[124] Since the time of Aristotle, the quality of a proposition has been understood to designate its being either affirmative or negative: that being formal, or belonging to its form only. Whether affirmative or negative, it may be true or false: and this is doubtless a quality, but belonging to its matter, not to its form. Plato seems to have taken no account of the formal distinction, negative or affirmative.
I shall now say a few words on Plato’s explanation of Non-Ens. It is given at considerable length, and was, in the judgment of Schleiermacher, eminently satisfactory to Plato himself. Some of Plato’s expressions[125] lead me to suspect that his satisfaction was not thus unqualified: but whether he was himself satisfied or not, I cannot think that the explanation ought to satisfy others.
[125] Plato, Sophistês, p. 259 A-B. Schleiermacher, Einleitung zum Sophistes, vol. iv. p. 134, of his translation of Plato.
Plato’s explanation of Non-Ens is not satisfactory — Objections to it.
Plato here lays down the position — That the word Not signifies nothing more than difference, with respect to that other word to which it is attached. It does not signify (he says) what is contrary; but simply what is different. Not-great, Not-beautiful — mean what is different from great or beautiful: Non-Ens means, not what is contrary to Ens, but simply what is different from Ens.
First, then, even if we admit that Non-Ens has this latter meaning and nothing beyond — yet when we turn to Plato’s own definition of Ens, we shall find it so all-comprehensive, that there can be absolutely nothing different from Ens:— these last words can have no place and no meaning. Plato defines Ens so as to include all that is knowable, conceivable, thinkable.[126] One portion of this total differs from another: but there can be nothing which differs from it all. The Form or nature of Diversum (to use Plato’s phrase) as it is among the knowable or conceivable, is already included in the total of Ens, and comes into communion (according to the Platonic phraseology) with one portion of that total as against another portion. But with Ens as a whole, it cannot come into communion, for there is nothing apart from Ens. Whenever we try to think of any thing apart from Ens, we do by the act of thought include it in Ens, as defined by Plato. Different from great — different from white (i.e. not great, not white, sensu Platonico) is very intelligible: but Different from Ens, is not intelligible: there is nothing except the inconceivable and incomprehensible: the words professing to describe it, are mere unmeaning sound. Now this is just[127] what Parmenides said about Non-Ens. Plato’s definition of Ens appears to me to make out the case of Parmenides about Non-Ens; and to render the Platonic explanation — different from Ens — open to quite as many difficulties, as those which attach to Non-Ens in the ordinary sense.
[126] Plato, Sophist. pp. 247-248.
[127] Compare Kratylus, 430 A.
Secondly, there is an objection still graver against Plato’s explanation. When he resolves negation into an affirmation of something different from what is denied, he effaces or puts out of sight one of the capital distinctions of logic. What he says is indeed perfectly true: Not-great, Not-beautiful, Non-Ens, are respectively different from great, beautiful, Ens. But this, though true, is only a part of the truth; leaving unsaid another portion of the truth which, while equally essential, is at the same time special and characteristic. The negative not only differs from the affirmative, but has such peculiar meaning of its own, as to exclude the affirmative: both cannot be true together. Not-great is certainly different from great: so also, white, hard, rough, just, valiant, &c, are all different from great. But there is nothing in these latter epithets to exclude the co-existence of great. Theætêtus is great — Theætêtus is white; in the second of these two propositions I affirm something respecting Theætêtus quite different from what I affirm in the first, yet nevertheless noway excluding what is affirmed in the first.[128] The two propositions may both be true. But when I say — Theætêtus is dead — Theætêtus is not dead: here are two propositions which cannot both be true, from the very form of the words. To explain not-great, as Plato does, by saying that it means only something different from great,[129] is to suppress this peculiar meaning and virtue of the negative, whereby it simply excludes the affirmative, without affirming any thing in its place. Plato is right in saying that not-great does not affirm the contrary of great, by which he means little.[130] The negative does not affirm any thing: it simply denies. Plato seems to consider the negative as a species of affirmative:[131] only affirming something different from what is affirmed by the term which it accompanies. Not-Great, Not-Beautiful, Not-Just — he declares to be Forms just as real and distinct as Great, Beautiful, Just: only different from these latter. This, in my opinion, is a conception logically erroneous. Negative stands opposed to affirmative, as one of the modes of distributing both terms and propositions. A purely negative term cannot stand alone in the subject of a proposition: Non-Entis nulla sunt prædicata — was the scholastic maxim. The apparent exceptions to this rule arise only from the fact, that many terms negative in their form have taken on an affirmative signification.
[128] Proklus, in his Commentary on the Parmenidês (p. 281, p. 785, Stallbaum), says, with reference to the doctrine laid down by Plato in the Sophistês, ὅλως γὰρ αἱ ἀποθάσεις ἐγγονοί εἰσι τῆς ἑτερότητος τῆς νοερᾶς· διὰ τοῦτο γὰρ οὐχ ἵππος, ὅτι ἕτερον — καὶ διὰ τοῦτο οὐκ ἄνθρωπος, ὅτι ἄλλο.