Analyticity, decidability and incompleteness. (English) Zbl 0849.00019

Woleński, Jan

Czermak, Johannes (ed.), Philosophy of mathematics. Proceedings of the 15th international Wittgenstein-Symposium, August 16-23, 1992, Kirchberg am Wechsel, Austria. Part I. Wien: Hölder-Pichler-Tempsky. Schriftenreihe der Wittgenstein-Gesellschaft. 20/I, 379-382 (1993).

This paper investigates the metamathematical problem of analyticity in the light of Gödel’s first incompleteness theorem. In critically extending suggestions of J. Klemeny [J. Symb. Logic 21, 49-161 (1956; Zbl 0073.24604)] and L. Borkowski [Stud. Logica 19, 59-72 (1966; Zbl 0305.02010)] the author divides analytical sentences into absolute and relative, and into syntactic, semantic and pragmatic. The author mentions the problem arising from his conditions for relative analytic sentences in extralogical theories, since there are no a priori reasons to consider the axioms of such theories as analytically true, although they are true in all their models.
For the entire collection see [Zbl 0836.00022].

Reviewer: V.Peckhaus (Erlangen)

MSC:

00A30	Philosophy of mathematics
03F03	Proof theory in general (including proof-theoretic semantics)
03A05	Philosophical and critical aspects of logic and foundations

Keywords:

incompleteness; metamathematics; analyticity

Citations:

Zbl 0073.24604; Zbl 0305.02010