PASSAGES REFERRING TO THE PYTHAGOREANS

FROM PLATO AND ARISTOTLE

TRANSLATED BY ARTHUR FAIRBANKS

PASSAGES IN PLATO REFERRING TO THE PYTHAGOREANS

Phaedo 62 B. The saying uttered in secret rites, to the effect that we men are in a sort of prison, and that one ought not to release himself from it nor yet to run away, seems to me something great and not easy to see through; but this at least I think is well said, that it is the Gods who care for us, and we men are one of the possessions of the Gods.

Crarylus 400 B. For some say that it [the body] is the tomb of the soul -- I think it was the followers of Orpheus in particular who introduced this word -- which has the soul enclosed like a prison in order that it may be kept safe.

Gorgias 493 A. I once heard one of the wise men say that now we are dead and the body (soma) is our tomb (sema), and that the part of the soul where desires are, it so happens, is open to persuasion, and moves upward or downward. And, indeed, a clever man -- perhaps some inhabitant in Sicily or Italy -- speaking allegorically, and taking the word from 'credible' (pithanos) and 'persuadable' (pistikos), called this a jar (pithos); and he called those without intelligence uninitiated, and that part of the soul of uninitiated persons where the desires are, he called its intemperatness, and said it was not water-tight, as a jar might be pierced with holes -- using the simile because of insatiate desires.

iv. 6; 213 b 22. And the Pythagoreans say that there is a void, and that it enters into the heaven itself from the infinite air, as though it [the heaven] were breathing; and this void defines the natures of things, inasmuch as it is a certain separation and definition of things that lie together; and this is true first in the case of numbers, for the void defines the nature of these.

And further, discerning in numbers the conditions and reasons of harmonies also -- since, moreover, other things seemed to be like numbers in their entire nature, and numbers were the first of every nature -- they assumed that the elements of numbers were the elements of all things, and that the whole heavens were harmony and number. And whatever characteristics in numbers and harmonies they could show were in agreement with the properties of the heavens and its parts and with its whole arrangement, these they collected and adapted; and if there chanced to be any gap anywhere, they eagerly sought that the whole system might be connected with these [stray phenomena]. To give an example of my meaning: inasmuch as ten seemed to be the perfect number and to embrace the whole nature of numbers, they asserted that the number of bodies moving through the heavens were ten, and when only nine were visible, for the reason just stated they postulated the counter-earth as the tenth. We have given a more definite account of these thinkers in other parts of our writings. But we have referred to them here with this purpose in view, that we might ascertain from them what they asserted as the first principles and in what manner they came upon the causes that have been enumerated. They certainly seem to consider Number as the first principle and, as it were, the matter in things and in their conditions and states; and the odd and the even are elements of number, and of these the one is Limited and the other Unlimited, and unity is the product of both of them, for it is both odd and even, and Number arises from the one, and the whole heaven, as has been said, is numbers.

A different party in this same school says that the first principles are ten, named according to the following table: Limited and Unlimited, Odd and Even, One and Many, Right and Left, Male and Female, Rest and Motion, Straight and Crooked, Light and Darkness, Good and Bad, Square and Oblong. After this manner Alcmaeon of Croton seems to have conceived them, and either he received this doctrine from them or they from him, for Alcmaeon arrived at maturity when Pythagoras was an old man, and his teachings resembled theirs. For he says that most human affairs are twofold, not meaning opposites reached by definition, as did the former party, but opposites by chance -- as, for example, white-black, sweet-bitter, good-bad, small-great. This philosopher let fall his indefinite opinions about the other contraries, but the Pythagoreans declared the number of the opposites and what they were. From both schools one may learn this much: that opposites are the first principles of things -- but from the latter he may learn the number of these, and what they are. Yet how it is possible to bring them into relation with the causes of which we have spoken they have not clearly worked out. They seem to range their elements under the category of matter, for they say that substance is compounded and formed from them, and that they inhere in it.

