Lecture 14 — Critique of the Platonic Ideas

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The first is divided into two parts.

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

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

In regard to the first he does two things.

First, he argues against this position of Plato;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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