[69] Schleiermacher, Einleitung zum Parmen. pp. 97-99.
[70] Indeed, the second demonstration, among the nine given by Parmenides (pp. 143 A, 155 C), coincides to a great degree with the conclusion which Zeno is represented as having maintained in his published dissertation (p. 127 E); and shows that the difficulties and contradictions belong to the world of invisible Ideas, as well as to that of sensible particulars, which Sokrates had called in question (p. 129 C-E).
The Aristotelian treatise (whether by Aristotle, Theophrastus, or any other author) De Zenone, Melisso, Xenophane, et Gorgiâ — affords some curious comparisons with the Parmenides of Plato. Aristotel. p. 974 seq. Bekk.; also Fragmenta Philosophorum Græcorum, ed. Didot, pp. 278-309.
Assumptions of Parmenides in his Demonstrations convey the minimum of determinate meaning. Views of Aristotle upon these indeterminate predicates, Ens, Unum, &c.
It may indeed be useful for the critic to perform for himself the process which Parmenides intended Sokrates to perform; and to analyse these subtleties with a view to measure their bearing upon the work of dogmatic theorising. We see double and contradictory conclusions elicited, in four separate Antinomies, from the same hypothesis, by distinct chains of interrogatory deduction; each question being sufficiently plausible to obtain the acquiescence of the respondent. The two assumptions successively laid down by Parmenides as principia for deduction — Si Unum est — Si Unum non est — convey the very minimum of determinate meaning. Indeed both words are essentially indeterminate. Both Unum and Ens are declared by Aristotle to be not univocal or generic words,[71] though at the same time not absolutely equivocal: but words bearing several distinct transitional meanings, derived either from each other, or from some common root, by an analogy more or less remote. Aristotle characterises in like manner all the most indeterminate predicates, which are not included in any one distinct category among the ten, but are made available to predication sometimes in one category, sometimes in another: such as Ens, Unum, Idem, Diversum, Contrarium, &c. Now in the Platonic Parmenides, the two first among these words are taken to form the proposition assumed as fundamental datum, and the remaining three are much employed in the demonstration: yet Plato neither notices nor discriminates their multifarious and fluctuating significations. Such contrast will be understood when we recollect that the purpose of the Platonic Parmenides is, to propound difficulties; while that of Aristotle is, not merely to propound, but also to assist in clearing them up.
[71] Aristot. Metaphys. iv. 1015-1017, ix. 1052, a. 15; Anal. Poster. ii. p. 92, b. 14. τὸ δ’ εἶναι οὐκ οὐσία οὐδενί. οὐ γὰρ γένος τὸ ὄν. — Topica, iv. p. 127, a. 28. πλείω γὰρ τὰ πᾶσιν ἑπόμενα· οἷον τὸ ὂν καὶ τὸ ἓν τῶν πᾶσιν ἑπομένων ἔστιν, Physica, i. p. 185, b. 6.
Simplikius noted it as one among the differences between Plato and Aristotle — That Plato admitted Unum as having only one meaning, not being aware of the diversity of meanings which it bore; while Aristotle expressly pointed it out as a πολλακῶς λεγόμενον (Schol. ad Aristot. Sophist. Elench. p. 320, b. 3, Brandis). Aristotle farther remarks that Plato considered τὸ γένος as ἓν ἀριθμῷ, and that this was an error; we ought rather to say that Plato did not clearly discriminate ἓν ἀριθμῷ from ἓν εἴδει (Aristot. Topic. vi. 143, b. 30).
Simplikius farther remarks, that it was Aristotle who first rendered to Logic the important service of bringing out clearly and emphatically the idea of τὸ ὁμώνυμον — the same word with several meanings either totally distinct and disparate, or ramifying in different directions from the same root, so that there came to be little or no affinity between many of them. It was Aristotle who first classified and named these distinctions (συνώνυμον — ὁμώνυμον, and the intermediate κατ’ ἀναλογίαν), though they had been partially noticed by Plato and even by Sokrates. ἕως Ἀριστοτέλους οὐ πάμπαν ἔκδηλον ἦν τὸ ὁμώνυμον· ἀλλὰ Πλάτων τε ἤρξατο περὶ τούτου ἢ μᾶλλον ἐκείνου Σωκράτης, Schol. ad Aristot. Physic. p. 323, b. 24, Brandis.
In the Platonic Demonstrations the same proposition in words is made to bear very different meanings.
Certainly, in Demonstrations 1 and 2 (as well as 4 and 5), the foundation assumed is in words the same proposition — Si Unum est: but we shall find this same proposition used in two very different senses. In the first Demonstration, the proposition is equivalent to Si Unum est Unum:[72] in the second, to Si Unum est Ens, or Si Unum existit. In the first the proposition is identical and the verb est serves only as copula: in the second, the verb est is not merely a copula but implies Ens as a predicate, and affirms existence. We might have imagined that the identical proposition — Unum est Unum — since it really affirms nothing — would have been barren of all consequences: and so indeed it is barren of all affirmative consequences. But Plato obtains for it one first step in the way of negative predicates — Si Unum est Unum, Unum non est Multa: and from hence he proceeds, by a series of gentle transitions ingeniously managed, to many other negative predications respecting the subject Unum. Since it is not Multa, it can have no parts, nor can it be a whole: it has neither beginning, middle, nor end: it has no boundary, or it is boundless: it has no figure, it is neither straight nor circular: it has therefore no place, being neither in itself, nor in anything else: it is neither in motion nor at rest: it is neither the same with anything else, nor the same with itself:[73] it is neither different from any thing else, nor different from itself: it is neither like, nor unlike, to itself, nor to anything else: it is neither equal, nor unequal, to itself nor to any thing else: it is neither older nor younger, nor of equal age, either with itself or with anything else: it exists therefore not in time, nor has it any participation with time: it neither has been nor will be, nor is: it does not exist in any way: it does not even exist so as to be Unum: you can neither name it, nor reason upon it, nor know it, nor perceive it, nor opine about it.