Thirdly, the Ideas are not things, but thoughts. There is no such thing as the horse-in-general. If there were, we should be able to find it somewhere, and it would then be a particular thing instead of a universal. But in saying that the Ideas are thoughts, there are two mistakes to be carefully avoided. The first is to suppose that they are the thoughts of a person, that they are your thoughts or my thoughts. The second is to suppose that they are thoughts in the mind of God. Both these views are wrong. It would be absurd to suppose that our thoughts can be the cause of the universe. Our concepts are indeed copies of the Ideas, but to confuse them with the Ideas themselves is, for Plato, as absurd as to confuse our idea of a mountain with the mountain itself. Nor are they the thoughts of God. They are indeed sometimes spoken of as the "Ideas in the divine mind." But this is only a figurative expression. We can, if we like, talk of the sum of all the Ideas as constituting the "divine mind." But this means nothing in particular, and is only a poetical phrase. Both these mistakes are due to the fact that we find it difficult to conceive of thoughts without a thinker. This, however, is just what Plato meant. They are not subjective ideas, that is, the ideas in a particular and existent [{189}] mind. They are objective Ideas, thoughts which have reality on their own account, independently of any mind.

Fourthly, each Idea is a unity. It is the one amid the many. The Idea of man is one, although individual men are many. There cannot be more than one Idea for each class of objects. If there were several Ideas of justice, we should have to seek for the common element among them, and this common element would itself constitute the one Idea of justice.

Fifthly, the Ideas are immutable and imperishable. A concept is the same as a definition. And the whole point in a definition is that it should always be the same. The object of a definition is to compare individual things with it, and to see whether they agree with it or not. But if the definition of a triangle differed from day to day, it would be useless, since we could never say whether any particular figure were a triangle or not, just as the standard yard in the Tower of London would be useless if it changed in length, and were twice as long to-day as it was yesterday. A definition is thus something absolutely permanent, and a definition is only the expression in words of the nature of an Idea. Consequently the Ideas cannot change. The many beautiful objects arise and pass away, but the one Beauty neither begins nor ends. It is eternal, unchangeable, and imperishable. The many beautiful things are but the fleeting expressions of the one eternal beauty. The definition of man would remain the same, even if all men were destroyed. The Idea of man is eternal, and remains untouched by the birth, old age, decay, and death, of individual men.

Sixthly, the Ideas are the Essences of all things. The definition gives us what is essential to a thing. If we [{190}] define man as a rational animal, this means that reason is of the essence of man. The fact that this man has a turned-up nose, and that man red hair, are accidental facts, not essential to their humanity. We do not include them in the definition of man.

Seventhly, each Idea is, in its own kind, an absolute perfection, and its perfection is the same as its reality. The perfect man is the one universal type-man, that is, the Idea of man, and all individual men deviate more or less from this perfect type. In so far as they fall short of it, they are imperfect and unreal.

Eighthly, the Ideas are outside space and time. That they are outside space is obvious. If they were in space, they would have to be in some particular place. We ought to be able to find them somewhere. A telescope or microscope might reveal them. And this would mean that they are individual and particular things, and not universals at all. They are also outside time. For they are unchangeable and eternal; and this does not mean that they are the same at all times. If that were so, their immutability would be a matter of experience, and not of reason. We should, so to speak, have to look at them from time to time to see that they had not really changed. But their immutability is not a matter of experience, but is known to thought. It is not merely that they are always the same in time, but that time is irrelevant to them. They are timeless. In the "Timaeus" eternity is distinguished from infinite time. The latter is described as a mere copy of eternity.

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.