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> | 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> | ||
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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. | 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. | ||
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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. | 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 | 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. | |||
<references/> | That, when a certain rule is given, a symbol is tautological ''shews'' a logical truth.<references /> | ||