e 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.

There is more difficulty in comprehending how he arrived at the
first term of the series, which is nowhere else mentioned, and has no
reference to any other part of his system. Nor indeed does the relation
of shadows to objects correspond to the relation of numbers to ideas.
Probably Plato has been led by the love of analogy (Timaeus) to make
four terms instead of three, although the objects perceived in both
divisions of the lower sphere are equally objects of sense. He is also
preparing the way, as his manner is, for the shadows of images at the
beginning of the seventh book, and the imitation of