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

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Logical so-called propositions ''show'' [the] logical properties of language and therefore of [the] Universe, but ''say'' nothing. [''Cf''. 6.12.]

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.

E.g., take φa, φa ⊃ ψa, ψa. By merely looking at these three, I can see that 3 follows from 1 and 2; i.e. I can see what is called the truth of a logical proposition, namely, of [the] proposition φa . φa ⊃ ψa : ⊃ : ψa. But this is ''not'' a proposition; but by seeing that it is a tautology I can see what I already saw by looking at the three propositions: the difference is that I ''now'' see THAT it is a tautology. [''Cf''. 6.1221.]

Therefore, if we say one ''logical'' proposition ''follows'' logically from another, this means something quite different from saying that a ''real'' proposition follows logically from ''another.'' For so-called ''proof'' of a logical proposition does not prove its ''truth '' (logical propositions are neither true nor false) but proves ''that'' it is a logical proposition (= is a tautology). [''Cf''. 6.1263.]

This same distinction between what can be ''shewn'' by the language but not ''said,'' explains the difficulty that is felt about types-e.g., as to [the] difference between things, facts, properties, relations. That M is a ''thing'' can't be ''said''; it is nonsense: but ''something'' is ''shewn'' by the symbol "M". In [the] same way, that a ''proposition'' is a subject-predicate proposition can't be said: but it is ''shown'' by the symbol.

Therefore a THEORY ''of types'' is impossible. It tries to say something about the types, when you can only talk about the symbols. But ''what'' you say about the symbols is not that this symbol has that type, which would be nonsense for [the] same reason: but you say simply: ''This'' is the symbol, to prevent a misunderstanding. E.g., in "aRb", "R" is ''not'' a symbol, but ''that'' "R" is between one name and another symbolizes. Here we have ''not'' said: this symbol is not of this type but of that, but only: ''This'' symbolizes and not that. This seems again to make the same mistake, because "symbolizes" is "typically ambiguous". The true analysis is: "R" is no proper name, and, that "R" stands between "a" and "b" expresses a ''relation.'' Here are two propositions ''of different type'' connected by "and".

In the above expression "aRb", we were talking only of this particular "R", whereas what we want to do is to talk of all similar symbols. We have to say: in ''any'' symbol of this form what corresponds to "R" is not a proper name, and the fact that ["R" stands between "a" and "b"] expresses a relation. This is what is sought to be expressed by the nonsensical assertion: Symbols like this are of a certain type. This you can't say, because in order to say it you must first know what the symbol is: and in knowing this you ''see'' [the] type and therefore also [the] type of [what is] symbolized. I.e. in knowing ''what'' symbolizes, you know all that is to be known; you can't ''say'' anything ''about'' the symbol.

For instance: Consider the two propositions (1) "What symbolizes here is a thing", (2) "What symbolizes here is a relational fact (= relation)". These are nonsensical for two reasons: (''a'') because they mention "thing" and "relation"; (''b'') because they mention them in propositions of the same form. The two propositions must be expressed in entirely different forms, if properly analysed; and neither the word "thing" nor "relation" must occur.

N.B. "x" can't be the name of this actual scratch y, because this isn't a thing: but it can be the name of ''a thing;'' and we must understand that what we are doing is to explain what would be meant by saying of an ideal symbol, which did actually consist in one ''thing's'' being to the left of another, that in it a ''thing'' symbolized.

(N.B. In [the] expression (∃y). φ''y,'' one ''is'' apt to say this means "There is a ''thing'' such that...". But in fact we should say "There is a y, such that..."; the fact that the y symbolizes expressing what we mean.)

In general: When such propositions are analysed, while the words "thing", "fact", etc. will disappear, there will appear instead of them a new symbol, of the same form as the one of which we are speaking; and hence it will be at once obvious that we ''cannot'' get the one kind of proposition from the other by substitution.

N.B. In any ordinary proposition, e.g., "Moore good", this ''shews'' and does not say that "''Moore''" is to the left of "good"; and ''here what'' is shewn can be ''said'' by another proposition. But this only applies to that ''part'' of what is shewn which is arbitrary. The ''logical'' properties which it shews are not arbitrary, and that it has these cannot be said in any proposition.

When we say of a proposition of [the] form "aRb" that what symbolizes is that "R" is between "a" and "b", it must be remembered that in fact the proposition is capable of further analysis because a, R, and b are not ''simples.'' But what seems certain is that when we have analysed it we shall in the end come to propositions of the same form in respect of the fact that they do consist in one thing being between two others.

How can we talk of the general form of a proposition, without knowing any unanalysable propositions in which particular names and relations occur? What justifies us in doing this is that though we don't know any unanalysable propositions of this kind, yet we can understand what is meant by a proposition of the form (∃x, y, R) . xRy (which is unanalysable), even though we know no proposition of the form xRy.

If you had any unanalysable proposition in which particular names and relations occurred (and ''unanalysable'' proposition = one in which only fundamental symbols = ones not capable of ''definition'', occur) then you can always form from it a proposition of the form (∃x, y, R). xRy, which though it contains no particular names and relations, is unanalysable.

(2) The point can here be brought out as follows. Take φa and φA: and ask what is meant by saying, "There is a thing in φa, and a complex in φA"?

''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.

Th ''Bedeutung'' of a proposition is the fact that corresponds to it, e.g., if our proposition be "aRb", if it's true, the corresponding fact would be the fact aRb, if false, the fact ~aRb. ''But'' both "the fact aRb" and "the fact ~aRb" are incomplete symbols, which must be analysed.

