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.