LESSON 10

The Platonic Theory of Ideas

Chapter 6: 987a 29-988a 17

             69. After the philosophies described came the system of Plato, which followed them in many respects, but also had other [theses] of its own in addition to the philosophy of the Italians. For Plato agreeing at the very beginning with the opinions of Cratylus (362) and Heraclitus that all sensible things are always in a state of flux, and that there is no scientific knowledge of them, also accepted this doctrine in later years. However, when Socrates, concerning himself with moral matters and neglecting nature as a whole, sought for the universal in these matters and fixed his thought on definition, Plato accepted him because of this kind of investigation, and assumed that this consideration refers to other entities and not to sensible ones. For [according to him] it is impossible that there should be a common definition of any one of these sensible things which are always changing. Such entities, then, he called Ideas or Forms (species); and he said that all sensible things exist because of them and in conformity with them; for there are many individuals of the same name because of participation in these Forms. With regard to participation, he [merely] changed the name; for while the Pythagoreans say that things exist by imitation of numbers, Plato says that they exist by participation, changing the name. Yet what this participation or imitation of Forms is they commonly neglected to investigate.

             70. Further, he says that besides sensible things and Ideas there are the objects of mathematics, which constitute an intermediate class. These differ from sensible things in being eternal and immobile; and from the Ideas in that there are many alike, whereas each Idea is itself only one.

             71. And since the Forms [or Ideas] are the causes of other things, he thought that the elements of these are the elements of all existing things. Hence, according to him, the great and small are principles as matter, and the one as substance [or form]; for it is from these by participation in the one that the Ideas are numbers.

             72. Yet Plato said that the one is substance and that no other being is to be called one, just as the Pythagoreans did; and like them too he said that numbers are the causes of real substance.

             73. But to posit a dyad in place of the indeterminate one, and to produce the unlimited out of the great and small, is peculiar to him. Moreover, he says that numbers exist apart from sensible things, whereas they say that things themselves are numbers. Further, they do not maintain that the objects of mathematics are an intermediate class.

             74. Therefore, his making the one and numbers to exist apart from things and not in things, as the Pythagoreans did, and his introducing the separate Forms, were due to his investigation into the intelligible structures of things; for the earlier philosophers were ignorant of dialectic.

             75. But his making the dyad [or duality] to be a different nature was due to the fact that all numbers, with the exception of prime numbers, are naturally generated from the number two as a matrix.

             76. Yet what happens is the contrary of this. For this view is not a reasonable one; because the Platonists produce many things from matter but their form generates only once.

             77. And from one matter one measure seems to be produced, whereas he who induces the form, even though he is one, produces many measures. The male is also related to the female in a similar way; for the latter is impregnated by one act, but the male impregnates many females. And such are the changes in these principles. Concerning the causes under investigation, then, Plato defines them thus.

             78. From the foregoing account it is evident that Plato used only two causes: one being the whatness of a thing, and the other, matter; for the Forms are the cause of the quiddity in other things, and the one is the cause of the quiddity in the Forms. What the underlying matter is of which the Forms are predicated in the case of sensible things, and the one in the case of the Forms, is also evident, namely, that it is this duality, the great and small. Moreover, he assigned the cause of good and evil to these two elements, one to each of them; which is rather a problem, as we say (48:C 100), that some of the first philosophers, such as Empedocles and Anaxagoras, [have attempted] to investigate.

COMMENTARY

             151. Having given the opinion of the ancient phiolsophers about the material and efficient cause, he gives a third opinion, that of Plato, who was the first to clearly introduce the formal cause. This is divided into two parts. First (69:C 151), he gives Plato's opinion. Second (79:C 171), from all of the foregoing remarks he makes a summary of the opinions which the other philosophers expressed about the four classes of causes ("We have examined").

             In regard to the first he does two things. First, he gives Plato's opinion about the substances of things; and second (71:C 159), his opinion about the principles of things ("And since the Forms").

