THE PRINCIPLE OF BIVALENCE AND SUSZKO THESIS
Jan Woleński · 2009
According to Suszko, every logic with structural consequence operation is bivalent, that is, evaluates sentences as either true or false. Truth and falsehoods are logical valuations. On the other hand, the Suszko thesis (ST) admits algebraic valuations as related to semantic correlates of sentences. Due to Frege’s axiom (materially equivalent sentences are identical), standard propositional calculus identifies logical and algebraic valuations. SCI (sentential calculus with identity) considers identity and equivalence as dierent connectives. Hence, we can ascribe separate semantic correlates to dierent true sentences. Thus, SCI is logically bivalent and algebraically multivalent. This paper argues that although ST can be defended, its justification is pragmatic, but not purely logical.