3. I have said, in the preceding chapter, that Plato, though he saw that scientific truths of great generality might be obtained and were to be arrived at by philosophers, overlooked the necessity of a _gradual_ and _successive_ advance from the less general to the more general; and I have described this as a 'dimness of vision.' I must now acknowledge that this is not a very appropriate phrase; for not only no acuteness of vision could have enabled Plato to see that gradual generalization in science of which, as yet, no example had appeared; but it was very fortunate for the progress of truth, at that time, that Plato had imagined to himself the object of science to be general and sublime truths which prove themselves to be true by the light of their own generality and symmetry. It is worth while to illustrate this notice of Plato by some references to his writings. In the Sixth Book of the _Republic_, Plato treats of the then existing sciences as the instruments of a philosophical education. Among the most conspicuous of these is astronomy. He there ridicules the notion that astronomy is a sublime science because it makes men look _upward_. He asserts that the really sublime science is that which makes men look at the _realities_, which are suggested by the appearances seen in the heavens: namely, the spheres which revolve and carry the luminaries in their revolutions. Now it was no doubt the determined search for such "realities" as these which gave birth to the Greek _Astronomy_, that first and critical step in the progress of science. Plato, by his exhortations, if not by his suggestions, contributed effectually, as I conceive, to this step in science. In the same manner he requires a science of _Harmonics_ which shall be free from the defects and inaccuracies which occur in actual instruments. This belief that the universe was full of mathematical relations, and that these were the true objects of scientific research, gave a vigour, largeness of mind, and confidence to the Greek speculators which no more cautious view of the problem of scientific discovery could have supplied. It was well that this advanced guard in the army of discoverers was filled with indomitable courage, boundless hopes, and creative minds.