History of Western Philosophy - Bertrand Russell [94]
There is a further point. Concerning sound and colour, Plato says 'both together are two, and each of them is one'. We have considered the two; now we must consider the one. There is here a mistake very analogous to that concerning existence. The predicate 'one' is not applicable to things, but only to unit classes. We can say 'the earth has one satellite', but it is a syntactical error to say 'the moon is one'. For what can such an assertion mean? You may just as well say 'the moon is many', since it has many parts. To say 'the earth has one satellite' is to give a property of the concept 'earth's satellite', namely the following property:
'There is a c such that "x is a satellite of the earth" is true when, and only when, x is c.'
This is an astronomical truth; but if, for 'a satellite of the earth', you substitute 'the moon' or any other proper name, the result is either meaningless or a mere tautology. 'One', therefore is a property of certain concepts, just as 'ten' is a property of the concept 'my finger'. But to argue, 'the earth has one satellite, namely the moon, therefore the moon is one' is as bad as to argue 'The Apostles were twelve; Peter was an apostle; therefore Peter was twelve,' which would be valid if for 'twelve' we substituted 'white'.
The above considerations have shown that, while there is a formal kind of knowledge, namely logic and mathematics, which is not derived from perception, Plato's arguments as regards all other knowledge are fallacious. This does not, of course, prove that his conclusion is false; it proves only that he has given no valid reason for supposing it true.
(2) I come now to the position of Protagoras, that man is the measure of all things, or, as it is interpreted, that each man is the measure of all things. Here it is essential to decide the level upon which the discussion is to proceed. It is obvious that, to begin with, we must distinguish between percepts and inferences. Among percepts, each man is inevitably confined to his own; what he knows of the percepts of others he knows by inference from his own percepts in hearing and reading. The percepts of dreamers and madmen, as percepts, are just as good as those of others; the only objection to them is that, as their context is unusual, they are apt to give rise to fallacious inferences.
But how about inferences? Are they equally personal and private? In a sense, we must admit that they are. What I am to believe, I must believe because of some reason that appeals to me. It is true that my reason may be some one else's assertion, but that may be a perfectly adequate reason—for instance, if I am a judge listening to evidence. And however Protagorean I may be, it is reasonable to accept the opinion of an accountant about a set of figures in preference to my own, for I may have repeatedly found that if, at first, I disagree with him, a little more care shows me that he was right. In this sense I may admit that another man is wiser than I am. The Protagorean position, rightly interpreted, does not involve the view that I never make mistakes, but only that the evidence of my mistakes must appear to me. My past self can be judged just as another person can be judged. But all this presupposes that, as regards inferences as opposed to percepts, there is some impersonal standard of correctness. If any inference that I happen to draw is just as good as any other, then the intellectual anarchy that Plato deduces from Protagoras does in fact follow. On this point, therefore, which is an important one, Plato seems to be in the right. But the empiricist would say that perceptions are the test of correctness in inference in empirical material.
(3) The doctrine of universal flux is caricatured by Plato, and it is difficult to suppose that any one ever held it in the extreme form that he gives to it. Let us suppose, for example, that the colours we see are