There still remained one last problem to solve, one point where the converging streams of ethical and metaphysical speculation met and mixed. Granted that knowledge is the soul’s highest energy, what is the object of this beatific vision? Granted that all particular energies co-operate for a common purpose, what is the end to which they are subordinated? Granted that dialectic leads us up through ascending gradations to one all-comprehensive idea, how is that idea to be defined? Plato only attempts to answer this last question by re-stating it under the form of an illustration. As the sun at once gives life to all Nature, and light to the eye by which Nature is perceived, so also the idea of Good is the cause of existence and of knowledge alike, but transcends them both as an absolute unity, of which we cannot even say that it is, for the distinction of subject and predicate would bring back relativity and plurality again. Here we seem to have the Socratic paradox reversed. Socrates identified virtue with knowledge, but, at the same time, entirely emptied the latter of its speculative content. Plato, inheriting the idea of knowledge in its artificially restricted significance, was irresistibly drawn back to the older philosophy whence it had been originally borrowed; then, just as his master had given an ethical application to science, so did he, travelling over the same ground in an opposite direction, extend the theory of ethics far beyond its legitimate range, until a principle which seemed to have no meaning, except in reference to human conduct, became the abstract bond of union between all reality and all thought. Whether Plato ever succeeded in making the idea of Good quite clear to others, or even to himself, is more than we can tell. In the _Republic_ he declines giving further explanations on the ground that his pupils have not passed through the necessary mathematical initiation. Whether quantitative reasoning was to furnish the form or the matter of transcendent dialectic is left undetermined. We are told that on one occasion a large audience assembled to hear Plato lecture on the Good, but that, much to their disappointment, the discourse was entirely filled with geometrical and astronomical investigations. Bearing in mind, however, that mathematical science deals chiefly with equations, and that astronomy, according to Plato, had for its object to prove the absolute uniformity of the celestial motions, we may perhaps conclude that the idea of Good meant no more than the abstract notion of identity or indistinguishable likeness. The more complex idea of law as a uniformity of relations, whether coexistent or successive, had not then dawned, but it has since been similarly employed to bring physics into harmony with ethics and logic. III.