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 connection 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 “Philebus” 22 C). The same difficulties about Unity and Being are raised in the “Sophist” (250 and following); 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
I. One is.
II. 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,
I.a. If one is one, it is nothing (137 C–142 B).
I.b. If one has being, it is all things (142 B–157 B).
To which are appended two subordinate consequences:
I.aa. If one has being, all other things are (157 B–159 B).
I.bb. If one is one, all other things are not (159 B–160 B).
The same distinction is then applied to the negative hypothesis:
II.a. If one is not one, it is all things (160 B–163 B).
II.b. If one has not being, it is nothing (163 B–164 B).
Involving two parallel consequences respecting the other or remainder:
II.aa. If one is not one, other things are all (164 B–165 E).
II.bb. If one has not being, other things are not (165 E to the end).
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