             In regard to the first he does two things. First, he gives Plato's opinion insofar as he posited Ideas; and second (70:C 157), insofar as he posited intermediate substances, namely, the separate mathematical entities ("Further, he says").

             He says, first (69), that after all the foregoing philosophers came the system of Plato, who immediately preceded Aristotle; for Aristotle is considered to have been his disciple. And even if Plato followed in many respects the natural philosophers who preceded him, such as Empedocles, Anaxagoras and the like, he nevertheless had certain other doctrines of his own in addition to those of the preceding philosophers, because of the philosophy of the Italians, or Pythagoreans. For insofar as he was devoted to the study of truth he sought out the philosophers of all lands in order to learn their teachings. Hence he came to Tarentum in Italy, and was instructed in the teachings of the Pythagoreans by Archytas of Tarentum, a disciple of Pythagoras.

             152. Now Plato would seem to follow the natural philosophers who lived in Greece; and of this group some of the later members held that all sensible things are always in a state of flux, and that there can be no scientific knowledge of them (which was the position of Heraclitus and Cratylus). And since Plato became accustomed to positions of this kind from the very beginning, and agreed with these men in this position, which he acknowledged to be true in later years, he therefore said that scientific knowledge of particular sensible things must be abandoned. And Socrates (who was Plato's master and the disciple of Archelaus, a pupil of Anaxagoras), because of this position, which arose in his time, that there can be no science of sensible things, was unwilling to make any investigation into the nature of physical things, but only busied himself with moral matters. And in this field he first began to investigate what the universal is, and to insist upon the need for definition.

             153. Hence, Plato, being Socrates' pupil, "accepted Socrates," i.e., followed him, and adopted this method for the purpose of investigating natural beings. He did so believing that in their case the universal in them could successfully be grasped and a definition be assigned to it, with no definition being given for any sensible thing; because, since sensible things are always "changing," i.e., being changed, no common intelligible structure can be assigned to any of them. For every definition must conform to each thing defined and must always do so, and thus requires some kind of immutability. Hence universal entities of this kind, which are separate from sensible things and that to which definitions are assigned, he called the Ideas or Forms of sensible things. He called them Ideas, or exemplars, inasmuch as sensible things are made in likeness to them; and he called them Forms inasmuch as [sensible things] have substantial being by participating in them. Or he called them Ideas inasmuch as they are principles of being, and Forms inasmuch as they are principles of knowledge. Hence all sensible things have being because of them and in conformity with them. They have being because of the Ideas insofar as the Ideas are the causes of the being of sensible things, and "in conformity with them" insofar as they are the exemplars of sensible things.

             154. The truth of this is clear from the fact that "many individuals of the same name" are attributed to one Form alone, i.e., there are many individuals which have the same Form predicated of them, and predicated by participation. For the Form or Idea [of man] is the specific nature itself by which there exists man essentially. But an individual is man by participation inasmuch as the specific nature [man] is participated in by this designated matter. For that which is something in its entirety does not participate in it but is essentially identical with it, whereas that which is not something in its entirety but has this other thing joined to it, is said properly to participate in that thing. Thus, if heat were a self-subsistent heat, it would not be said to participate in heat, because it would contain nothing but heat. But since fire is something other than heat, it is said to participate in heat.

             155. In a similar way, since the separate Idea of man contains nothing but the specific nature itself, it is man essentially; and for this reason it was called by him man-in-itself. But since Socrates and Plato have in addition to their specific nature an individuating principle, which is designated matter, they are therefore said to participate in a Form, according to Plato.

             156. Now Plato took this term participation from Pythagoras, although [in doing so] he made a change in the term. For the Pythagoreans said that numbers are the causes of things, just as the Platonists said that the Ideas are, and claimed that sensible things of this kind exist as certain imitations of numbers. For inasmuch as numbers, which have no position of themselves, received positions, they caused bodies. But because Plato held that the Ideas are unchangeable in order that there might be scientific knowledge of them, he did not agree that the term imitation could be used of the Ideas, but in place of it he used the term participation. However, it must be noted that, even though the Pythagoreans posited participation or imitation, they still did not investigate the way in which a common Form is participated in by individual sensible things or imitated by them. But the Platonists have treated this.

