2. Plato supposes that when the tablet has been made blank the artist will fill in the lineaments of the ideal state. Is this a pattern laid up in heaven, or mere vacancy on which he is supposed to gaze with wondering eye? The answer is, that such ideals are framed partly by the omission of particulars, partly by imagination perfecting the form which experience supplies (Phaedo). Plato represents these ideals in a figure as belonging to another world; and in modern times the idea will sometimes seem to precede, at other times to co-operate with the hand of the artist. As in science, so also in creative art, there is a synthetical as well as an analytical method. One man will have the whole in his mind before he begins; to another the processes of mind and hand will be simultaneous. 3. There is no difficulty in seeing that Plato’s divisions of knowledge are based, first, on the fundamental antithesis of sensible and intellectual which pervades the whole pre-Socratic philosophy; in which is implied also the opposition of the permanent and transient, of the universal and particular. But the age of philosophy in which he lived seemed to require a further distinction;—numbers and figures were beginning to separate from ideas. The world could no longer regard justice as a cube, and was learning to see, though imperfectly, that the abstractions of sense were distinct from the abstractions of mind. Between the Eleatic being or essence and the shadows of phenomena, the Pythagorean principle of number found a place, and was, as Aristotle remarks, a conducting medium from one to the other. Hence Plato is led to introduce a third term which had not hitherto entered into the scheme of his philosophy. He had observed the use of mathematics in education; they were the best preparation for higher studies. The subjective relation between them further suggested an objective one; although the passage from one to the other is really imaginary (Metaph.). For metaphysical and moral philosophy has no connexion with mathematics; number and figure are the abstractions of time and space, not the expressions of purely intellectual conceptions. When divested of metaphor, a straight line or a square has no more to do with right and justice than a crooked line with vice. The figurative association was mistaken for a real one; and thus the three latter divisions of the Platonic proportion were constructed.