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

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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>

It seems at first sight as if the ab notation must be wrong, because it seems to treat true and false as on exactly the same level. It must be possible to see from the symbols themselves that there is some essential difference between the poles, if the notation is to be right; and it seems as if in fact this was impossible.

The interpretation of a symbolism must not depend upon giving a different interpretation to symbols of the same types.

How asymmetry is introduced is by giving a description of a particular form of symbol which we call a "tautology". The description of the ah-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.

''Logical propositions'', 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.

What is unarbitrary about our symbols is not them, nor the rules we give; but the fact that, having given certain rules, others are fixed = follow logically. [''Cf.'' 3.342.]

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.

Logical constants can't be made into variables: because in them ''what'' symbolizes is ''not'' the same; all symbols for which a variable can be substituted symbolize in the ''same'' way.

We describe a symbol, and say arbitrarily "A symbol of this description is a tautology". And then, it follows at once, both that any other symbol which answers to the same description is a tautology, and that any symbol which does ''not'' isn't. That is, we have arbitrarily fixed that any symbol of that description is to be a tautology; and this being fixed it is no longer arbitrary with regard to any other symbol whether it is a tautology or not.

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

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 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>
+It seems at first sight as if the ab notation must be wrong, because it seems to treat true and false as on exactly the same level. It must be possible to see from the symbols themselves that there is some essential difference between the poles, if the notation is to be right; and it seems as if in fact this was impossible.
+The interpretation of a symbolism must not depend upon giving a different interpretation to symbols of the same types.
+How asymmetry is introduced is by giving a description of a particular form of symbol which we call a "tautology". The description of the ah-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.
+''Logical propositions'', 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.
+What is unarbitrary about our symbols is not them, nor the rules we give; but the fact that, having given certain rules, others are fixed = follow logically. [''Cf.'' 3.342.]
+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.
+Logical constants can't be made into variables: because in them ''what'' symbolizes is ''not'' the same; all symbols for which a variable can be substituted symbolize in the ''same'' way.
+We describe a symbol, and say arbitrarily "A symbol of this description is a tautology". And then, it follows at once, both that any other symbol which answers to the same description is a tautology, and that any symbol which does ''not'' isn't. That is, we have arbitrarily fixed that any symbol of that description is to be a tautology; and this being fixed it is no longer arbitrary with regard to any other symbol whether it is a tautology or not.
+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
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