IV. The one and the many or others are reduced to their strictest arithmetical meaning. That one is three or three one, is a proposition which has, perhaps, given rise to more controversy in the world than any other. But no one has ever meant to say that three and one are to be taken in the same sense. Whereas the one and many of the Parmenides have precisely the same meaning; there is no notion of one personality or substance having many attributes or qualities. The truth seems to be rather the opposite of that which Socrates implies: There is no contradiction in the concrete, but in the abstract; and the more abstract the idea, the more palpable will be the contradiction. For just as nothing can persuade us that the number one is the number three, so neither can we be persuaded that any abstract idea is identical with its opposite, although they may both inhere together in some external object, or some more comprehensive conception. Ideas, persons, things may be one in one sense and many in another, and may have various degrees of unity and plurality. But in whatever sense and in whatever degree they are one they cease to be many; and in whatever degree or sense they are many they cease to be one.
Two points remain to be considered: 1st, the connexion between the first and second parts of the dialogue; 2ndly, the relation of the Parmenides to the other dialogues.
I. In both divisions of the dialogue the principal speaker is the same, and the method pursued by him is also the same, being a criticism on received opinions: first, on the doctrine of Ideas; secondly, of Being. From the Platonic Ideas we naturally proceed to the Eleatic One or Being which is the foundation of them. They are the same philosophy in two forms, and the simpler form is the truer and deeper. For the Platonic Ideas are mere numerical differences, and the moment we attempt to distinguish between them, their transcendental character is lost; ideas of justice, temperance, and good, are really distinguishable only with reference to their application in the world. If we once ask how they are related to individuals or to the ideas of the divine mind, they are again merged in the aboriginal notion of Being. No one can answer the questions which Parmenides asks of Socrates. And yet these questions are asked with the express acknowledgment that the denial of ideas will be the destruction of the human mind. The true answer to the difficulty here thrown out is the establishment of a rational psychology; and this is a work which is commenced in the Sophist. Plato, in urging the difficulty of his own doctrine of Ideas, is far from denying that some doctrine of Ideas is necessary, and for this he is paving the way.
In a similar spirit he criticizes the Eleatic doctrine of Being, not intending to deny Ontology, but showing that the old Eleatic notion, and the very name 'Being,' is unable to maintain itself against the subtleties of the Megarians. He did not mean to say that Being or Substance had no existence, but he is preparing for the development of his later view, that ideas were capable of relation. The fact that contradictory consequences follow from the existence or non-existence of one or many, does not prove that they have or have not existence, but rather that some different mode of conceiving them is required. Parmenides may still have thought that 'Being was,' just as Kant would have asserted the existence of 'things in themselves,' while denying the transcendental use of the Categories.
Several lesser links also connect the first and second parts of the dialogue: (1) The thesis is the same as that which Zeno has been already discussing: (2) Parmenides has intimated in the first part, that the method of Zeno should, as Socrates desired, be extended to Ideas: (3) The difficulty of participating in greatness, smallness, equality is urged against the Ideas as well as against the One.
II. The Parmenides is not only a criticism of the Eleatic notion of Being, but also of the methods of reasoning then in existence, and in this point of view, as well as in the other, may be regarded as an introduction to the Sophist. Long ago, in the Euthydemus, the vulgar application of the 'both and neither' Eristic had been subjected to a similar criticism, which there takes the form of banter and irony, here of illustration.
The attack upon the Ideas is resumed in the Philebus, and is followed by a return to a more rational philosophy. The perplexity of the One and Many is there confined to the region of Ideas, and replaced by a theory of classification; the Good arranged in classes is also contrasted with the barren abstraction of the Megarians. The war is carried on against the Eristics in all the later dialogues, sometimes with a playful irony, at other times with a sort of contempt. But there is no lengthened refutation of them. The Parmenides belongs to that stage of the dialogues of Plato in which he is partially under their influence, using them as a sort of 'critics or diviners' of the truth of his own, and of the Eleatic theories. In the Theaetetus a similar negative dialectic is employed in the attempt to define science, which after every effort remains undefined still. The same question is revived from the objective side in the Sophist: Being and Not-being are no longer exhibited in opposition, but are now reconciled; and the true nature of Not-being is discovered and made the basis of the correlation of ideas. Some links are probably missing which might have been supplied if we had trustworthy accounts of Plato's oral teaching.
To sum up: the Parmenides of Plato is a critique, first, of the Platonic Ideas, and secondly, of the Eleatic doctrine of Being. Neither are absolutely denied. But certain difficulties and consequences are shown in the assumption of either, which prove that the Platonic as well as the Eleatic doctrine must be remodelled. The negation and contradiction which are involved in the conception of the One and Many are preliminary to their final adjustment. The Platonic Ideas are tested by the interrogative method of Socrates; the Eleatic One or Being is tried by the severer and perhaps impossible method of hypothetical consequences, negative and affirmative. In the latter we have an example of the Zenonian or Megarian dialectic, which proceeded, not 'by assailing premises, but conclusions'; this is worked out and improved by Plato. When primary abstractions are used in every conceivable sense, any or every conclusion may be deduced from them. The words 'one,' 'other,' 'being,' 'like,' 'same,' 'whole,' and their opposites, have slightly different meanings, as they are applied to objects of thought or objects of sense—to number, time, place, and to the higher ideas of the reason;—and out of their different meanings this 'feast' of contradictions 'has been provided.'
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The Parmenides of Plato belongs to a stage of philosophy which has passed away. At first we read it with a purely antiquarian or historical interest; and with difficulty throw ourselves back into a state of the human mind in which Unity and Being occupied the attention of philosophers. We admire the precision of the language, in which, as in some curious puzzle, each word is exactly fitted into every other, and long trains of argument are carried out with a sort of geometrical accuracy. We doubt whether any abstract notion could stand the searching cross-examination of Parmenides; and may at last perhaps arrive at the conclusion that Plato has been using an imaginary method to work out an unmeaning conclusion. But the truth is, that he is carrying on a process which is not either useless or unnecessary in any age of philosophy. We fail to understand him, because we do not realize that the questions which he is discussing could have had any value or importance. We suppose them to be like the speculations of some of the Schoolmen, which end in nothing. But in truth he is trying to get rid of the stumbling-blocks of thought which beset his contemporaries. Seeing that the Megarians and Cynics were making knowledge impossible, he takes their 'catch-words' and analyzes them from every conceivable point of view. He is criticizing the simplest and most general of our ideas, in which, as they are the most comprehensive, the danger of error is the most serious; for, if they remain unexamined, as in a mathematical demonstration, all that flows from them is affected, and the error pervades knowledge far and wide. In the beginning of philosophy this correction of human ideas was even more necessary than in our own times, because they were more bound up with words; and words when once presented to the mind exercised a greater power over thought. There is a natural realism which says, 'Can there be a word devoid of meaning, or an idea which is an idea of nothing?' In modern times mankind have often given too great importance to a word or idea. The philosophy of the ancients was still more in slavery to them, because they had not the experience of error, which would have placed them above the illusion.