The answer is, that in these and all other determinations of any notion we are attributing to it 'Not-being.' We went in search of Not-being and seemed to lose Being, and now in the hunt after Being we recover both. Not-being is a kind of Being, and in a sense co-extensive with Being. And there are as many divisions of Not-being as of Being. To every positive idea 'just,' 'beautiful,' and the like, there is a corresponding negative idea 'not-just,' 'not-beautiful,' and the like.
A doubt may be raised whether this account of the negative is really the true one. The common logicians would say that the 'not-just,' 'not-beautiful,' are not really classes at all, but are merged in one great class of the infinite or negative. The conception of Plato, in the days before logic, seems to be more correct than this. For the word 'not' does not altogether annihilate the positive meaning of the word 'just': at least, it does not prevent our looking for the 'not-just' in or about the same class in which we might expect to find the 'just.' 'Not-just is not-honourable' is neither a false nor an unmeaning proposition. The reason is that the negative proposition has really passed into an undefined positive. To say that 'not-just' has no more meaning than 'not-honourable' that is to say, that the two cannot in any degree be distinguished, is clearly repugnant to the common use of language.
The ordinary logic is also jealous of the explanation of negation as relation, because seeming to take away the principle of contradiction. Plato, as far as we know, is the first philosopher who distinctly enunciated this principle; and though we need not suppose him to have been always consistent with himself, there is no real inconsistency between his explanation of the negative and the principle of contradiction. Neither the Platonic notion of the negative as the principle of difference, nor the Hegelian identity of Being and Not-being, at all touch the principle of contradiction. For what is asserted about Being and Not-Being only relates to our most abstract notions, and in no way interferes with the principle of contradiction employed in the concrete. Because Not-being is identified with Other, or Being with Not-being, this does not make the proposition 'Some have not eaten' any the less a contradiction of 'All have eaten.'
The explanation of the negative given by Plato in the Sophist is a true but partial one; for the word 'not,' besides the meaning of 'other,' may also imply 'opposition.' And difference or opposition may be either total or partial: the not-beautiful may be other than the beautiful, or in no relation to the beautiful, or a specific class in various degrees opposed to the beautiful. And the negative may be a negation of fact or of thought (ou and me). Lastly, there are certain ideas, such as 'beginning,' 'becoming,' 'the finite,' 'the abstract,' in which the negative cannot be separated from the positive, and 'Being' and 'Not-being' are inextricably blended.
Plato restricts the conception of Not-being to difference. Man is a rational animal, and is not as many other things as are not included under this definition. He is and is not, and is because he is not. Besides the positive class to which he belongs, there are endless negative classes to which he may be referred. This is certainly intelligible, but useless. To refer a subject to a negative class is unmeaning, unless the 'not' is a mere modification of the positive, as in the example of 'not honourable' and 'dishonourable'; or unless the class is characterized by the absence rather than the presence of a particular quality.
Nor is it easy to see how Not-being any more than Sameness or Otherness is one of the classes of Being. They are aspects rather than classes of Being. Not-being can only be included in Being, as the denial of some particular class of Being. If we attempt to pursue such airy phantoms at all, the Hegelian identity of Being and Not-being is a more apt and intelligible expression of the same mental phenomenon. For Plato has not distinguished between the Being which is prior to Not-being, and the Being which is the negation of Not-being (compare Parm.).
But he is not thinking of this when he says that Being comprehends Not-being. Again, we should probably go back for the true explanation to the influence which the Eleatic philosophy exercised over him. Under 'Not-being' the Eleatic had included all the realities of the sensible world. Led by this association and by the common use of language, which has been already noticed, we cannot be much surprised that Plato should have made classes of Not-being. It is observable that he does not absolutely deny that there is an opposite of Being. He is inclined to leave the question, merely remarking that the opposition, if admissible at all, is not expressed by the term 'Not-being.'
On the whole, we must allow that the great service rendered by Plato to metaphysics in the Sophist, is not his explanation of 'Not-being' as difference. With this he certainly laid the ghost of 'Not-being'; and we may attribute to him in a measure the credit of anticipating Spinoza and Hegel. But his conception is not clear or consistent; he does not recognize the different senses of the negative, and he confuses the different classes of Not-being with the abstract notion. As the Pre-Socratic philosopher failed to distinguish between the universal and the true, while he placed the particulars of sense under the false and apparent, so Plato appears to identify negation with falsehood, or is unable to distinguish them. The greatest service rendered by him to mental science is the recognition of the communion of classes, which, although based by him on his account of 'Not-being,' is independent of it. He clearly saw that the isolation of ideas or classes is the annihilation of reasoning. Thus, after wandering in many diverging paths, we return to common sense. And for this reason we may be inclined to do less than justice to Plato, because the truth which he attains by a real effort of thought is to us a familiar and unconscious truism, which no one would any longer think either of doubting or examining.
IV. The later dialogues of Plato contain many references to contemporary philosophy. Both in the Theaetetus and in the Sophist he recognizes that he is in the midst of a fray; a huge irregular battle everywhere surrounds him (Theaet.). First, there are the two great philosophies going back into cosmogony and poetry: the philosophy of Heracleitus, supposed to have a poetical origin in Homer, and that of the Eleatics, which in a similar spirit he conceives to be even older than Xenophanes (compare Protag.). Still older were theories of two and three principles, hot and cold, moist and dry, which were ever marrying and being given in marriage: in speaking of these, he is probably referring to Pherecydes and the early Ionians. In the philosophy of motion there were different accounts of the relation of plurality and unity, which were supposed to be joined and severed by love and hate, some maintaining that this process was perpetually going on (e.g. Heracleitus); others (e.g. Empedocles) that there was an alternation of them. Of the Pythagoreans or of Anaxagoras he makes no distinct mention. His chief opponents are, first, Eristics or Megarians; secondly, the Materialists.
The picture which he gives of both these latter schools is indistinct; and he appears reluctant to mention the names of their teachers. Nor can we easily determine how much is to be assigned to the Cynics, how much to the Megarians, or whether the 'repellent Materialists' (Theaet.) are Cynics or Atomists, or represent some unknown phase of opinion at Athens. To the Cynics and Antisthenes is commonly attributed, on the authority of Aristotle, the denial of predication, while the Megarians are said to have been Nominalists, asserting the One Good under many names to be the true Being of Zeno and the Eleatics, and, like Zeno, employing their negative dialectic in the refutation of opponents. But the later Megarians also denied predication; and this tenet, which is attributed to all of them by Simplicius, is certainly in accordance with their over-refining philosophy. The 'tyros young and old,' of whom Plato speaks, probably include both. At any rate, we shall be safer in accepting the general description of them which he has given, and in not attempting to draw a precise line between them.