3. THE DOCTRINE OF IDEAS IN ITS GENESIS.—The Platonic doctrine of ideas is the common product of the Socratic method of forming conceptions, the Heraclitic doctrine of absolute becoming, and the Eleatic doctrine of absolute being. To the first of these Plato owes the idea of a knowing through conceptions, to the second the recognition of the becoming in the field of the sensuous, to the third the position of a field of absolute reality. Elsewhere (_in the Philebus_) Plato connects the doctrine of ideas with the Pythagorean thought that every thing may be formed from unity and multiplicity, from the limit and the unlimited. The aim of the Theatætus, the Sophist, and the Parmenides is to refute the principles of the Eleatics and Heraclitics: this refutation is effected in the Theatætus by combating directly the principle of an absolute becoming, in the Sophist by combating directly the principle of abstract being, and in the Parmenides by taking up the Eleatic one and showing its true relations. We have already spoken of the Theatætus; we will now look for the development of the doctrine of ideas in the Sophist and Parmenides. The ostensible end of the former of these dialogues is to show that the Sophist is really but a caricature of the philosopher, but its true end is to fix the reality of the appearance, _i. e._ of the not-being, and to discuss speculatively the relation of being and not-being. The doctrine of the Eleatics ended with the rejection of all sensuous knowledge, declaring that what we receive as the perception of a multiplicity of things or of a becoming is only an appearance. In this the contradiction was clear, the not-being was absolutely denied, and yet its existence was admitted in the notion of men. Plato at once draws attention to this contradiction, showing that a delusive opinion, which gives rise to a false image or representation, is not possible, since the whole theory rests upon the assumption that the false, the not-true, _i. e._ not-being cannot even be thought. This, Plato continues, is the great difficulty in thinking of not-being, that both he who denies and he who affirms its reality is driven to contradict himself. For though it is inexpressible and inconceivable either as one or as many, still, when speaking of it, we must attribute to it both being and multiplicity. If we admit that there is such a thing as a false opinion, we assume in this very fact the notion of not-being, for only that opinion can be said to be false which supposes either the not-being to be, or makes that, which is not, to be. In short, if there actually exists a false notion, so does there actually and truly exist a not-being. After Plato had thus fixed the reality of not-being, he discusses the relation of being and not-being, _i. e._ the relation of conceptions generally in their combinations and differences. If not-being has no less reality than being, and being no more than not-being, if, therefore, _e.