We may begin by remarking that the theses of Parmenides are expressly said to follow the method of Zeno, and that the complex dilemma, though declared to be capable of universal application, is applied in this instance to Zeno's familiar question of the 'one and many.' Here, then, is a double indication of the connexion of the Parmenides with the Eristic school. The old Eleatics had asserted the existence of Being, which they at first regarded as finite, then as infinite, then as neither finite nor infinite, to which some of them had given what Aristotle calls 'a form,' others had ascribed a material nature only. The tendency of their philosophy was to deny to Being all predicates. The Megarians, who succeeded them, like the Cynics, affirmed that no predicate could be asserted of any subject; they also converted the idea of Being into an abstraction of Good, perhaps with the view of preserving a sort of neutrality or indifference between the mind and things. As if they had said, in the language of modern philosophy: 'Being is not only neither finite nor infinite, neither at rest nor in motion, but neither subjective nor objective.'
This is the track along which Plato is leading us. Zeno had attempted to prove the existence of the one by disproving the existence of the many, and Parmenides seems to aim at proving the existence of the subject by showing the contradictions which follow from the assertion of any predicates. Take the simplest of all notions, 'unity'; you cannot even assert being or time of this without involving a contradiction. But is the contradiction also the final conclusion? Probably no more than of Zeno's denial of the many, or of Parmenides' assault upon the Ideas; no more than of the earlier dialogues 'of search.' To us there seems to be no residuum of this long piece of dialectics. But to the mind of Parmenides and Plato, 'Gott-betrunkene Menschen,' there still remained the idea of 'being' or 'good,' which could not be conceived, defined, uttered, but could not be got rid of. Neither of them would have imagined that their disputation ever touched the Divine Being (compare Phil.). The same difficulties about Unity and Being are raised in the Sophist; but there only as preliminary to their final solution.
If this view is correct, the real aim of the hypotheses of Parmenides is to criticize the earlier Eleatic philosophy from the point of view of Zeno or the Megarians. It is the same kind of criticism which Plato has extended to his own doctrine of Ideas. Nor is there any want of poetical consistency in attributing to the 'father Parmenides' the last review of the Eleatic doctrines. The latest phases of all philosophies were fathered upon the founder of the school.
Other critics have regarded the final conclusion of the Parmenides either as sceptical or as Heracleitean. In the first case, they assume that Plato means to show the impossibility of any truth. But this is not the spirit of Plato, and could not with propriety be put into the mouth of Parmenides, who, in this very dialogue, is urging Socrates, not to doubt everything, but to discipline his mind with a view to the more precise attainment of truth. The same remark applies to the second of the two theories. Plato everywhere ridicules (perhaps unfairly) his Heracleitean contemporaries: and if he had intended to support an Heracleitean thesis, would hardly have chosen Parmenides, the condemner of the 'undiscerning tribe who say that things both are and are not,' to be the speaker. Nor, thirdly, can we easily persuade ourselves with Zeller that by the 'one' he means the Idea; and that he is seeking to prove indirectly the unity of the Idea in the multiplicity of phenomena.
We may now endeavour to thread the mazes of the labyrinth which Parmenides knew so well, and trembled at the thought of them.
The argument has two divisions: There is the hypothesis that
1. One is.
2. One is not.
If one is, it is nothing.
If one is not, it is everything.
But is and is not may be taken in two senses:
Either one is one,
Or, one has being,
from which opposite consequences are deduced,
1. a. If one is one, it is nothing.
1. b. If one has being, it is all things.
To which are appended two subordinate consequences:
1. aa. If one has being, all other things are.
1. bb. If one is one, all other things are not.
The same distinction is then applied to the negative hypothesis:
2. a. If one is not one, it is all things.
2. b. If one has not being, it is nothing.
Involving two parallel consequences respecting the other or remainder:
2. aa. If one is not one, other things are all.
2. bb. If one has not being, other things are not.
…
'I cannot refuse,' said Parmenides, 'since, as Zeno remarks, we are alone, though I may say with Ibycus, who in his old age fell in love, I, like the old racehorse, tremble at the prospect of the course which I am to run, and which I know so well. But as I must attempt this laborious game, what shall be the subject? Suppose I take my own hypothesis of the one.' 'By all means,' said Zeno. 'And who will answer me? Shall I propose the youngest? he will be the most likely to say what he thinks, and his answers will give me time to breathe.' 'I am the youngest,' said Aristoteles, 'and at your service; proceed with your questions.' – The result may be summed up as follows: —
1. a. One is not many, and therefore has no parts, and therefore is not a whole, which is a sum of parts, and therefore has neither beginning, middle, nor end, and is therefore unlimited, and therefore formless, being neither round nor straight, for neither round nor straight can be defined without assuming that they have parts; and therefore is not in place, whether in another which would encircle and touch the one at many points; or in itself, because that which is self-containing is also contained, and therefore not one but two. This being premised, let us consider whether one is capable either of motion or rest. For motion is either change of substance, or motion on an axis, or from one place to another. But the one is incapable of change of substance, which implies that it ceases to be itself, or of motion on an axis, because there would be parts around the axis; and any other motion involves change of place. But existence in place has been already shown to be impossible; and yet more impossible is coming into being in place, which implies partial existence in two places at once, or entire existence neither within nor without the same; and how can this be? And more impossible still is the coming into being either as a whole or parts of that which is neither a whole nor parts. The one, then, is incapable of motion. But neither can the one be in anything, and therefore not in the same, whether itself or some other, and is therefore incapable of rest. Neither is one the same with itself or any other, or other than itself or any other. For if other than itself, then other than one, and therefore not one; and, if the same with other, it would be other, and other than one. Neither can one while remaining one be other than other; for other, and not one, is the other than other. But if not other by virtue of being one, not by virtue of itself; and if not by virtue of itself, not itself other, and if not itself other, not other than anything. Neither will one be the same with itself. For the nature of the same is not that of the one, but a thing which becomes the same with anything does not become one; for example, that which becomes the same with the many becomes many and not one. And therefore if the one is the same with itself, the one is not one with itself; and therefore one and not one. And therefore one is neither other than other, nor the same with itself. Neither will the one be like or unlike itself or other; for likeness is sameness of affections, and the one and the same are different. And one having any affection which is other than being one would be more than one. The one, then, cannot have the same affection with and therefore cannot be like itself or other; nor can the one have any other affection than its own, that is, be unlike itself or any other, for this would imply that it was more than one. The one, then, is neither like nor unlike itself or other. This being the case, neither can the one be equal or unequal to itself or other. For equality implies sameness of measure, as inequality implies a greater or less number of measures. But the one, not having sameness, cannot have sameness of measure; nor a greater or less