987 a 9-27. Down to the Italian philosophers, and with their exception, the rest have spoken more reasonably about these principles, except that, as we said, they do indeed use two principles, and the one of these, whence is motion, some regard as one and others as twofold. The Pythagoreans, however, while they in similar manner assume two first principles, add this which is peculiar to themselves: that they do not think that the Limited and the Unlimited and the One are certain other things by nature, such as fire or earth or any other such thing, but the Unlimited itself and Unity itself are the essence of things of which they are predicated, and so they make Number the essence of all things. So they taught after this manner about them, and began to discourse and to define what essence is, but they made it altogether too simple a matter. For they made their definition superficially, and to whatever first the definition might apply, this they thought to be the essence of the matter, as if one should say that twofold and two were the same, because the twofold subsists in the two. But undoubtedly the two and the twofold are not the same, otherwise one thing will be many -- a consequence which they actually drew. So much then may be learned from the earlier philosophers and from their successors.

i. 6; 987 b 10. And Plato only changed the name, for the Pythagoreans say that things exist by 'imitation' of numbers, but Plato, by 'participation.'

i. 6; 987 b 22. Plato concurred with the Pythagoreans in saying that the One is the real essence of things, and not something else with unity as an attribute. In harmony with them he affirms that Numbers are the principles of being for other things. But it is peculiar to him that instead of a single Indefinite he posits a double Indefinite, an Infinite of greatness and of littleness; and it is also peculiar to him that he separates Numbers from things that are seen, while they say that Numbers are the things themselves, and do not interpose mathematical objects between them. This separation of the One and Numbers from things, in contrast with the position of the Pythagoreans, and the introduction of Forms, are the consequence of his investigation by definitions.

xii. 7; 1072 b 31. And they are wrong who assume, as do the Pythagoreans and Speusippus, that the most beautiful and the best is not in the beginning of things, because the first principles of plants and animals are indeed causes, but that which is beautiful and perfect is in what comes from these first principles.

xiii. 4; 1078 b 21. The Pythagoreans [before Democritus] only defined a few things, the concepts of which they reduced to numbers, as for instance opportunity or justice or marriage...

xii. 6; 1080 b 16. The Pythagoreans say that there is but one number, the mathematical, but that things of sense are not separated from this, for they are composed of it; indeed, they construct the whole heaven out of numbers, but not out of abstract numbers, for they assume that the units have magnitude; but how the first unit was so constituted to have magnitude they seem at a loss to say.

xiii. 6; 1080 b 31. All, as many as regard the one as the element and first principle of things, except the Pythagoreans, assert that numbers are based on the unit; but the Pythagoreans assert, as has been remarked, that numbers have magnitude.

xiii. 8; 1083 b 9. The Pythagorean standpoint has on the one hand fewer difficulties than those that have been discussed, but it has new difficulties of its own. The fact that they do not regard number as separate removes many of the contradictions; but it is impossible that bodies should consist of numbers, and that this number should be mathematical. Nor is it true that indivisible elements have magnitude; but, granted that they have this quality of indivisibility, the units have no magnitude -- for how can magnitude be composed of indivisible elements? But arithmetical number consists of units. For these say that things are number; at least, they adapt their speculations to bodies as if they consist of numbers.

xiv. 3; 1090 a 20. On the other hand the Pythagoreans, because they see many qualities of numbers in bodies perceived by sense, regard objects as numbers, not as separate numbers, but as derived from numbers. And why? Because the qualities of numbers exist in a musical scale, in the heaven and in many other things. But for those who hold that number is mathematical only, it is impossible on the basis of their hypothesis to say any such thing, and it has already been remarked that there can be no science of these numbers. But we say, as above, that there is a science of numbers. Evidently the mathematical does not exist by itself, for in that case its qualities could not exist in bodies. In such a matter the Pythagoreans are restrained by nothing; when, however, they construct out of numbers physical bodies -- out of numbers that have neither weight nor lightness, bodies that have weight and lightness -- they seem to be speaking about another heaven and other bodies than those perceived by sense.

Moralia. i. 1; 1182 a 11. First Pythagoras attempted to speak concerning virtue, but he did not speak correctly; for bringing virtues into correspondence with numbers, he did not make any distinct.