Volume 13, 2008
Logic and Philosophy of Logic
Semantics with Only One Bedeutung
Rethinking Frege's Semantics
The modification of Frege's semantics that consists in using only one reference (Bedeutung, denotate) truth instead of two references truth and falsity is proposed. According to Frege 1) every true sentence stands for truth, 2) every false sentence stands for falsity. We modify the second statement: 2*) every false sentence doesn't stand for truth. The modification of sentential logic interpretation will consist in change of semantic rules: a) every formula A stands either for truth or falsity, b.1) the formula A has value T iff the formula A stands for truth, b.2) the formula A has value F iff the formula A stands for falsity. Let’s change rules a) and b.2) on: a*) every formula A either stands or doesn't stand for truth, b.2*) the formula A has value F iff the formula A doesn't stand for truth. So, we have only one reference but still two values. The proposed approach can be extended to non-classical cases, for which the bivalence principle doesn't take place. An ordered pair of the sentences A, ~A is put in correspondence to the sentence A. Each sentence of ordered pair can either stands or doesn't stand for truth
independently from the other. Thus for each pair of sentences we have four possible variants of reference which are generate four functional values.