There seem to be two great aims in the philosophy of Plato,—first, to realize abstractions; secondly, to connect them. According to him, the true education is that which draws men from becoming to being, and to a comprehensive survey of all being. He desires to develop in the human mind the faculty of seeing the universal in all things; until at last the particulars of sense drop away and the universal alone remains. He then seeks to combine the universals which he has disengaged from sense, not perceiving that the correlation of them has no other basis but the common use of language. He never understands that abstractions, as Hegel says, are ‘mere abstractions’—of use when employed in the arrangement of facts, but adding nothing to the sum of knowledge when pursued apart from them, or with reference to an imaginary idea of good. Still the exercise of the faculty of abstraction apart from facts has enlarged the mind, and played a great part in the education of the human race. Plato appreciated the value of this faculty, and saw that it might be quickened by the study of number and relation. All things in which there is opposition or proportion are suggestive of reflection. The mere impression of sense evokes no power of thought or of mind, but when sensible objects ask to be compared and distinguished, then philosophy begins. The science of arithmetic first suggests such distinctions. The follow in order the other sciences of plain and solid geometry, and of solids in motion, one branch of which is astronomy or the harmony of the spheres,—to this is appended the sister science of the harmony of sounds. Plato seems also to hint at the possibility of other applications of arithmetical or mathematical proportions, such as we employ in chemistry and natural philosophy, such as the Pythagoreans and even Aristotle make use of in Ethics and Politics, e.g. his distinction between arithmetical and geometrical proportion in the Ethics (Book V), or between numerical and proportional equality in the Politics.