The Republic

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 an imitation in the tenth. The line may be regarded as reaching from unity to infinity, and is divided into two unequal parts, and subdivided into two more; each lower sphere is the multiplication of the preceding. Of the four faculties, faith in the lower division has an intermediate position (cp. for the use of the word faith or belief, (Greek), Timaeus), contrasting equally with the vagueness of the perception of shadows (Greek) and the higher certainty of understanding (Greek) and reason (Greek).

The difference between understanding and mind or reason (Greek) is analogous to the difference between acquiring knowledge in the parts and the contemplation of the whole. True knowledge is a whole, and is at rest; consistency and universality are the tests of truth. To this self-evidencing knowledge of the whole the faculty of mind is supposed to correspond. But there is a knowledge of the understanding which is incomplete and in motion always, because unable to rest in the subordinate ideas. Those ideas are called both images and hypotheses—images because they are clothed in sense, hypotheses because they are assumptions only, until they are brought into connexion with the idea of good.