Most modern men take it for granted that empirical knowledge is dependent upon, or derived from, perception. There is however in Plato and among philosophers of certain other schools a very different doctrine, to the effect that there is nothing worthy to be called 'knowledge' to be derived from the senses, and that the only real knowledge has to do with concepts. In this view, '2 + 2 = 4' is genuine knowledge, but such a statement as 'snow is white' is so full of ambiguity and uncertainty that it cannot find a place in the philosopher's corpus of truths.

This view is perhaps traceable to Parmenides, but in its explicit form the philosophic world owes it to Plato. I propose, in this chapter, to deal with Plato's criticism of the view that knowledge is the same thing as perception, which occupies the first half of the Theaetetus.

This dialogue is concerned to find a definition of 'knowledge', but ends without arriving at any but a negative conclusion; several definitions are proposed and rejected, but no definition that is considered satisfactory is suggested.

The first of the suggested definitions, and the only one that I shall consider, is set forth by Theaetetus in the words:

'It seems to me that one who knows something is perceiving the thing that he knows, and, so far as I can see at present, knowledge is nothing but perception.'

Socrates identifies this doctrine with that of Protagoras, that 'man is the measure of all things', i.e. that any given thing 'is to me such as it appears to me, and is to you such as it appears to you.' Socrates adds: 'Perception, then, is always something that is, and, as being knowledge, it is infallible.'

A large part of the argument that follows is concerned with the characterization of perception; when once this is completed, it does not take long to prove that such a thing as perception has turned out to be cannot be knowledge.

Socrates adds to the doctrine of Protagoras the doctrine of Heraclitus, that everything is always changing, i.e. that 'all the things we are pleased to say "are" really are in process of becoming'. Plato believes this to be true of objects of sense, but not of the objects of real knowledge. Throughout the dialogue, however, his positive doctrines remain in the background.

From the doctrine of Heraclitus, even if it be only applicable to objects of sense, together with the definition of knowledge as perception, it follows that knowledge is of what becomes, not of what is.

There are, at this point, some puzzles of a very elementary character. We are told that, since 6 is greater than 4 but less than 12, 6 is both great and small, which is a contradiction. Again, Socrates is now taller than Theaetetus, who is a youth not yet full grown; but in a few years Socrates will be shorter than Theaetetus. Therefore Socrates is both tall and short. The idea of a relational proposition seems to have puzzled Plato, as it did most of the great philosophers down to Hegel (inclusive). These puzzles, however, are not very germane to the argument, and may be ignored.

Returning to perception, it is regarded as due to an interaction between the object and the sense-organ, both of which, according to the doctrine of Heraclitus, are always changing, and both of which, in changing, change the percept. Socrates remarks that when he is well he finds wine sweet, but when ill, sour. Here it is a change in the percipient that causes the change in the percept.

Certain objections to the doctrine of Protagoras are advanced, and some of these are subsequently withdrawn. It is urged that Protagoras ought equally to have admitted pigs and baboons as measures of all things, since they also are percipients. Questions are raised as to the validity of perception in dreams and in madness. It is suggested that, if Protagoras is right, one man knows no more than another: not only is Protagoras as wise as the gods, but, what is more serious, he is no wiser than a fool. Further, if one man's judgments are as correct as another's, the people who judge that Protagoras is mistaken have the same reason to be thought right as he has.

Socrates undertakes to find an answer to many of these objections, putting himself, for the moment, in the place of Protagoras. As for dreams, the percepts are true as percepts. As for the argument about pigs and baboons, this is dismissed as vulgar abuse. As for the argument that, if each man is the measure of all things, one man is as wise as another, Socrates suggests, on behalf of Protagoras, a very interesting answer, namely that, while one judgment cannot be truer than another, it can be better, in the sense of having better consequences. This suggests pragmatism.1

This answer, however, though Socrates has invented it, does not satisfy him. He urges, for example, that when a doctor foretells the course of my illness, he actually knows more of my future than I do. And when men differ as to what it is wise for the State to decree, the issue shows that some men had a greater knowledge as to the future than others had. Thus we cannot escape the conclusion that a wise man is a better measure of things than a fool.

All these are objections to the doctrine that each man is the measure of all things, and only indirectly to the doctrine that 'knowledge' means 'perception', in so far as this doctrine leads to the other. There is, however, a direct argument, namely that memory must be allowed as well as perception. This is admitted, and to this extent the proposed definition is amended.