             157. Further, he says (70).

             Here he gives Plato's opinion about the mathematical substances. He says that Plato posited other substances--the objects of mathematics--in addition to the Forms and sensible things. Moreover, he said that beings of this kind were an intermediate class among the three kinds of substances; or that they were above sensible substances and below the Forms, and differed from both. The mathematical substances differed from sensible substances, because sensible substances are corruptible and changeable, whereas the mathematical substances are eternal and immobile. The Platonists got this idea from the way in which mathematical science conceives its objects; for mathematical science abstracts from motion. The mathematical substances also differed from the Forms, because the objects of mathematics are found to be numerically different and specifically the same, otherwise the demonstrations of mathematics would prove nothing. For unless two triangles belonged to the same class, geometry would attempt in vain to demonstrate that some triangles are alike; and the same thing is true of other figures. But this does not happen in the case of the Forms. For, since a Form is just the specific nature itself of a thing, each Form can only be unique. For even though the Form of man is one thing, and the Form of ass another thing, nevertheless the Form of man is unique, and so is the Form of ass; and the same thing is true of other things.

             158. Now to one who carefully examines Plato's arguments it is evident that Plato's opinion was false, because he believed that the mode of being which the thing known has in reality is the same as the one which it has in the act of being known. Therefore, since he found that our intellect understands abstractions in two ways: in one way as we understand universals abstracted from singulars, and in another way as we understand the objects of mathematics abstracted from sensible things, he claimed that for each abstraction of the intellect there is a corresponding abstraction in the essences of things. Hence he held that both the objects of mathematics and the Forms are separate. But this is not necessary. For even though the intellect understands things insofar as it becomes assimilated to them through the intelligible form by which it is put into act, it still is not necessary that a form should have the same mode of being in the intellect that it has in the thing known; for everything that exists in something else exists there according to the mode of the recipient. Therefore, considering the nature of the intellect, which is other than the nature of the thing known, the mode of understanding, by which the intellect understands, must be one kind of mode, and the mode of being, by which things exist, must be another. For although the object which the intellect understands must exist in reality, it does not exist there according to the same mode [which it has in the intellect]. Hence, even though the intellect understands mathematical entities without simultaneously understanding sensible substances, and understands universals without understanding particulars, it is not therefore necessary that the objects of mathematics should exist apart from sensible things, or that universals should exist apart from particulars. For we also see that sight perceives color apart from flavor, even though flavor and color are found together in sensible substances.

             159. And since the Forms (71).

             Here he gives Plato's opinion concerning the principles of things; and in regard to this he does two things. First (71), he states the principles which Plato assigned to things; and second (78:C 169), the class of cause to which they are reduced ("From the foregoing").

             In regard to the first he does two things. First, he tells us what kind of principles Plato had assigned to things. Second (72:C 160), he shows in what respect Plato agreed with the Pythagoreans, and in what respect he differed from them ("Yet Plato").

             He says, first (71), that, since the Forms are the causes of all other beings according to Plato, the Platonists therefore thought that the elements of the Forms are the elements of all beings. Hence, they assigned as the material principle of things the great and small, and said that "the substance of things," i.e., their form, is the one. They did this because they held these to be the principles of the Forms. For they said that just as the Forms are the formal principles of sensible things, in a similar way the one is the formal principle of the Forms. Therefore, just as sensible things are constituted of universal principles by participation in the Forms, in a similar way the Forms, which he said are numbers, are constituted "of these," i.e., of the great and small. For the unit constitutes different species of numbers by addition and subtraction, in which the notion of the great and small consists. Hence, since the one was thought to be the substance of being (because he did not distinguish between the one which is the principle of number, and the one which is convertible with being), it seemed to him that a plurality of different Forms might be produced from the one, which is their common substance, in the same way that a plurality of different species of numbers is produced from the unit.