That a proposition has a relation (in wide sense) to Reality, other than that of ''Bedeutung,'' is shewn by the fact that you can understand it when you don't know the ''Bedeutung'', i.e. don't know whether it is true or false. Let us express this by saying "It has ''sense"'' (''Sinn'')''.''

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

The relation is as follows: Its ''simples'' have meaning = are names of simples; and its relations have a quite different relation to relations; and these two facts already establish a sort of correspondence between proposition which contains these and only these, and reality: i.e. if all the simples of a proposition are known, we already know that we CAN describe reality by saying that it ''behaves''<ref>Presumably "verhält sich zu", i.e. "is related." [''Edd''.]</ref> in a certain way to the whole proposition. (This amounts to saying that we can ''compare'' reality with the proposition. In the case of two lines we can ''compare'' them in respect of their length without any convention: the comarison is automatic. But in our case the possibility of comparison depends upon the conventions by which we have given meanings to our simples (names and relations).)

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'')''.''

There seems at first sight to be a certain ambiguity in what is meant by saying that a proposition is "true", owing to the fact that it seems as if, in the case of different propositions, the way in which they correspond to the facts to which they correspond is quite different. But what is really common to all cases is that they must have ''the general form of a proposition.'' In giving the general form of a proposition you are explaining what kind of ways of putting together the symbols of things and relations will correspond to (be analogous to) the things having those relations in reality. In doing thus you are saying what is meant by saying that a proposition is true; and you must do it once for all. To say "This proposition ''has sense''"'' ''means '"This proposition is true" means ... .' ("p" is true = "p" . p. Def. : only instead of "p" we must here introduce the general form of a proposition.)<ref>The reader should remember that according to Wittgenstein '"p"' is not a name but a description of the fact constituting the proposition. See above, p. 109. [''Edd''.]</ref>

How asymmetry is introduced is by giving a description of a particular form of symbol which we call a "tautology". The description of the ab-symbol alone is symmetrical with respect to a and b; but this description plus the fact that what satisfies the description of a tautology ''is'' a tautology is asymmetrical with regard to them. (To say that a description was symmetrical with regard to two symbols, would mean that we could substitute one for the other, and yet the description remain the same, i.e. mean the same.)

Take p.q and q. When you write p.q in the ab notation, it is impossible to see from the symbol alone that q follows from it, for if you were to interpret the true-pole as the false, the same symbol would stand for p ∨ q, from which q doesn't follow. But the moment you say ''which'' symbols are tautologies, it at once becomes possible to see from the fact that they are and the original symbol that q does follow.

Having thus fixed what is a tautology and what is not, we can then, having fixed arbitrarily again that the relation a-b is transitive get from the two facts together that "p ≡ ~(~p)" is a tautology. For ~(~p) = a-b-a-p-b-a-b. The point is: that the process of reasoning by which we arrive at the result that a-b-a-p-b-a-b is the ''same symbol'' as a-p-b, is exactly the same as that by which we discover that its meaning is the same, viz. where we reason if b-a-p-b-a, then ''not'' a-p-b, if a-b-a-p-b-a-b then ''not'' b-a-p-b-a, therefore if a-b-a-p-b-a-b, then a-p-b.

It follows from the fact that a-b is transitive, that where we have a-b-a the first a has to the second the same relation that it has to b. It is just as from the fact that a-true implies b-false, and b-false implies c-true, we get that a-true implies c-true. And we shall be able to see, having fixed the description of a tautology, that p ≡ ~(~p) is a tautology.

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.

We could, of course, symbolize any ab-function without using two ''outside'' poles at all, merely, e.g., omitting the b-pole; and here what would symbolize would be that the three pairs of inside poles of the propositions were connected in a certain way with the a-pole, while the other pair was ''not'' connected with it. And thus the difference between the scratches a and b, where we do use them, merely shews that it is a different state of things that is symbolizing in the one case and the other: in the one case that certain inside poles ''are '' connected in a certain way with an outside pole, in the other ''that'' they are ''not.''

The reason why "The property of not being green is not green" is ''nonsense,'' is because we have only given meaning to the fact that "green" stands to the right of a name; and "the property of not being green" is obviously not ''that.''

φ cannot possibly stand to the left of (or in any other relation to) the symbol of a property. For the symbol of a property, e.g., ψx is ''that'' ψ stands to the left of a name form, and another symbol φ cannot possibly stand to the left of such a ''fact'': if it could, we should have an illogical language, which is impossible.<blockquote>p is false = ~(p is true) Def.</blockquote>It is very important that the apparent logical relations ∨, ⊃, etc. need brackets, dots, etc., i.e. have "ranges"; which by itself shews they are not relations. This fact has been overlooked, because it is so universal —the very thing which makes it so important. [''Cf''. 5.461.]

The proposition (∃x) . φx . x = a : ≡ : φa can be seen to be a tau­tology, if one expresses the ''conditions'' of the truth of (∃x) . φx . 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) . φx . x = a; and then also for φa. 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

It's obvious that the dots and brackets are symbols, and obvious that they haven't any ''independent'' meaning. You must, therefore, in order to introduce so-called "logical constants" properly, introduce the general notion of ''all possible'' combinations of them = the general

form of a proposition. You thus introduce both ab-functions, identity,

The ''variable proposition'' p ⊃ p is not identical with the ''variable proposition'' ~(p . ~p). The corresponding universals ''would'' be identical. The variable proposition ~(p . ~p) shews that out of ~ (p.q) you get a tautology by substituting ~p for q, whereas the other does not shew this.

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.

The relation of "I believe p" to "p" can be compared to the relation of' "p" says (besagt) p' to p: it is just as impossible that ''I'' should be a simple as that "p" should be. [''Cf'' 5.542.]

 

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