A History of Western Philosophy

by Bertrand Russell

  To return to likeness and unlikeness, it is quite possible, when I perceive two colours simultaneously, for their likeness or unlikeness to be part of the datum, and to be asserted in a judgement of perception. Plato’s argument that we have no sense-organ for perceiving likeness and unlikeness ignores the cortex, and assumes that all sense-organs must be at the surface of the body.

  The argument for including likeness and unlikeness as possible perceptive data is as follows. Let us assume that we see two shades of colour A and B, and that we judge “A is like B.” Let us assume further, as Plato does, that such a judgement is in general correct, and, in particular, is correct in the case we are considering. There is; then, a relation of likeness between A and B, and not merely a judgement on our part asserting likeness. If there were only our judgement, it would be an arbitrary judgement, incapable of truth or falsehood. Since it obviously is capable of truth or falsehood, the likeness can subsist between A and B, and cannot be merely something “mental.” The judgement “A is like B” is true (if it is true) in virtue of a “fact,” just as much as the judgement “A is red” or “A is round.” The mind is no more involved in the perception of likeness than in the perception of colour.

  I come now to existence, on which Plato lays great stress. We have, he says, as regards sound and colour, a thought which includes both at once, namely that they exist. Existence belongs to everything, and is among the things that the mind apprehends by itself; without reaching existence, it is impossible to reach truth.

  The argument against Plato here is quite different from that in the case of likeness and unlikeness. The argument here is that all that Plato says about existence is bad grammar, or rather bad syntax. This point is important, not only in connection with Plato, but also with other matters such as the ontological argument for the existence of the Deity.

  Suppose you say to a child “lions exist, but unicorns don’t,” you can prove your point so far as lions are concerned by taking him to the Zoo and saying “look, that’s a lion.” You will not, unless you are a philosopher, add: “And you can see that that exists.” If, being a philosopher, you do add this, you are uttering nonsense. To say “lions exist” means “there are lions,” i.e. “‘x is a lion’ is true for a suitable x.” But we cannot say of the suitable x that it “exists”; we can only apply this verb to a description, complete or incomplete. “Lion” is an incomplete description, because it applies to many objects: “The largest lion in the Zoo” is complete, because it applies to only one object.

  Now suppose that I am looking at a bright red patch. I may say “this is my present percept”; I may also say “my present percept exists”; but I must not say “this exists,” because the word “exists” is only significant when applied to a description as opposed to a name.* This disposes of existence as one of the things that the mind is aware of in objects.

  I come now to understanding of numbers. Here there are two very different things to be considered: on the one hand, the propositions of arithmetic, and on the other hand, empirical propositions of enumeration. “ 2 + 2 = 4” is of the former kind; “I have ten fingers” is of the latter.

  I should agree with Plato that arithmetic, and pure mathematics generally, is not derived from perception. Pure mathematics consists of tautologies, analogous to “men are men,” but usually more complicated. To know that a mathematical proposition is correct, we do not have to study the world, but only the meanings of the symbols; and the symbols, when we dispense with definitions (of which the purpose is merely abbreviation), are found to be such words as “or” and “not,” and “all” and “some,” which do not, like “Socrates,” denote anything in the actual world. A mathematical equation asserts that two groups of symbols have the same meaning; and so long as we confine ourselves to pure mathematics, this meaning must be one that can be understood without knowing anything about what can be perceived. Mathematical truth, therefore, is, as Plato contends, independent of perception; but it is truth of a very peculiar sort, and is concerned only with symbols.

  Propositions of enumeration, such as “I have ten fingers,” are in quite a different category, and are obviously, at least in part, dependent on perception. Clearly the concept “finger” is abstracted from perception; but how about the concept “ten”? Here we may seem to have arrived at a true universal or Platonic idea. We cannot say that “ten” is abstracted from perception, for any percept which can be viewed as ten of some kind of thing can equally well be viewed otherwise. Suppose I give the name “digitary” to all the fingers of one hand taken together; then I can say “I have two digitaries,” and this describes the same fact of perception as I formerly described by the help of the number ten. Thus in the statement “I have ten fingers” perception plays a smaller part, and conception a larger part, than in such a statement as “this is red.” The matter, however, is only one of degree.

