INTRODUCTION.

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 by 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 a contradiction between two beliefs or conclusions that are in themselves reasonable 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 was 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