Validity

Pořádá Oddělení logiky AV ČR

Göran Sundholm
(Göran Sundholm (Leiden University))

Plakát

Validity, in many guises and shapes, is an omnipresent notion within modern logic. However, is current practice with respect to validity a valid one? I argue it is not; in particular the customary [Bolzano] conflation between inferential validity and the logical holding of consequence will be discussed and the role (need?) of a completeness theorem rejected. Some consequences for epistemology and the philosophy of mathematics are also noted. Different notions known as "validity" from logical literature will be distinguished, to wit,
1. Validity of a proof (demonstration);
2. Validity of an inference;
3. (Logical) Validity of a wff (proposition);
4. (Logical) Validity of a consequence among wff's (propositions);
5. (Prawitz-)Validity of derivations in the sense of Proof-Theoretical Semantics.
Here the common conflation of 1. and 2., as well as the almost universal accepted reduction of 2. to 4., will, at the hand of writings of Frege and Tarski, be given special attention.