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Plato investigates the relations of the One and the many, Being and not-being, quite in the abstract. He decides the principles involved, and leaves it to the reader to apply them to the theory of Ideas. Whether the Absolute is one or many, Being or not-being, can be decided independently of any particular theory of the nature of the Absolute, and therefore independently of Plato's own theory, which was that the Absolute consists of Ideas. Plato does not accept the Eleatic abstraction. The One cannot be simply one, for every unity must necessarily be a multiplicity. The many and the One are correlative ideas which involve each other. Neither is thinkable without the other. A One which is not many is as absurd an abstraction as a whole which has no parts. For the One can only be defined as that which is not many, and the many can only be defined as the not-one. The One is unthinkable except as standing out against a background of the many. The idea of the One therefore involves the idea of the many, and cannot be thought without it. Moreover, an abstract One is unthinkable and unknowable, because all thought and knowledge consist in applying predicates to subjects, and all predication involves the duality of its subject.

Consider the simplest affirmation that can be made about the One, namely, "The One is." Here we have two things, "the One," and "is," that is to say, being. The proposition means that the One is Being. Hence the One is two. Firstly, it is itself, "One." Secondly, it is "Being," and the proposition affirms that these two things are one. Similarly with any other predicate we apply to the One. Whatever we say of it involves its duality. Thus we find that all systems of thought which {197} postulate an abstract unity as ultimate reality, such as Eleaticism, Hinduism, and the system of Spinoza, attempt to avoid the difficulty by saying nothing positive about the One. They apply to it only negative predicates, which tell us not what it is, but what it is not. Thus the Hindus speak of Brahman as formless, immutable, imperishable, unmoved, uncreated. But this, of course, is a futile expedient. In the first place, even a negative predicate involves the duality of the subject. And, in the second place, a negative predicate is always, by implication, a positive one. You cannot have a negative without a positive. To deny one thing is to affirm its opposite. To deny motion of the One, by calling it the unmoved, is to affirm rest of it. Thus a One which is not also a many is unthinkable. Similarly, the idea of the many is inconceivable without the idea of the One. For the many is many ones. Hence the One and the many cannot be separated in the Eleatic manner. Every unity must be a unity of the many. And every many is ipso facto a unity, since we think the many in one idea, and, if we did not, we should not even know that it is a many. The Absolute must therefore be neither an abstract One, nor an abstract many. It must be a many in one.

Similarly, Being cannot totally exclude not-being. They are, just as much as the One and the many, correlatives, which mutually involve each other. The being of anything is the not-being of its opposite. The being of light is the not-being of darkness. All being, therefore, has not-being in it.

Let us apply these principles to the theory of Ideas. The absolute reality, the world of Ideas, is many, since {198} there are many Ideas, but it is one, because the Ideas are not isolated units, but members of a single organized system. There is, in fact, a hierarchy of Ideas. Just as the one Idea presides over many individual things of which it is the common element, so one higher Idea presides over many lower Ideas, and is the common element in them. And over this higher Idea, together with many others, a still higher Idea will rule. For example, the Ideas of whiteness, redness, blueness, are all subsumed under the one Idea of colour. The Ideas of sweetness and bitterness come under the one Idea of taste. But the Ideas of colour and taste themselves stand under the still higher Idea of quality. In this way, the Ideas form, as it were, a pyramid, and to this pyramid there must be an apex. There must be one highest Idea, which is supreme over all the others. This Idea will be the one final and absolutely real Being which is the ultimate ground, of itself, of the other Ideas, and of the entire universe. This Idea is, Plato tells us, the Idea of the Good. We have seen that the world of Ideas is many, and we now see that it is one. For it is one single system culminating in one supreme Idea, which is the highest expression of its unity. Moreover, each separate Idea is, in the same way, a many in one. It is one in regard to itself. That is to say, if we ignore its relations to other Ideas, it is, in itself, single. But as it has also many relations to other Ideas, it is, in this way, a multiplicity.

Every Idea is likewise a Being which contains not-being. For each Idea combines with some Ideas and not with others. Thus the Idea of corporeal body combines both with the Idea of rest and that of motion. {199} But the Ideas of rest and motion will not combine with each other. The Idea of rest, therefore, is Being in regard to itself, not-being in regard to the Idea of motion, for the being of rest is the not-being of motion. All Ideas are Being in regard to themselves, and not-being in regard to all those other Ideas with which they do not combine.

