Socrates attempts to support his view of the ideas by the parallel of the day, which is one and in many places; but he is easily driven from his position by a counter illustration of Parmenides, who compares the idea of greatness to a sail. He truly explains to Socrates that he has attained the conception of ideas by a process of generalization. At the same time, he points out a difficulty, which appears to be involved – viz. that the process of generalization will go on to infinity. Socrates meets the supposed difficulty by a flash of light, which is indeed the true answer 'that the ideas are in our minds only.' Neither realism is the truth, nor nominalism is the truth, but conceptualism; and conceptualism or any other psychological theory falls very far short of the infinite subtlety of language and thought.
But the realism of ancient philosophy will not admit of this answer, which is repelled by Parmenides with another truth or half-truth of later philosophy, 'Every subject or subjective must have an object.' Here is the great though unconscious truth (shall we say?) or error, which underlay the early Greek philosophy. 'Ideas must have a real existence;' they are not mere forms or opinions, which may be changed arbitrarily by individuals. But the early Greek philosopher never clearly saw that true ideas were only universal facts, and that there might be error in universals as well as in particulars.
Socrates makes one more attempt to defend the Platonic Ideas by representing them as paradigms; this is again answered by the 'argumentum ad infinitum.' We may remark, in passing, that the process which is thus described has no real existence. The mind, after having obtained a general idea, does not really go on to form another which includes that, and all the individuals contained under it, and another and another without end. The difficulty belongs in fact to the Megarian age of philosophy, and is due to their illogical logic, and to the general ignorance of the ancients respecting the part played by language in the process of thought. No such perplexity could ever trouble a modern metaphysician, any more than the fallacy of 'calvus' or 'acervus,' or of 'Achilles and the tortoise.' These 'surds' of metaphysics ought to occasion no more difficulty in speculation than a perpetually recurring fraction in arithmetic.
It is otherwise with the objection which follows: How are we to bridge the chasm between human truth and absolute truth, between gods and men? This is the difficulty of philosophy in all ages: How can we get beyond the circle of our own ideas, or how, remaining within them, can we have any criterion of a truth beyond and independent of them? Parmenides draws out this difficulty with great clearness. According to him, there are not only one but two chasms: the first, between individuals and the ideas which have a common name; the second, between the ideas in us and the ideas absolute. The first of these two difficulties mankind, as we may say, a little parodying the language of the Philebus, have long agreed to treat as obsolete; the second remains a difficulty for us as well as for the Greeks of the fourth century before Christ, and is the stumbling-block of Kant's Kritik, and of the Hamiltonian adaptation of Kant, as well as of the Platonic ideas. It has been said that 'you cannot criticize Revelation.' 'Then how do you know what is Revelation, or that there is one at all,' is the immediate rejoinder – 'You know nothing of things in themselves.' 'Then how do you know that there are things in themselves?' In some respects, the difficulty pressed harder upon the Greek than upon ourselves. For conceiving of God more under the attribute of knowledge than we do, he was more under the necessity of separating the divine from the human, as two spheres which had no communication with one another.
It is remarkable that Plato, speaking by the mouth of Parmenides, does not treat even this second class of difficulties as hopeless or insoluble. He says only that they cannot be explained without a long and laborious demonstration: 'The teacher will require superhuman ability, and the learner will be hard of understanding.' But an attempt must be made to find an answer to them; for, as Socrates and Parmenides both admit, the denial of abstract ideas is the destruction of the mind. We can easily imagine that among the Greek schools of philosophy in the fourth century before Christ a panic might arise from the denial of universals, similar to that which arose in the last century from Hume's denial of our ideas of cause and effect. Men do not at first recognize that thought, like digestion, will go on much the same, notwithstanding any theories which may be entertained respecting the nature of the process. Parmenides attributes the difficulties in which Socrates is involved to a want of comprehensiveness in his mode of reasoning; he should consider every question on the negative as well as the positive hypothesis, with reference to the consequences which flow from the denial as well as from the assertion of a given statement.
The argument which follows is the most singular in Plato. It appears to be an imitation, or parody, of the Zenonian dialectic, just as the speeches in the Phaedrus are an imitation of the style of Lysias, or as the derivations in the Cratylus or the fallacies of the Euthydemus are a parody of some contemporary Sophist. The interlocutor is not supposed, as in most of the other Platonic dialogues, to take a living part in the argument; he is only required to say 'Yes' and 'No' in the right places. A hint has been already given that the paradoxes of Zeno admitted of a higher application. This hint is the thread by which Plato connects the two parts of the dialogue.
The paradoxes of Parmenides seem trivial to us, because the words to which they relate have become trivial; their true nature as abstract terms is perfectly understood by us, and we are inclined to regard the treatment of them in Plato as a mere straw-splitting, or legerdemain of words. Yet there was a power in them which fascinated the Neoplatonists for centuries afterwards. Something that they found in them, or brought to them – some echo or anticipation of a great truth or error, exercised a wonderful influence over their minds. To do the Parmenides justice, we should imagine similar aporiai raised on themes as sacred to us, as the notions of One or Being were to an ancient Eleatic. 'If God is, what follows? If God is not, what follows?' Or again: If God is or is not the world; or if God is or is not many, or has or has not parts, or is or is not in the world, or in time; or is or is not finite or infinite. Or if the world is or is not; or has or has not a beginning or end; or is or is not infinite, or infinitely divisible. Or again: if God is or is not identical with his laws; or if man is or is not identical with the laws of nature. We can easily see that here are many subjects for thought, and that from these and similar hypotheses questions of great interest might arise. And we also remark, that the conclusions derived from either of the two alternative propositions might be equally impossible and contradictory.
When we ask what is the object of these paradoxes, some have answered that they are a mere logical puzzle, while others have seen in them an Hegelian propaedeutic of the doctrine of Ideas. The first of these views derives support from the manner in which Parmenides speaks of a similar method being applied to all Ideas. Yet it is hard to suppose that Plato would have furnished so elaborate an example, not of his own but of the Eleatic dialectic, had he intended only to give an illustration of method. The second view has been often overstated by those who, like Hegel himself, have tended to confuse ancient with modern philosophy. We need not deny that Plato, trained in the school of Cratylus and Heracleitus, may have seen that a contradiction in terms is sometimes the best expression of a truth higher than either (compare Soph.). But his ideal theory is not based on antinomies. The correlation of Ideas was the metaphysical difficulty of the age in which he lived; and the Megarian and Cynic philosophy was a 'reductio ad absurdum' of their isolation. To restore them to their natural connexion and to detect the negative element in them is the aim of Plato in the Sophist. But his view of their connexion falls very far short of the Hegelian identity of Being and Not-being. The Being and Not-being of Plato never merge in each other, though he is aware that 'determination is only negation.'
After criticizing the hypotheses of others, it may appear presumptuous to add another guess to the many which have been already offered. May we say, in Platonic language, that we still seem to see vestiges of a track which has not yet been taken? It is quite possible that the obscurity of the Parmenides would not have existed to a contemporary student of philosophy, and, like the similar difficulty in the Philebus, is really due to our ignorance of the mind of the age. There is an obscure Megarian influence on Plato which cannot wholly be cleared up, and