Notes Dictated to G.E. Moore in Norway: Difference between revisions

It is impossible to ''say'' what these properties are, because in order to do so, you would need a language, which hadn't got the properties in question, and it is impossible that this should be a ''proper'' language. Impossible to construct [an] illogical language.

How, usually, logical propositions do shew these properties is this: We give a certain description of a kind of symbol; we find that other symbols, combined in certain ways, yield a symbol of this description; and ''that'' they do shews something about these symbols.

Every ''real'' proposition ''shews'' something, besides what it says, about the Universe: ''for,'' if it has no sense, it can't be used; and if it has a sense, it mirrors some logical property of the Universe.

We want to say, in order to understand [the] above, what properties a symbol must have, in order to be a tautology.

This is the actual procedure of [the] ''old'' Logic: it gives so-called primitive propositions; so-called rules of deduction; and then says that what you get by applying the rules to the propositions is a ''logical'' proposition that you have ''proved.'' The truth is, it tells you something ''about'' the kind of propositions you have got, viz. that it can be derived from the first symbols by these rules of combination (= is a tautology).

Logical propositions ''shew'' something, ''because'' the language in which they are expressed can ''say'' everything that can be ''said.''

:(1) means: (∃x) . ''φ''x . x = a

''Use of logical propositions.'' You may have one so complicated that you cannot, by looking at it, see that it is a tautology; but you have shewn that it can be derived by certain operations from certain other propositions according to our rule for constructing tautologies; and hence you are enabled to see that one thing follows from another, when you would not have been able to see it otherwise. E.g., if our tautology is of [the] form p ⊃ q you can see that q follows from p; and so on.

In analysing ''Bedeutung,'' you come upon ''Sinn'' as follows: We want to explain the relation of propositions to reality.

It only remains to fix the method of comparison by saying ''what'' about our simples is to ''say'' what about reality. E.g., suppose we take two lines of unequal length: and say that the fact that the shorter is of the length it is is to mean that the longer is of the length ''it'' is. We should then have established a convention as to the meaning of the shorter, of the sort we are now to give.

From this it results that "true" and "false" are not accidental properties of a proposition, such that, when it has meaning, we can say it is also true or false: on the contrary, to have meaning ''means '' to be true or false: the being true or false actually constitutes the relation of the proposition to reality, which we mean by saying that it has meaning (''Sinn'')''.''

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''Logical propositions'', {{small caps|of course}}, all shew something different: all of them shew, ''in the same way'', viz. by the fact that they are tautologies, but they are different tautologies and therefore shew each something different.

Thus, though it would be possible to interpret the form which we take as the form of a tautology as that of a contradiction and vice versa, they ''are'' different in logical form because though the apparent form of the symbols is the same, what ''symbolizes'' in them is different, and hence what follows about the symbols from the one interpretation will be different from what follows from the other. But the difference between a and b is ''not'' one of logical form, so that nothing will follow from this difference alone as to the interpretation of other symbols. Thus, e.g., p.q, p ∨ q seem symbols of exactly the ''same'' logical form in the ab notation. Yet they say something entirely different; and, if you ask why, the answer seems to be: In the one case the scratch at the top has the shape b, in the other the shape a. Whereas the interpretation of a tautology as a tautology is an interpretation of a ''logical form,'' not the giving of a meaning to a scratch of a particular shape. The important thing is that the interpretation of the form of the symbolism must be fixed by giving an interpretation to its ''logical properties'', ''not'' by giving interpretations to particular scratches.

That, when a certain rule is given, a symbol is tautological ''shews'' a logical truth.

In settling that it is to be interpreted as a tautology and not as a contradiction, I am not assigning a ''meaning'' to a and b; i.e. saying that they symbolize different things but in the same way. What I am doing is to say that the way in which the a-pole is connected with the whole symbol symbolizes in a ''different way'' from that in which it would symbolize if the symbol were interpreted as a contradiction. And I add the scratches a and b merely in order to shew in which ways the connexion is symbolizing, so that it may be evident that wherever the same scratch occurs in the corresponding place in another symbol, there also the connexion is symbolizing in the same way.

:p is false = ~(p is true) Def.

There are ''internal'' relations between one proposition and another; but a proposition cannot have to another ''the'' internal relation which a ''name'' has to the proposition of which it is a constituent, and which ought to be meant by saying it "occurs" in it. In this sense one proposition can't "occur" in another.

The proposition (∃x) . ''φ''x . x = a : ≡ : ''φ''a can be seen to be a tau­tology, if one expresses the ''conditions'' of the truth of (∃x) . ''φ''x . x = a, successively, e.g., by saying: This is true ''if'' so and so; and this again is true ''if'' so and so, etc., for (∃x) . ''φ''x . x = a; and then also for ''φ''a. To express the matter in this way is itself a cumbrous notation, of which the ab-notation is a neater translation.

The question whether a proposition has sense (''Sinn'') can never depend on the ''truth'' of another proposition about a constituent of the first. E.g., the question whether (x) x = x has meaning (''Sinn'') can't depend on the question whether (∃x) x = x is ''true.'' It doesn't describe reality at all, and deals therefore solely with symbols; and it says that they must ''symbolize'', but not ''what'' they symbolize.

It's very important to realize that when you have two different relations (a,b)R, (c,d)S this does ''not'' establish a correlation between a and c, and b and d, or a and d, and b and c: there is no correlation whatsoever thus established. Of course, in the case of two pairs of terms united by the ''same'' relation, there is a correlation. This shews that the theory which held that a relational fact contained the terms and relations united by a ''copula'' (ε₂) is untrue; for if this were so there would be a correspondence between the terms of different relations.

A tautology (''not'' a logical proposition) is not nonsense in the same sense in which, e.g., a proposition in which words which have no meaning occur is nonsense. What happens in it is that all its simple parts have meaning, but it is such that the connexions between these paralyse or destroy one another, so that they are all connected only in some irrelevant manner.

Different logical types can have nothing whatever in common. But the mere fact that we can talk of the possibility of a relation of n places, or of an analogy between one with two places and one with four, shews that relations with different numbers of places have something in common, that therefore the difference is not one of type, but like the difference between different names-something which depends on experience. This answers the question how we can know that we have really got the most general form of a proposition. We have only to introduce what is ''common'' to all relations of whatever number of places.