             160. Yet Plato (72).

             Here he compares the position of Plato with that of Pythagoras. First (72), he shows in what respect they agreed; and second (73:C 160), in what respect they differed ("But to posit").

             Now they agreed in two positions; and the first is that the one is the substance of things. For the Platonists, like the Pythagoreans, said that what I call the one is not predicated of some other being as an accident is of a subject, but signifies a thing's substance. They said this, as we have pointed out (71:C 159), because they did not distinguish between the one which is convertible with being and the one which is the principle of number.

             161. The second position follows from the first; for the Platonists, like the Pythagoreans, said that numbers are the causes of the substance of all beings; and they held this because [in their opinion] number is just a collection of units. Hence if the one is substance, number must also be such.

             162. But to posit (73).

             Here he shows in what respect they differed; and in regard to this he does two things. First, he states how they differed. Second (74:C 164), he gives the reason for this difference ("Therefore, his making").

             Now this difference involves two things. First, the Pythagoreans, as has already been stated, posited two principles of which things are constituted, namely, the limited and the unlimited, of which one, i.e., the unlimited, has the character of matter. But in place of this one principle--the unlimited--which the Pythagoreans posited, Plato created a dyad, holding that the great and small have the character of matter. Hence the unlimited, which Pythagoras claimed to be one principle, Plato claimed to consist of the great and small. This is his own opinion in contrast with that of Pythagoras.

             163. The second difference is that Plato held that numbers are separate from sensible things, and this in two ways. For he said that the Forms themselves are numbers, as was pointed out above (71:C 159); and he also held, as was stated above (70:C 157), that the objects of mathematics are an intermediate class between the Forms and sensible things, and that they are numbers by their very essence. But the Pythagoreans said that sensible things themselves are numbers, and did not make the objects of mathematics an intermediate class between the Forms and sensible things; nor again did they hold that the Forms are separate from things.

             164. Therefore, his making (74).

             Here he gives the reason for the difference. First (74), he gives the reason for the second difference; and then (75:C 165), the reason for the first difference ("But his making").

             He says, then, that the Platonists adopted the position that both the one and numbers exist apart from sensible things and not in sensible things, as the Pythagoreans claimed; and they also introduced separate Forms because of the investigation "which was made into the intelligible structures of things," i.e., because of their investigation of the definitions of things, which they thought could not be attributed to sensible substances, as has been stated (69:C 151). This is the reason they were compelled to hold that there are certain things to which definitions are assigned. But the Pythagoreans, who came before Plato, were ignorant of dialectic, whose office it is to investigate definitions and universals of this kind, the study of which led to the introduction of the Ideas.

             165. But his making (75).

             Here he gives the reason for the other difference, that is, the one concerning matter. First (75), he gives the reason for such a difference. Second (76:C 166), he shows that Plato was not reasonably motivated ("Yet what happens").

             He accordingly says (75) that the Platonists made the dyad [or duality] to be a number of a different nature than the Forms, because all numbers with the exception of prime numbers are produced from it. They called prime numbers those which are not measured by any other number, such as three, five, seven, eleven, and so on; for these are produced immediately from unity alone. But numbers which are measured by some other number are not called prime numbers but composite ones, for example, the number four, which is measured by the number two; and in general every even number is measured by the number two. Hence even numbers are attributed to matter, since unlimitedness, which belongs to matter, is attributed to them, as has been stated above (59:C 125). This is why he posited the dyad, from which as "a matrix," or exemplar, all other even numbers are produced.

             166. Yet what happens (76).

             Here he proves that Plato made unreasonable assumptions; and in regard to this he does two things. For, first (76), he proves this by an argument from nature. Second (77:C 167), he gives the argument based on the nature of things, which led Plato to adopt this position ("And from one matter").

