by Aristotle
The argument that tries to establish Ideas from relatives is as follows. In those cases where some same thing is predicated of several things not homonymously but as revealing some single nature, it is true of them either by their strictly being what [83.1] is indicated by what is predicated, as when we say Socrates is a man and Plato is; or by their being likenesses of the genuine things, as when we predicate man of painted men (for in the case of these latter we reveal the likenesses of men by indicating the same particular nature in all of them); or on the grounds of one of them being the [5] pattern, while the rest are likenesses, as if we were to call both Socrates and likenesses of him men. And we predicate the equal itself of things here, although it is predicated of them only homonymously; for neither does the same account fit all of them, nor do we indicate things that are truly equal; for among perceptibles quantity changes and shifts continuously and is not determinate. Nor moreover do [10] any of the things here accurately receive the account of the equal. And no more indeed on the grounds of one of them being pattern, the other likeness; for one is no more pattern or likeness than the other. And even if someone were to accept that the likeness is not homonymous with its pattern, it still follows that these equal things are equal as likenesses of that which is strictly and truly equal. And if this is the case, there is some equal itself quite strictly, relative to which things here, as [15] likenesses, are both produced and called equal, and this is an Idea, a pattern for those things which are produced relative to it.
This argument, Aristotle says, establishes Ideas even of relative terms. At any rate the present proof has been advanced in the case of the equal, which is a relative; but they used to say that there were no Ideas of relatives because while Ideas, being for them kinds of substances, existed in their own right, relatives had their being in [25] their relationship to one another. And again, if the equal is equal to an equal, there will be more than one Idea of the equal; for the equal-itself is equal to an equal-itself; for if it were not equal to something, it would not be equal at all. Again, by the same argument there will have to be Ideas of unequals too; for opposites are [30] in a similar case—there will or will not be Ideas of both; and the unequal is admitted by them too to involve more things than one.
The argument which introduces the third man is as follows. They say that what are commonly predicated of substances both are strictly such things and are Ideas. [84.1] And again, things that are like each other are like each other by sharing in the same certain thing, which is strictly the thing in question; and this is the Idea. But if this is the case, and what is commonly predicated of certain things, if it is not the same as any one of those things of which it is predicated, is some other thing apart from it (for that is why man-himself is a genus—because while being predicated of the [5] particulars it is not the same man as any of them), then there will be some third man apart both from the particular, e.g. Socrates and Plato, and from the Idea; and this too will be itself one in number.
And there was an argument presented by the sophists introducing the third man as follows. If when we say ‘a man is walking’ we are saying neither that man as [10] an Idea is walking (for the Idea is not capable of motion) nor that some particular individual is (how could we when we do not know who it is? For while we know that a man is walking we do not know which particular man it is of whom we are saying it), we are saying that some other third man apart from these is walking: so there [15] will be a third man of whom we predicated the walking. Now this argument, which is sophistical, is given encouragement by those who separate what is common from the particulars, as those who posit the Ideas do. And Phanias says, in Against Diodorus, that the sophist Polyxenus introduced the third man by saying “If it is both by participation and sharing in the Idea, i.e. in man-himself, that man exists, then there must be some man who will have his existence relative to the Idea. But [20] neither man-himself, i.e. the Idea, exists by participation in the Idea, nor does any particular man. It remains then that there is some third man who has his existence relative to the Idea.”
The third man is proved also in the following way. If what is predicated truly of several items is also something other apart from the things of which it is predicated, separated from them (for it is this that those who posit the Ideas think to [25] prove; for in their opinion man-himself is something because man is predicated truly of particular men, who are more than one in number, and is different from these particular men)—but if this is so, there will be some third man. For if the man that is predicated is different from those of whom he is predicated, and exists on his own, and man is predicated both of the particular men and of the Idea, then there [85.1] will be some third man apart both from the particular and from the Idea. On this basis there will be also a fourth man, predicated of the third man, of the Idea, and of the particulars; and similarly also a fifth, and so on ad infinitum.
This argument is the same as the first; this comes about for them because they [5] supposed that like things were like by sharing in the same thing; for both men and the Ideas are like. Now he refuted both these arguments though they were thought to be rather refined, the one on the grounds that it established Ideas even of relative terms, and the other because it introduces a third man and then multiplies men to infinity. And a similar multiplication will be suffered by any of the other things of which they say there are Ideas. While others have used the first exposition of the third man—there is a specially clear use by Eudemus in his On Diction—the last [10] was used by Aristotle himself both in the first book of On Ideas and a little later on in the present work [i.e. the Metaphysics].
Now they are more—in fact most—concerned to establish that there are first [15] principles; for first principles are for them first principles of the Ideas themselves. And the one and indefinite dyad are first principles, as he has said a little earlier and has himself explained in his On the Good; but in their view these are the first principles of number too. Now he says that these arguments for establishing the Ideas destroy these first principles.
