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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 one could remain one and yet be divided among many individuals, or 'how ideas could be in and out of themselves,' and the like. Secondly, that in this mixed class we find the idea of beauty. Good, when exhibited under the aspect of measure or symmetry, becomes beauty. And if we translate his language into corresponding modern terms, we shall not be far wrong in saying that here, as well as in the Republic, Plato conceives beauty under the idea of proportion.

4. Last and highest in the list of principles or elements is the cause of the union of the finite and infinite, to which Plato ascribes the order of the world. Reasoning from man to the universe, he argues that as there is a mind in the one, there must be a mind in the other, which he identifies with the royal mind of Zeus. This is the first cause of which 'our ancestors spoke,' as he says, appealing to tradition, in the Philebus as well as in the Timaeus. The 'one and many' is also supposed to have been revealed by tradition. For the mythical element has not altogether disappeared.

Some characteristic differences may here be noted, which distinguish the ancient from the modern mode of conceiving God.

a. To Plato, the idea of God or mind is both personal and impersonal. Nor in ascribing, as appears to us, both these attributes to him, and in speaking of God both in the masculine and neuter gender, did he seem to himself inconsistent. For the difference between the personal and impersonal was not marked to him as to ourselves. We make a fundamental distinction between a thing and a person, while to Plato, by the help of various intermediate abstractions, such as end, good, cause, they appear almost to meet in one, or to be two aspects of the same. Hence, without any reconciliation or even remark, in the Republic he speaks at one time of God or Gods, and at another time of the Good. So in the Phaedrus he seems to pass unconsciously from the concrete to the abstract conception of the Ideas in the same dialogue. Nor in the Philebus is he careful to show in what relation the idea of the divine mind stands to the supreme principle of measure.

b. Again, to us there is a strongly-marked distinction between a first cause and a final cause. And we should commonly identify a first cause with God, and the final cause with the world, which is His work. But Plato, though not a Pantheist, and very far from confounding God with the world, tends to identify the first with the final cause. The cause of the union of the finite and infinite might be described as a higher law; the final measure which is the highest expression of the good may also be described as the supreme law. Both these conceptions are realized chiefly by the help of the material world; and therefore when we pass into the sphere of ideas can hardly be distinguished.