We come next to criticisms of the doctrine of Heraclitus. This is first pushed to extremes, in accordance, we are told, with the practice of his disciples among the bright youths of Ephesus. A thing may change in two ways, by locomotion, and by a change of quality, and the doctrine of flux is held to state that everything is always changing in both respects.2 And not only is everything always undergoing some qualitative change, but everything is always changing all its qualities—so, we are told, clever people think at Ephesus. This has awkward consequences. We cannot say 'this is white', for if it was white when we began speaking it will have ceased to be white before we end our sentence. We cannot be right in saying we are seeing a thing, for seeing is perpetually changing into not-seeing.3 If everything is changing in every kind of way, seeing has no right to be called seeing rather than not-seeing, or perception to be called perception rather than not-perception. And when we say 'perception is knowledge', we might just as well say 'perception is not-knowledge.'

What the above argument amounts to is that, whatever else may be in perpetual flux, the meanings of words must be fixed, at least for a time, since otherwise no assertion is definite, and no assertion is true rather than false. There must be something more or less constant, if discourse and knowledge are

to be possible. This, I think, should be admitted. But a great deal of flux is compatible with this admission.

There is, at this point, a refusal to discuss Parmenides, on the ground that he is too great and grand. He is a 'reverend and awful figure'. 'There was a sort of depth in him that was altogether noble.' He is 'one being whom I respect above all'. In these remarks Plato shows his love for a static universe, and his dislike of the Heraclitean flux which he has been admitting for the sake of argument. But after this expression of reverence he abstains from developing the Parmenidean alternative to Heraclitus.

We now reach Plato's final argument against the identification of knowledge with perception. He begins by pointing out that we perceive through eyes and ears, rather than with them, and he goes on to point out that some of our knowledge is not connected with any sense-organ. We can know, for instance, that sounds and colours are unlike, though no organ of sense can perceive both. There is no special organ for 'existence and non-existence, likeness and unlikeness, sameness and differences, and also unity and numbers in general'. The same applies to honourable and dishonourable, and good and bad. 'The mind contemplates some things through its own instrumentality, others through the bodily faculties.' We perceive hard and soft through touch, but it is the mind that judges that they exist and that they are contraries. Only the mind can reach existence, and we cannot reach truth if we do not reach existence. It follows that we cannot know things through the senses alone, since through the senses alone we cannot know that things exist. Therefore knowledge consists in reflection, not in impressions, and perception is not knowledge, because it 'has no part in apprehending truth, since it has none in apprehending existence'.

To disentangle what can be accepted from what must be rejected in this argument against the identification of knowledge with perception is by no means easy. There are three inter-connected theses that Plato discusses, namely:

(1) Knowledge is perception;

(2) Man is the measure of all things;

(3) Everything is in a state of flux.

(1) The first of these, with which alone the argument is primarily concerned, is hardly discussed on its own account except in the final passage with which we have just been concerned. Here it is argued that comparison, knowledge of existence, and understanding of number, are essential to knowledge, but cannot be included in perception since they are not effected through any sense-organ. The things to be said about these are different. Let us begin with likeness and unlikeness.

That two shades of colour, both of which I am seeing, are similar or dissimilar as the case may be, is something which I, for my part, should accept, not indeed as a 'percept', but as a 'judgment of perception'. A percept, I should say, is not knowledge, but merely something that happens, and that belongs equally to the world of physics and to the world of psychology. We naturally think of perception, as Plato does, as a relation between a percipient and an object: we say 'I see a table.' But here 'I' and 'table' are logical constructions. The core of crude occurrence is merely certain patches of colour. These are associated with images of touch, they may cause words, and they may become a source of memories. The percept as filled out with images of touch becomes an 'object', which is supposed physical; the percept as filled out with words and memories becomes a 'perception', which is part of a 'subject' and is considered mental. The percept is just an occurrence, and neither true nor false; the percept as filled out with words is a judgment, and capable of truth or falsehood. This judgment I call a 'judgment of perception'. The proposition 'knowledge is perception' must be interpreted as meaning 'knowledge is judgments of perception'. It is only in this form that it is grammatically capable of being correct.

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 judgment 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 judgment 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 judgment on our part asserting likeness. If there were only our judgment, it would be an arbitrary judgment, 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 judgment 'A is like B' is true (if it is true) in virtue of a 'fact', just as much as the judgment '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.4This disposes of existenceas 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" is 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 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 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.

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