In this way there arises a science of Ideas which is called dialectic. This word is sometimes used as identical with the phrase, "theory of Ideas." But it is also used, in a narrower sense, to mean the science which has to do with the knowledge of which Ideas will combine and which not. Dialectic is the correct joining and disjoining of Ideas. It is the knowledge of the relations of all the Ideas to each other.

The attainment of this knowledge is, in Plato's opinion, the chief problem of philosophy. To know all the Ideas, each in itself and in its relations to other Ideas, is the supreme task. This involves two steps. The first is the formation of concepts. Its object is to know each Idea separately, and its procedure is by inductive reason to find the common element in which the many individual objects participate. The second step consists in the knowledge of the inter-relation of Ideas, and involves the two processes of classification and division. Classification and division both have for their object to arrange the lower Ideas under the proper higher Ideas, but they do this in opposite ways. One may begin with the lower Ideas, such as redness, whiteness, etc., and range them under their higher Idea, that of colour. This is classification. Or one may begin with the higher Idea, colour, and divide it into the lower Ideas, red, white, {200} etc. Classification proceeds from below upwards. Division proceeds from above downwards. Most of the examples of division which Plato gives are divisions by dichotomy. We may either divide colour straight away into red, blue, white, etc.; or we may divide each class into two sub-classes. Thus colour will be divided into red and not-red, not-red into white and not-white, not-white into blue and not-blue, and so on. This latter process is division by dichotomy, and Plato prefers it because, though it is tedious, it is very exhaustive and systematic.

Plato's actual performance of the supreme task of dialectic, the classification and arrangement of all Ideas, is not great. He has made no attempt to complete it. All he has done is to give us numerous examples. And this is, in reality, all that can be expected, for the number of Ideas is obviously infinite, and therefore the task of arranging them cannot be completed. There is, however, one important defect in the dialectic, which Plato ought certainly to have remedied. The supreme Idea, he tells us, is the Good. This, as being the ultimate reality, is the ground of all other Ideas. Plato ought therefore to have derived all other Ideas from it, but this he has not done. He merely asserts, in a more or less dogmatic way, that the Idea of the Good is the highest, but does nothing to connect it with the other Ideas. It is easy to see, however, why he made this assertion. It is, in fact, a necessary logical outcome of his system. For every Idea is perfection in its kind. All the Ideas have perfection in common. And just as the one beauty is the Idea which presides over all beautiful things, so the one perfection must be the supreme Idea which presides {201} over all the perfect Ideas. The supreme Idea, therefore, must be perfection itself, that is to say, the Idea of the Good. On the other hand it might, with equal force, be argued that since all the Ideas are substances, therefore the highest Idea is the Idea of substance. All that can be said is that Plato has left these matters in obscurity, and has merely asserted that the highest Idea is the Good.

Consideration of the Idea of the Good leads us naturally to enquire how far Plato's system is teleological in character. A little consideration will show that it is out and out teleological. We can see this both by studying the many lower Ideas, and the one supreme Idea. Each Idea is perfection of its kind. And each Idea is the ground of the existence of the individual objects which come under it. Thus the explanation of white objects is the perfect whiteness, of beautiful objects the perfect beauty. Or we may take as our example the Idea of the State which Plato describes in the "Republic." The ordinary view is that Plato was describing a State which was the invention of his own fancy, and is therefore to be regarded as entirely unreal. This is completely to misunderstand Plato. So far was he from thinking the ideal State unreal, that he regarded it, on the contrary, as the only real State. All existent States, such as the Athenian or the Spartan, are unreal in so far as they differ from the ideal State. And moreover, this one reality, the ideal State, is the ground of the existence of all actual States. They owe their existence to its reality. Their existence can only be explained by it. Now since the ideal State is not yet reached in fact, but is the perfect State towards which all actual States tend, it is clear that we have here {202} a teleological principle. The real explanation of the State is not to be found in its beginnings in history, in an original contract, or in biological necessities, but in its end, the final or perfect State. Or, if we prefer to put it so; the true beginning is the end. The end must be in the beginning, potentially and ideally, otherwise it could never begin: It is the same with all other things. Man is explained by the ideal man, the perfect man; white things by the perfect whiteness, and so on. Everything is explained by its end, and not by its beginning. Things are not explained by mechanical causes, but by reasons.

And the teleology of Plato culminates in the Idea of the Good. That Idea is the final explanation of all other Ideas, and of the entire universe. And to place the final ground

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