Axiomatic truth, syntax and metatheoretic reasoning

Review of Symbolic Logic 6 (4):613-636 (2013)
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Abstract

Following recent developments in the literature on axiomatic theories of truth, we investigate an alternative to the widespread habit of formalizing the syntax of the object-language into the object-language itself. We first argue for the proposed revision, elaborating philosophical evidences in favor of it. Secondly, we present a general framework for axiomatic theories of truth with theories of syntax. Different choices of the object theory O will be considered. Moreover, some strengthenings of these theories will be introduced: we will consider extending the theories by the addition of coding axioms or by extending the schemas of O, if present, to the entire vocabulary of our theory of truth. Finally, we touch on the philosophical consequences that the theories described can have on the debate about the metaphysical status of the truth predicate and on the formalization of our informal metatheoretic reasoning

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Citations of this work

Deflationism beyond arithmetic.Kentaro Fujimoto - 2019 - Synthese 196 (3):1045-1069.
Consistency and the theory of truth.Richard Heck - 2015 - Review of Symbolic Logic 8 (3):424-466.
A Note on Typed Truth and Consistency Assertions.Carlo Nicolai - 2016 - Journal of Philosophical Logic 45 (1):89-119.

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References found in this work

The semantic conception of truth and the foundations of semantics.Alfred Tarski - 1943 - Philosophy and Phenomenological Research 4 (3):341-376.
Reflecting on incompleteness.Solomon Feferman - 1991 - Journal of Symbolic Logic 56 (1):1-49.
How we learn mathematical language.Vann McGee - 1997 - Philosophical Review 106 (1):35-68.
The incompleteness theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of Mathematical Logic. North-Holland. pp. 821 -- 865.

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