And if these are destroyed, the things after the first principles will also be [20] destroyed, given that they come from the first principles; so consequently the Ideas too will be. For if in the case of all things which have a common predicate it is both separated and an Idea, and if the dyad is predicated of the indefinite dyad too, there will be something primary and an Idea of this latter; and consequently the indefinite dyad will no longer be a first principle. But nor will the dyad in its turn be both primary and a first principle; for number is predicated of it in its turn since it is an [25] Idea; for the Ideas are assumed by them to be numbers: consequently number, being a kind of Idea, will be primary for them. And if this is so, number will be prior to the [86.1] indefinite dyad, which is for them a first principle, but not the dyad to number; and if this is so, the dyad would no longer be a first principle, if it is what it is by sharing in something. Again, while it is assumed to be a first principle of number, yet according to the argument just stated number becomes prior to it; but if number is relative (for every number is a number of something), and number is first of the [5] things that exist, given that it is prior even to the dyad which they assumed as a first principle, then on their view what is relative will be prior to what exists in its own right. And that is absurd; for everything relative is secondary. For a relative indicates the condition of a pre-existing nature, which is prior to that condition which happens to belong to it. . . . But even if someone were to say that number is a [10] quantity and not a relative, it would have as a consequence that quantity was prior to substance.
Again, they are committed to saying that what is relative is both a first principle of and prior to what exists in its own right, in so far as the Idea is in their view a first principle of substances, and what it is for an Idea to be an Idea lies in its [15] being a pattern, and a pattern is relative; for a pattern is a pattern of something. Again, if being for Ideas lies in their being patterns, then things that come into bei
ng in relation to them and of which they are Ideas will be likenesses of them; and so someone might say that according to them all naturally constituted things become relative; for all things are likenesses and patterns. Again, if being for Ideas [20] lies in their being patterns, and a pattern exists for the sake of what comes into being relative to it, and what exists on account of something else is less worthy than that thing, then the Ideas will be less worthy than what comes into being relative to them.
The following are some of the arguments which, in addition to those already stated, through the positing of Ideas destroy their first principles. If what is [87.5] commonly predicated of certain things is both the first principle and Idea of those things, and if first principle is commonly predicated of the first principles and element of the elements, there will be something prior to and a first principle of the first principles and of the elements; and in this way there will be neither first principles nor elements. Again Idea is not prior to Idea; for all Ideas similarly are first principles. And the one-itself and the dyad-itself are alike Ideas—as is [10] man-itself and horse-itself and each of the other Ideas; so there will not be any of these that is prior to any other—so that none will be a first principle either; so it is not the case that the one and the indefinite dyad are first principles. Again, it is absurd that an Idea should be given form by an Idea; for all are Forms; but if the one and the indefinite dyad are first principles, there will be Ideas given form by Ideas; for the dyad-itself will be given form by the one-itself; for it is in this way that they say that these are first principles—in the sense that one is form, the dyad [15] matter; so these are not first principles. And if they say that the indefinite dyad is not an Idea, then first there will be something prior to it although it is a first principle; for there is the dyad-itself, by sharing in which even this is a dyad, since this is not the dyad-itself; for it is by virtue of sharing that dyad will be predicated of it, since the same goes for particular dyads. Again, if the Ideas are simple, they will not come from different first principles, but the one and the indefinite dyad are [20] different. Again, the number of dyads will be amazing if one is the dyad-itself, another the indefinite dyad, another the mathematical dyad, which we use in counting and which is not the same as either of the former, and again besides these another in numerable and perceptible things. This is absurd; so that clearly by [88.1] following the very assumptions made by them it is possible to destroy the first principles, which are for them more important than the Ideas.
(Alexander, Commentarius in Metaphysica 97.27–98.24):
That it is not, as Eudoxus and some others thought, by mixture with the Ideas that other things exist: Aristotle says it is easy to infer many impossibilities as consequences of this opinion. If the Ideas are mixed with the other things, in the [98.1] first place, they will be bodies; for it is of bodies that there is mixture. Again, they will be contrary to each other; for mixture occurs with respect to contrariety. Again, mixture will occur in such a way that either a whole Idea will be in each of the things with which it is mixed or else part of one. But if a whole, then what is one in number will be in several things; for an Idea is one in number. While if in parts, a [5] man will be what participates in a part of man-himself, not what participates in man-himself as a whole. Again, Ideas will be divisible and partible, although they are impassive. Then they will be uniform if all things which have some part from it are like each other. But how can the Forms be uniform? For part of man cannot be a [10] man, as a part of gold is gold. Again, as Aristotle himself says a little later [sc. in the Metaphysics], in each thing there will not be one Idea mixed but many; for if there is one Idea of animal and another of man, and a man is both an animal and a man, he will participate in both Ideas. And man-himself, the Idea, insofar as it is also an animal, will also itself participate in animal; and consequently the Ideas will no longer be simple but composed from many, and some of them primary, others [15] secondary. But if it is not an animal, surely it is absurd to say that man is not an animal? And again, if they are mixed with things that are relative to them, how can they still be patterns, as they say they are? For it is not in this way, as the result of a mixture, that patterns are causes of the similarity that their likenesses have to them. And again, they will be destroyed along with the destruction of the things they are in. Nor yet will they be in themselves separable, but will be in the things that [20] participate in them. In addition to these points, they will no longer be unchangeable—and all the other absurdities which Aristotle in his examination of this opinion in the second book of his On Ideas showed it to have. For it was for this reason that he said ‘for it is easy to infer many impossibilities against this view’—for they were inferred there.
