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* Compare the advertisement: «That’s Shell, that was.»
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not 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 «judgement 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 judgement, and capable of truth or falsehood. This
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judgement I call a «judgement of perception.» The proposition «knowledge is perception» must be interpreted as meaning «knowledge is judgements 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 judgement of perception. Plato’s argument that we have no sense-organ for perceiving likeness and unlikeness ignores the cortex, and assumes that all senseorgans 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
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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
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* On this subject see the last chapter of the present work.
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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
