This log was inspired by "How to Read Wittgenstein" and "Ludwig Wittgenstein: the duty of genius" by Ray Monk. It is based on reading Tractatus Logico-Philosophicus by Ludwig Wittgenstein translated by D. F. Pears & B. F. McGuinness (Routledge and Kegan Paul:1963)

Tuesday, April 1, 2008

Every proposition must make sense on its own.

To illustrate the concept of truth, imagine a black spot on white paper. One can describe the shape of the spot by saying, for each point on the sheet, whether it is black or white. To the fact that a point is black there corresponds a positive fact, and to the fact that a point is white (not black), a negative fact. If I designate a point on the sheet (a truth-value according to Frege), then that corresponds to the supposition being evaluated, etc. etc.

But in order to be able to say that a point is black or white, I must first know when a point is called black, and when white. In order to be able to say, " 'p' is true (or false)", I must have determined in what circumstances I call 'p' true, and by that have already determined the sense of the proposition. But now the the simile breaks down.

We can indicate a point on the paper even if we do not know what black or white is. but if a proposition makes no sense, nothing corresponds to it, since it does not designate an object (truth value) which might have properties called 'false' or 'true'. The predicate of a proposition is not 'is true' or 'is false', as Frege thought: rather, that which 'is true' must already include that predicate.

Every proposition must make sense on its own. It cannot be given a sense by affirmation since its sense is just what is affirmed; and the same applies to negation, etc. One could say that negation must be related to the logical space determined by the negated proposition. The negation determines a logical space different from that of the negated proposition. The negation determines a logical space with the help of the negated proposition, for it describes the former as lying outside the latter's logical space. That a negation can be negated shows that what is negated is already a proposition, and not a mere preliminary.

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