm that some common predicate might signify this particular thing, he therefore criticizes this when he says “But if it is (292).”
He explains the untenable consequence resulting from this. For if a common predicate were a particular thing, it would follow that everything to which that common predicate is applied would be this particular thing which is common. But it is clear that both animal and man are predicated of Socrates, and that each of these—animal and man—is a common predicate. Hence, if every common predicate were a particular thing, it would follow that Socrates would be three particular things; for Socrates is Socrates, which is a particular thing; and he is also a man, which is a particular thing according to the above; and he is also an animal, which is similarly a particular thing. Hence he would be three particular things. Further, it would follow that there would be three animals; for animal is predicated of itself, of man, and of Socrates. Therefore, since this is impossible, it is also impossible for a common predicate to be a particular thing. These, then, will be the impossible consequences which follow if principles are universals.
527. However, if they are not (293).
He argues the other side of the question. Since all sciences are universal, they are not concerned with singulars but with universals. Therefore, if some principles were not universals but were singular things, they would not be knowable in themselves. Hence, if any science were to be had of them, there would have to be certain prior principles, which would be universals. It is necessary, then, that first principles be universals in order that science may be had of things; because if principles remain unknown, other things must remain unknown.
528. This question will be answered in Book VII (1584) of this work, where it is shown that universals are neither substances nor the principles of things. However, it does not follow for this reason that, if the principles and substances of things were singulars, there could be no science of them, both because immaterial things, even though they subsist as singulars, are nevertheless also intelligible, and also because there is science of singulars according to their universal concepts which are apprehended by the intellect.