             He says (76) that, although Plato posited a dyad on the part of matter, still what happens is the contrary of this, as the opinions of all the other natural philosophers testify; for they claimed that contrariety pertains to form and unity to matter, as is clear in Book I of the Physics. For they held that the material principle of things is air or water or something of this kind, from which the diversity of things is produced by rarefaction and condensation, which they regarded as formal principles; for Plato's position is not a reasonable one. Now the natural philosophers adopted this position because they saw that many things are generated from matter as a result of a succession of forms in matter. For that matter which now supports one form may afterwards support many forms as a result of one form being corrupted and another being generated. But one specifying principle or form "generates only once," i.e., constitutes the thing which is generated. For when something is generated it receives a form, and the same form numerically cannot become the form of another thing that is generated but ceases to be when that which was generated undergoes corruption. In this argument it is clearly apparent that one matter is related to many forms, and not the reverse, i.e., one form to many matters. Thus it seems more reasonable to hold that unity pertains to matter but duality or contrariety to form, as the philosophers of nature claimed. This is the opposite of what Plato held.

             167. And from one matter (77).

             Here he gives an opposite argument taken from sensible things according to the opinion of Plato. For Plato saw that each thing is received in something else according to the measure of the recipient. Hence receptions seem to differ according as the capacities of recipients differ. But one matter is one capacity for reception. And Plato also saw that the agent who induces the form, although he is one, causes many things to have this form; and this comes about because of diversity on the part of matter. An example of this is evident in the case of male and female; for a male is related to a female as an agent and one who impresses a form on matter. But a female is impregnated by one act of a male, whereas one male can impregnate many females. This is why he held that unity pertains to form and duality to matter.

             168. Now we must note that this difference between Plato and the philosophers of nature is a result of the fact that they considered things from different points of view. For the philosophers of nature considered sensible things only insofar as they are subject to change, in which one subject successively acquires contrary qualities. Hence they attributed unity to matter and contrariety to form. But Plato, because of his investigation of universals, went on to give the principles of sensible things. Therefore, since the cause of the diversity of the many singular things which come under one universal is the division of matter, he held that diversity pertains to matter and unity to form. "And such are the changes of those principles" which Plato posited, i.e., participations, or, as I may say, influences in the things generated. For Pythagoras understands the word change in this way. Or Aristotle says "changes" inasmuch as Plato changed the opinion which the first philosophers of nature had about principles, as is evident from the foregoing. Hence it is evident from the foregoing that Plato dealt thus with the causes which we are investigating.

             169. From the foregoing (78).

             Here he shows to what class of cause the principles given by Plato are referred. He says that it is evident from the foregoing that Plato used only two kinds of causes. For he used as "one" cause of a thing the cause of its "whatness," i.e., its quiddity, or its formal cause, which determines its quiddity; and he also used matter itself. This is also evident from the fact that the Forms which he posited "are the causes of other things," i.e., the causes of the whatness of sensible things, namely, their formal causes, whereas the formal cause of the Forms themselves is what I call the one, which seems to be the substance of which the Forms are composed. And just as he holds that the one is the formal cause of the Forms, in a similar fashion he holds that the great and small are their material cause, as was stated above (71:C 159). And these causes--the formal and the material cause--are referred not only to the Forms but also to sensible substances, because [there is some subject of which] the one is predicated in the case of the Forms. That is to say, that which is related to sensible substances in the same way as the one is to the Forms is itself a Form, because that duality which relates to sensible things as their matter is the great and small.

             170. Furthermore, Plato indicated the cause of good and evil in the world, and he did this with reference to each of the elements which he posited. For he made Form the cause of good and matter the cause of evil. However, some of the first philosophers attempted to investigate the cause of good and evil, namely, Anaxagoras and Empedocles, who established certain causes in the world with this special end in view that by means of these causes they might be able to give the principles of good and evil. And in touching upon these causes of good and evil they came very close to positing the final cause, although they did not posit this cause directly but only indirectly, as is stated below (84:C 177).