  The complete answer, as regards propositions in which the word “ten” occurs, is that, when these propositions are correctly analysed, they are found to contain no constituent corresponding to the word “ten.” To explain this in the case of such a large number as ten would be complicated; let us, therefore, substitute “I have two hands.” This means:

  “There is an a such that there is a b such that a and b are not identical and whatever x may be, ‘x is a hand of mine’ true when, and only when, x is a or x is b.”

  Here the word “two” does not occur. It is true that two letters a and b occur, but we do not need to know that they are two, any more than we need to know that they are black, or white, or whatever colour they may happen to be.

  Thus numbers are, in a certain precise sense, formal. The facts which verify various propositions asserting that various collections each have two members, have in common, not a constituent, but a form. In this they differ from propositions about the Statue of Liberty, or the moon, or George Washington. Such propositions refer to a particular portion of space-time; it is this that is in common between all the statements that can be made about the Statue of Liberty. But there is nothing in common among propositions “there are two so-and-so’s” except a common form. The relation of the symbol “two” to the meaning of a proposition in which it occurs is far more complicated than the relation of the symbol “red” to the meaning of a proposition in which it occurs. We may say, in a certain sense, that the symbol “two” means nothing, for, when it occurs in a true statement 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 f
rom 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 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 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 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, Alexander 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 says: “It would be unfortunate if philosophy had no better testimonial to show for herself than the character of Alexander…. Arrogant, drunken, cruel, vindictive, and grossly superstitious, he united the vices of a Highland chieftain to the frenzy of an Oriental despot.”*

  For my part, while I agree with Benn about the character of Alexander, I nevertheless think that his work was enormously important and enormously beneficial, since, but for him, the whole tradition of Hellenic civilization might well have perished. As to Aristotle’s influence on him, we are left free to conjecture whatever seems to us most plausible. For my part, I should suppose it nil. Alexander was an ambitious and passionate boy, on bad terms with his father, and presumably impatient of schooling. Aristotle thought no State should have as many as one hundred thousand citizens,* and preached the doctrine of the golden mean. I cannot imagine his pupil regarding him as anything but a prosy old pedant, set over him by his father to keep him out of mischief. Alexander, it is true, had a certain snobbish respect for Athenian civilization, but this was common to his whole dynasty, who wished to prove that they were not barbarians. It was analogous to the feeling of nineteenth-century Russian aristocrats for Paris. This, therefore, was not attributable to Aristotle’s influence. And I do not see anything else in Alexander that could possibly have come from this source.

  It is more surprising that Alexander had so little influence on Aristotle, whose speculations on politics were blandly oblivious of the fact that the era of City States had given way to the era of empires. I suspect that Aristotle, to the end, thought of him as “that idle and headstrong boy, who never could understand anything of philosophy.” On the whole, the contacts of these two great men seem to have been as unfruitful as if they had lived in different
worlds.

  From 335 B.C. to 323 B.C. (in which latter year Alexander died), Aristotle lived at Athens. It was during these twelve years that he founded his school and wrote most of his books. At the death of Alexander, the Athenians rebelled, and turned on his friends, including Aristotle, who was indicted for impiety, but, unlike Socrates, fled to avoid punishment. In the next year (322) he died.

  Aristotle, as a philosopher, is in many ways very different from all his predecessors. He is the first to write like a professor: his treatises are systematic, his discussions are divided into heads, he is a professional teacher, not an inspired prophet. His work is critical, careful, pedestrian, without any trace of Bacchic enthusiasm. The Orphic elements in Plato are watered down in Aristotle, and mixed with a strong dose of common sense; where he is Platonic, one feels that his natural temperament has been overpowered by the teaching to which he has been subjected. He is not passionate, or in any profound sense religious. The errors of his predecessors were the glorious errors of youth attempting the impossible; his errors are those of age which cannot free itself of habitual prejudices. He is best in detail and in criticism; he fails in large construction, for lack of fundamental clarity and Titanic fire.