Truth and Diagonalization

(Logik & Philosophie der Mathematik, Englisch)

n this paper we present a classical, disquotational theory of truth over Peano arithmetic that is ω-consistent and has the same deductive strength as Z^{-}_{2}, i.e. comprehension for all parameter-free Π^{1}_{n}- and Σ^{1}_{n}-formulae (for every n in ω). The theory is obtained by restricting the T-schema to sentences "not obtained by diagonalization". This is done in a more or less syntactical fashion, without resorting to possible extensions of the truth predicate or some ground model. We will indicate why the existence of such a theory is philosophically interesting. In particular, we will argue that the present system is the first well-motivated and useful formal theory of truth that squares with the philosophical doctrine of minimalism, and that the theory goes a long way towards solving some problems that pertain to classical theories of truth in general. The latter is due to its deductive power. As the present system exceeds all of the previously existing theories in proof-theoretic strength by far, it "swallows" all of them. This enables us to enjoy all of the desirable features of the other truth theories, while avoiding some of their pitfalls at the same time.

Chair: Christine Schurz

Zeit: 12:15-12:45, 14. September 2013 (Samstag)

Ort: HS 104

Anmerkung: ÄNDERUNG. Der Vortrag entfällt!

Thomas Schindler

(LMU Munich, Deutschland)

Thomas Schindler is a PhD fellow at the Munich Center for Mathematical Philosophy. His works focuses on semantic and axiomatic theories of truth, on semantic paradoxes, and on the notion of semantical dependence.

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Letzte Aktualisierung: 2013-02-14.