Notes on Logic: Difference between revisions

An analogy for the theory of truth: Consider a black patch on white paper. Then we can describe the form of the patch by mentioning, for each point of the surface, whether it is white or black. To the fact that a point is black corresponds a positive fact; to the fact that a point is white (not black) corresponds a negative fact. If I designate a point of the surface (one of Frege's "truth-values"), this is as if I set up an assumption to be decided upon. But in order to be able to say of a point that it is black or it is white, I must first know when a point is to be called black and when it is to be called white. In order to be able to say that "p" is true (or false), I must first have determined under what circumstances I call a proposition true, and thereby I determine the ''sense'' of a proposition. The point in which the analogy fails is this: I can indicate a point of the paper which is white and black, but to a proposition without sense nothing corresponds, for it does not designate a thing (truth-value) whose properties might be called "false" or "true". The verb of a proposition is not "is true" or "is false", as Frege believes, but what is true must already contain the verb. [''Cf.'' 4.063.]

One is tempted to interpret "not-p" as "everything else, only not p". That from a single fact p an infinity of others, not-not-p, etc., follow is hardly credible. [''See'' 5.43.] Man possesses an innate capacity for constructing symbols with which ''some'' sense can be expressed without having the slightest idea what each word signifies. [''Cf.'' 4.002.] The best example of this is mathematics, for man has until recently used the symbols for numbers without knowing what they signify or that they signify nothing.