sciences, but not the impure pleasures. We have next to discover what element of goodness is contained in this mixture. There are three criteria of goodness – beauty, symmetry, truth. These are clearly more akin to reason than to pleasure, and will enable us to fix the places of both of them in the scale of good. First in the scale is measure; the second place is assigned to symmetry; the third, to reason and wisdom; the fourth, to knowledge and true opinion; the fifth, to pure pleasures; and here the Muse says 'Enough.'
'Bidding farewell to Philebus and Socrates,' we may now consider the metaphysical conceptions which are presented to us. These are (I) the paradox of unity and plurality; (II) the table of categories or elements; (III) the kinds of pleasure; (IV) the kinds of knowledge; (V) the conception of the good. We may then proceed to examine (VI) the relation of the Philebus to the Republic, and to other dialogues.
I. The paradox of the one and many originated in the restless dialectic of Zeno, who sought to prove the absolute existence of the one by showing the contradictions that are involved in admitting the existence of the many (compare Parm.). Zeno illustrated the contradiction by well-known examples taken from outward objects. But Socrates seems to intimate that the time had arrived for discarding these hackneyed illustrations; such difficulties had long been solved by common sense ('solvitur ambulando'); the fact of the co-existence of opposites was a sufficient answer to them. He will leave them to Cynics and Eristics; the youth of Athens may discourse of them to their parents. To no rational man could the circumstance that the body is one, but has many members, be any longer a stumbling-block.
Plato's difficulty seems to begin in the region of ideas. He cannot understand how an absolute unity, such as the Eleatic Being, can be broken up into a number of individuals, or be in and out of them at once. Philosophy had so deepened or intensified the nature of one or Being, by the thoughts of successive generations, that the mind could no longer imagine 'Being' as in a state of change or division. To say that the verb of existence is the copula, or that unity is a mere unit, is to us easy; but to the Greek in a particular stage of thought such an analysis involved the same kind of difficulty as the conception of God existing both in and out of the world would to ourselves. Nor was he assisted by the analogy of sensible objects. The sphere of mind was dark and mysterious to him; but instead of being illustrated by sense, the greatest light appeared to be thrown on the nature of ideas when they were contrasted with sense.
Both here and in the Parmenides, where similar difficulties are raised, Plato seems prepared to desert his ancient ground. He cannot tell the relation in which abstract ideas stand to one another, and therefore he transfers the one and many out of his transcendental world, and proceeds to lay down practical rules for their application to different branches of knowledge. As in the Republic he supposes the philosopher to proceed by regular steps, until he arrives at the idea of good; as in the Sophist and Politicus he insists that in dividing the whole into its parts we should bisect in the middle in the hope of finding species; as in the Phaedrus (see above) he would have 'no limb broken' of the organism of knowledge; – so in the Philebus he urges the necessity of filling up all the intermediate links which occur (compare Bacon's 'media axiomata') in the passage from unity to infinity. With him the idea of science may be said to anticipate science; at a time when the sciences were not yet divided, he wants to impress upon us the importance of classification; neither neglecting the many individuals, nor attempting to count them all, but finding the genera and species under which they naturally fall. Here, then, and in the parallel passages of the Phaedrus and of the Sophist, is found the germ of the most fruitful notion of modern science.
Plato describes with ludicrous exaggeration the influence exerted by the one and many on the minds of young men in their first fervour of metaphysical enthusiasm (compare Republic). But they are none the less an everlasting quality of reason or reasoning which never grows old in us. At first we have but a confused conception of them, analogous to the eyes blinking at the light in the Republic. To this Plato opposes the revelation from Heaven of the real relations of them, which some Prometheus, who gave the true fire from heaven, is supposed to have imparted to us. Plato is speaking of two things – (1) the crude notion of the one and many, which powerfully affects the ordinary mind when first beginning to think; (2) the same notion when cleared up by the help of dialectic.
To us the problem of the one and many has lost its chief interest and perplexity. We readily acknowledge that a whole has many parts, that the continuous is also the divisible, that in all objects of sense there is a one and many, and that a like principle may be applied to analogy to purely intellectual conceptions. If we attend to the meaning of the words, we are compelled to admit that two contradictory statements are true. But the antinomy is so familiar as to be scarcely observed by us. Our sense of the contradiction, like Plato's, only begins in a higher sphere, when we speak of necessity and free-will, of mind and body, of Three Persons and One Substance, and the like. The world of knowledge is always dividing more and more; every truth is at first the enemy of every other truth. Yet without this division there can be no truth; nor any complete truth without the reunion of the parts into a whole. And hence the coexistence of opposites in the unity of the idea is regarded by Hegel as the supreme principle of philosophy; and the law of contradiction, which is affirmed by logicians to be an ultimate principle of the human mind, is displaced by another law, which asserts the coexistence of contradictories as imperfect and divided elements of the truth. Without entering further into the depths of Hegelianism, we may remark that this and all similar attempts to reconcile antinomies have their origin in the old Platonic problem of the 'One and Many.'
II. 1. The first of Plato's categories or elements is the infinite. This is the negative of measure or limit; the unthinkable, the unknowable; of which nothing can be affirmed; the mixture or chaos which preceded distinct kinds in the creation of the world; the first vague impression of sense; the more or less which refuses to be reduced to rule, having certain affinities with evil, with pleasure, with ignorance, and which in the scale of being is farthest removed from the beautiful and good. To a Greek of the age of Plato, the idea of an infinite mind would have been an absurdity. He would have insisted that 'the good is of the nature of the finite,' and that the infinite is a mere negative, which is on the level of sensation, and not of thought. He was aware that there was a distinction between the infinitely great and the infinitely small, but he would have equally denied the claim of either to true existence. Of that positive infinity, or infinite reality, which we attribute to God, he had no conception.
The Greek conception of the infinite would be more truly described, in our way of speaking, as the indefinite. To us, the notion of infinity is subsequent rather than prior to the finite, expressing not absolute vacancy or negation, but only the removal of limit or restraint, which we suppose to exist not before but after we have already set bounds to thought and matter, and divided them after their kinds. From different points of view, either the finite or infinite may be looked upon respectively both as positive and negative (compare 'Omnis determinatio est negatio')' and the conception of the one determines that of the other. The Greeks and the moderns seem to be nearly at the opposite poles in their manner of regarding them. And both are surprised when they make the discovery, as Plato has done in the Sophist, how large an element negation forms in the framework of their thoughts.
2, 3. The finite element which mingles with and regulates the infinite is best expressed to us by the word 'law.' It is that which measures all things and assigns to them their limit; which preserves them in their natural state, and brings them within the sphere of human cognition. This is described by the terms harmony, health, order, perfection, and the like. All things, in as far as they are good, even pleasures, which are for the most part indefinite, partake of this element. We should be wrong in attributing to Plato the conception of laws of nature derived from observation and experiment. And yet he has as intense a conviction as any modern philosopher that nature does not proceed by chance. But observing that the wonderful construction of number and figure, which he had within himself, and which seemed to be prior to himself, explained a part of the phenomena of the external world, he extended their principles to the whole, finding in them the true type both of human life and of the order of nature.
Two other points may be noticed respecting the third class. First, that Plato seems to be unconscious of any interval or chasm which separates the finite from the infinite. The one is in various ways and degrees working in the other. Hence he has implicitly answered the difficulty with which he started, of how the