Demonstration VII. is founded upon the genuine doctrine of Parmenides.
These two last counter-demonstrations (6 and 7), forming the third Antinomy, deserve attention in this respect — That the seventh is founded upon the genuine Parmenidean or Eleatic doctrine about Non-Ens, as not merely having no attributes, but as being unknowable, unperceivable, unnameable: while the sixth is founded upon a different apprehension of Non-Ens, which is explained and defended by Plato in the Sophistes, as a substitute for, and refutation of, the Eleatic doctrine.[100] According to Number 7, when you deny, of Unum, the predicate existence, you deny of it also all other predicates: and the name Unum is left without any subject to apply to. This is the Eleatic dogma. Unum having been declared to be Non-Ens, is (like Non-Ens) neither knowable nor nameable. According to Number 6, the proposition Unum est non-Ens, does not carry with it any such consequences. Existence is only one predicate, which may be denied of the subject Unum, but which, when denied, does not lead to the denial of all other predicates — nor, therefore, to the loss of the subject itself. Unum still remains Unum, knowable, and different from other things. Upon this first premiss are built up several other affirmations; so that we thus arrive circuitously at the affirmation of existence, in a certain way: Unum, though non-existent, does nevertheless exist quodam modo. This coincides with that which the Eleatic stranger seeks to prove in the Sophistes, against Parmenides.
[100] Plato, Sophistes, pp. 258-259.
Demonstrations VI. and VII. considered — Unwarrantable steps in the reasoning — The fundamental premiss differently interpreted, though the same in words.
If we compare the two foregoing counter-demonstrations (7 and 6), we shall see that the negative results of the seventh follow properly enough from the assumed premisses: but that the affirmative results of the sixth are not obtained without very unwarrantable jumps in the reasoning, besides its extreme subtlety. But apart from this defect, we farther remark that here also (as in Numbers 1 and 2) the fundamental principle assumed is in terms the same, in signification materially different. The signification of Unum non est, as it is construed in Number 7, is the natural one, belonging to the words: but as construed in Number 6, the meaning of the predicate is altogether effaced (as it had been before in Number 1): we cannot tell what it is which is really denied about Unum. As, in Number 1, the proposition Unum est is so construed as to affirm nothing except Unum est Unum — so in Number 7, the proposition Unum non est is so construed as to deny nothing except Unum non est Unum, yet conveying along with such denial a farther affirmation — Unum non est Unum, sed tamen est aliquid scibile, differens ab aliis.[101] Here this aliquid scibile is assumed as a substratum underlying Unum, and remaining even when Unum is taken away: contrary to the opinion — that Unum was a separate nature and the fundamental Subject of all — which Aristotle announces as having been held by Plato.[102] There must be always some meaning (the Platonic Parmenides argues) attached to the word Unum, even when you talk of Unum non Ens: and that meaning is equivalent to Aliquid scibile, differens ab aliis. From this he proceeds to evolve, step by step, though often in a manner obscure and inconclusive, his series of contradictory affirmations respecting Unum.
[101] Plato, Parmenid. p. 160 C.
[102] Aristot. Metaph. B. 1001, a. 6-20.
The last couple of Demonstrations — 8 and 9 — composing the fourth Antinomy, are in some respects the most ingenious and singular of all the nine. Si Unum non est, what is true about Cætera? The eighth demonstrates the Both of the affirmative predicates, the ninth proves the Neither.
Demonstrations VIII. and IX. — Analysis of Demonstration VIII.
Si Unum non est (is the argument of the eighth), Cætera must nevertheless somehow still be Cætera: otherwise you could not talk about Cætera.[103] (This is an argument like that in Demonstration 6: What is talked about must exist, somehow.) But if Cætera can be named and talked about, they must be different from something, — and from something, which is also different from them. What can this Something be? Not certainly Unum: for Unum, by the Hypothesis, does not exist, and cannot therefore be the term of comparison. Cætera therefore must be different among themselves and from each other. But they cannot be compared with each other by units: for Unum does not exist. They must therefore be compared with each other by heaps or multitudes: each of which will appear at first sight to be an unit, though it be not an unit in reality. There will be numbers of such heaps, each in appearance one, though not in reality:[104] numbers odd and even, great and little, in appearance: heaps appearing to be greater and less than each other, and equal to each other, though not being really so. Each of these heaps will appear to have a beginning, middle, and end, yet will not really have any such: for whenever you grasp any one of them in your thoughts, there will appear another beginning before the beginning,[105] another end after the end, another centre more centrical than the centre, — minima ever decreasing because you cannot reach any stable unit. Each will be a heap without any unity; looking like one, at a distance, — but when you come near, each a boundless and countless multitude. They will thus appear one and many, like and unlike, equal and unequal, at rest and moving, separate and coalescing: in short, invested with an indefinite number of opposite attributes.[106]