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ment, there is no corresponding constituent in the meaning of the statement. We may continue, if we like, to say that numbers are eternal, immutable, and so on, but we must add that they are logical fictions.
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
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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 continually changing. Such a word as «red» applies to many shades of colour, and if we say «I see red,» there is no reason why this should not remain true throughout the time that it takes to say it. Plato gets his results by applying to processes of continuous change such logical oppositions as perceiving and not-perceiving, knowing and not-knowing. Such oppositions, however, are not suitable for describing such processes. Suppose, on a foggy day, you watch a man walking away from you along a road: he grows dimmer and dimmer, and there comes a moment when you are sure that you no longer see him, but there is an intermediate period of doubt. Logical oppositions have been invented for our convenience, but continuous change requires a quantitative apparatus, the possibility of which Plato
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ignores. What he says on this subject, therefore, is largely beside the mark.
At the same time, it must be admitted that, unless words, to some extent, had fixed meanings, discourse would be impossible. Here again, however, it is easy to be too absolute. Words do change their meanings; take, for example, the word «idea.» It is only by a considerable process of education that we learn to give to this word something like the meaning which Plato gave to it. It is necessary that the changes in the meanings of words should be slower than the changes that the words describe; but it is not necessary that there should be no changes in the meanings of words. Perhaps this does not apply to the abstract words of logic and mathematics, but these words, as we have seen, apply only to the form, not to the matter, of propositions. Here, again, we find that logic and mathematics are peculiar. Plato, under the influence of the Pythagoreans, assimilated other knowledge too much to mathematics. He shared this mistake with many of the greatest philosophers, but it was a mistake none the less.
CHAPTER XIX Aristotle’s Metaphysics
IN reading any important philosopher, but most of all in reading Aristotle, it is necessary to study him in two ways: with reference to his predecessors, and with reference to his successors. In the former aspect, Aristotle’s merits are enormous; in the latter, his demerits are equally enormous. For his demerits, however, his successors are more responsible than he is. He came at the end of the creative period in Greek thought, and after his death it was two thousand years before the world produced any philosopher who could be regarded as approximately his equal. Towards the end of this long period his authority had become almost as unquestioned as that of the Church, and in science, as well as in philosophy, had become a serious obstacle to progress. Ever since the beginning of
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the seventeenth century, almost every serious intellectual advance has had to begin with an attack on some Aristotelian doctrine; in logic, this is still true at the present day. But it would have been at least as disastrous if any of his predecessors (except perhaps Democritus) had acquired equal authority. To do him justice, we must, to begin with, forget his excessive posthumous fame, and the equally excessive posthumous condemnation to which it led.
Aristotle was born, probably in 384 B.C., at Stagyra in Thrace. His father had inherited the position of family physician to the king of Macedonia. At about the age of eighteen Aristotle came to Athens and became a pupil of Plato; he remained in the Academy for nearly twenty years, until the death of Plato in 348-7 B.C. He then travelled for a time, and married either the sister or the niece of a tyrant named Hermias. ( Scandal said she was the daughter or concubine of Hermias, but both stories are disproved by the fact that he was a eunuch.) In 343 B.C. he became tutor to Alexander, then thirteen years old, and continued in that position until, at the age of sixteen, s was pronounced by his father to be of age, and was appointed regent during Philip’s absence. Everything one would wish to know of the relations of Aristotle and Alexander is unascertainable, the more so as legends were soon invented on the subject. There are letters between them which are generally regarded as forgeries. People who admire both men suppose that the tutor influenced the pupil. Hegel thinks that Alexander’s career shows the practical usefulness of philosophy. As to this, A. W. Benn
