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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.

This may seem, at first sight, a very singular doctrine. That there can be no knowledge of sense-objects would, it might seem to us moderns, involve the denial that modern physical science, with all its exactitude and accumulated knowledge, is knowledge at all. And surely, though all earthly things arise and pass away, many of them last long enough to admit of knowledge. Surely the mountains are sufficiently permanent to allow us to know something of them. They have relative, though not absolute, permanence. This criticism is partly justified. Plato did underestimate the value of physical knowledge. But for the most part, the criticism is a misunderstanding. By the world of sense Plato means bare sensation with no rational element in it. Now physical science has not such crude sensation for its object. Its objects are rationalized sensations. {193} If, in Plato's manner, we think only of pure sensation, then it is true that it is nothing but a constant flux without stability; and knowledge of it is impossible. The mountains are comparatively permanent. But our sensation of the mountains is perpetually changing. Every change of light, every cloud that passes over the sun, changes the colours and the shades. Every time we move from one situation to another, the mountain appears a different shape. The permanence of the mountain itself is due to the fact that all these varying sensations are identified as sensations of one and the same object. The idea of identity is involved here, and it is, as it were, a thread upon which these fleeting sensations are strung. But the idea of identity cannot be obtained from the senses. It is introduced into things by reason. Hence knowledge of this permanent mountain is only possible through the exercise of reason. In Plato's language, all we can know of the mountain is the Ideas in which it participates. To revert to a previous example, even the knowledge "this paper is white" involves the activity of intellect, and is impossible through sensation alone. Bare sensation is a flow, of which no knowledge is possible.

Aristotle observes that Plato's theory of Ideas has three sources, the teachings of the Eleatics, of Heracleitus, and of Socrates. From Heracleitus, Plato took the notion of a sphere of Becoming, and it appears in his system as the world of sense. From the Eleatics he took the idea of a sphere of absolute Being. From Socrates he took the doctrine of concepts, and proceeded to identify the Eleatic Being with the Socratic concepts. This gives him his theory of Ideas.

{194}

Sense objects, so far as they are knowable, that is so far as they are more than bare sensations, are so only because the Idea resides in them. And this yields the clue to Plato's teaching regarding the relation of sense objects to the Ideas. The Ideas are, in the first place the cause, that is to say, the ground (not the mechanical cause) of sense-objects. The Ideas are the absolute reality by which individual things must be explained. The being of things flows into them from the Ideas. They are "copies," "imitations," of the Ideas. In so far as they resemble the Idea, they are real; in so far as they differ from it, they are unreal. In general, sense objects are, in Plato's opinion, only very dim, poor and imperfect copies of the Ideas. They are mere shadows, and half-realities. Another expression frequently used by Plato to express this relationship is that of "participation." Things participate in the Ideas. White objects participate in the one whiteness, beautiful objects, in the one beauty. In this way beauty itself is the cause or explanation of beautiful objects, and so of all other Ideas. The Ideas are thus both transcendent and immanent; immanent in so far as they reside in the things of sense, transcendent inasmuch as they have a reality of their own apart from the objects of sense which participate in them. The Idea of man would still be real even if all men were destroyed, and it was real before any man existed, if there ever was such a time. For the Ideas, being timeless, cannot be real now and not then.

Of what kinds of things are there Ideas? That there are moral Ideas, such as Justice, Goodness, and Beauty, Ideas of corporeal things, such as horse, man, tree, star, river, and Ideas of qualities, such as whiteness, heaviness, {195} sweetness, we have already seen. But there are Ideas not only of natural corporeal objects, but likewise of manufactured articles; there are Ideas of beds, tables, clothes. And there are Ideas not only of exalted moral entities, such as Beauty and Justice. There are also the Ideal Ugliness, and the Ideal Injustice. There are even Ideas of the positively nauseating, such as hair, filth, and dirt. This is asserted in the "Parmenides." In that dialogue Plato's teaching is put into the mouth of Parmenides. He questions the young Socrates whether there are Ideas of hair, filth, and dirt. Socrates denies that there can be Ideas of such base things. But Parmenides corrects him, and tells him that, when he has attained the highest philosophy, he will no longer despise such things. Moreover, these Ideas of base things are just as much perfection in their kind as Beauty and Goodness are in theirs. In general, the principle is that there must be an Idea wherever a concept can be formed; that is, wherever there is a class of many things called by one name.

We saw, in treating of the Eleatics, that for them the absolute Being contained no not-being, and the absolute One no multiplicity. And it was just because they denied all not-being and multiplicity of the absolute reality that they were unable to explain the world of existence, and were forced to deny it altogether. The same problem arises for Plato. Is Being absolutely excludent of not-being? Is the Absolute an abstract One, utterly exclusive of the many? Is his philosophy a pure monism? Is it a pluralism? Or is it a combination of the two? These questions are discussed in the "Sophist" and the "Parmenides."

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