F 191 R3 (Apollonius, historiae mirabiles 6):
Again in Caulonia, according to Aristotle . . .1 in addition to much other information about him, he says that in Tyrrhenia he killed a deadly biting snake by biting it himself. He also says that Pythagoras foretold to the Pythagoreans the coming political strife; that is why he departed to Metapontum unobserved by anyone, and while he was crossing the Cosas he, with others, heard the river say “Good morning, Pythagoras”—and those present were terrified. He once appeared both at Croton and at Metapontum on the same day and at the same hour. Once, while sitting in the theatre, he stood up—so Aristotle tells—and showed those sitting there his own thigh, which was golden.
F 191 R3 (Aelian, varia historia II 26):
Aristotle says that Pythagoras was called by the people of Croton the Hyperborean Apollo. The son of Nicomachus adds that Pythagoras was once seen by many people, on the same day and at the same hour, both at Metapontum and at Croton; and at Olympia, during the games, he got up and showed that one of his thighs was golden.2 The same writer says that while crossing the river Cosas he was hailed by the river, and that many people heard him so hailed.
F 192 R3 (lamblichus, vita pythagorica VI 31):
Aristotle relates in his books On the Pythagorean Philosophy that the following division was preserved by the Pythagoreans as one of their greatest secrets: of rational living creatures, some are gods, some men, and some beings like Pythagoras.
F 193 R3 (Apuleius, de deo Socratis XX 166–7):
But I suppose Aristotle is a sufficient witness to the fact that the Pythagoreans marvelled greatly at anyone who said he had never seen a divine being.
F 194 R3 (Aulus Gellius, IV xi 12):
Since the fact is unexpected, I add Plutarch’s own words: ‘Aristotle says the Pythagoreans abstain from eating womb and heart, the sea anemone, and certain other such things, but use all other kinds’.
F 194 R3 (Diogenes Laertius, VIII 19):
Aristotle says that at times they [sc. the Pythagoreans] abstain from womb and red mullet.
F 195 R3 (Diogenes Laertius, VIII 34):
Aristotle says in his work On the Pythagoreans that he [sc. Pythagoras] enjoyed abstention from beans either because they are like the genitals or because they are like the gates of Hades . . .1 (for they alone have no joints), or because they are destructive, or because they are like the nature of the universe, or because they are oligarchical (being used in the choice of rulers by lot).
F 196 R3 (Porphyry, Vita Pythagorae 41):
Pythagoras used to say certain things in a mystical and symbolic way, and Aristotle has recorded many of these; e.g. that he called the sea the tears of Cronos, the Bears the hands of Rhea, the Pleiades the lyre of the Muses, the planets the dogs of Persephone; the ringing sound of bronze when struck was, he said, the voice of a divine being imprisoned in the bronze.
F 197 R3 (Porphyry, Vita Pythagorae 42):
There was also another kind of symbol, of the following sort: ‘Do not step over a balance’, i.e. do not be covetous: ‘Do not poke the fire with a sword’, i.e. do not vex with sharp words a man swollen with anger; ‘Do not pluck the crown’, i.e. do not offend against the laws which are the crowns of cities. Or again, ‘Do not eat heart’, i.e. do not vex
yourself with grief: ‘Do not sit on the corn ration’, i.e. do not live in idleness; ‘When on a journey do not turn back’, i.e. when you are dying, do not cling to this life; ‘Do not walk the highway’, i.e. do not follow the opinions of the many but pursue those of the few and educated; ‘Do not receive swallows in your house’, i.e. do not take into your house talkative men who cannot control their tongues; ‘Add to the burdens of the burdened, do not lighten them’, i.e. contribute to no man’s sloth, but to his excellence; ‘Do not carry images of the gods in your rings’, i.e. do not make your thought and speech about the gods manifest and obvious, nor show it to many; ‘Make your libations to the gods at the ear of the cup’, i.e. celebrate and honour the gods with music, for this goes through the ears.
F 198 R3 (Martianus Capella, VII 731):
(Philosophy speaks). ‘Although Aristotle, one of my followers, reasoning from the fact that it [sc. the unit] itself is one alone and wishes always to be sought after, asserts that it is called Desire because it desires itself, since it has nothing beyond itself and, never carried beyond itself or linked with other things, turns its own ardours on itself.’
F 199 R3 (Theo of Smyrna, p. 22. 5–9 Hiller):
But Aristotle in his Pythagoreans says that the One partakes of the nature of both; for added to an even number it makes an odd, and added to an odd an even, which it could not do if it did not share in both natures; and that for this reason the One was called even-odd.