Ninthly, the Ideas are rational, that is to say, they are apprehended through reason. The finding of the common element in the manifold is the work of inductive {191} reason, and through this alone is knowledge of the Ideas possible. This should be noted by those persons who imagine that Plato was some sort of benevolent mystic. The imperishable One, the absolute reality, is apprehended, not by intuition, or in any kind of mystic ecstasy, but only by rational cognition and laborious thought. Lastly, towards the end of his life, Plato identified the Ideas with the Pythagorean numbers. We know this from Aristotle, but it is not mentioned in the dialogues of Plato himself. It appears to have been a theory adopted in old age, and set forth in the lectures which Aristotle attended. It is a retrograde step, and tends to degrade the great and lucid idealism of Plato into a mathematical mysticism. In this, as in other respects, the influence of the Pythagoreans upon Plato was harmful. It results from this whole theory of Ideas that there are two sources of human experience, sense-perception and reason. Sense-perception has for its object the world of sense; reason has for its object the Ideas. The world of sense has all the opposite characteristics to the Ideas. The Ideas are absolute reality, absolute Being. Objects of sense are absolute unreality, not-being, except in so far as the Ideas are in them. Whatever reality they have they owe to the Ideas. There is in Plato's system a principle of absolute not-being which we shall consider when we come to deal with his Physics. Objects of sense participate both in the Ideas and in this not-being. They are, therefore, half way between Being and not-being. They are half real. Ideas, again, are universal; things of sense are always particular and individual. The Idea is one, the sense-object is always {192} a multiplicity. Ideas are outside space and time, things of sense are both temporal and spatial. The Idea is eternal and immutable; sense-objects are changeable and in perpetual flux. As regards the last point, Plato adopts the view of Heracleitus that there is an absolute Becoming, and he identifies it with the world of sense, which contains nothing stable and permanent, but is a constant flow. The Idea always is, and never becomes; the thing of sense always becomes, and never is. It is for this reason that, in the opinion of Plato, no knowledge of the world of sense is possible, for one can have no knowledge of that which changes from moment to moment. Knowledge is only possible if its subject stands fixed before the mind, is permanent and changeless. The only knowledge, then, is knowledge of the Ideas.