David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Mind 108 (429):69-94 (1999)
Deflationsism about truth is a pot-pourri, variously claiming that truth is redundant, or is constituted by the totality of 'T-sentences', or is a purely logical device (required solely for disquotational purposes or for re-expressing finitarily infinite conjunctions and/or disjunctions). In 1980, Hartry Field proposed what might be called a 'deflationary theory of mathematics', in which it is alleged that all uses of mathematics within science are dispensable. Field's criterion for the dispensability of mathematics turns on a property of theories, called conservativeness. I present some technical results, some of which may be found in Tarski (1936), concerning the logical properties of truth theories; in particular, concerning the conservativeness of adding a truth theory for an object level language to any theory expressed in it. It transpires that various deflationary truth theories behave somewhat differently from the standard Tarskian truth theory. These results suggest that Tarskian theories of truth are not redundant or dispensable. Finally, I hint at an analogy between the behaviour of mathematical theories and of standard (Tarskian) theories of truth with respect to their indispensability to, as Quine would put, our 'scientific world-view'.
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Graham E. Leigh & Carlo Nicolai (2013). Axiomatic Truth, Syntax and Metatheoretic Reasoning. Review of Symbolic Logic 6 (4):613-636.
Martin Fischer & Leon Horsten (2015). The Expressive Power of Truth. Review of Symbolic Logic 8 (2):345-369.
Hartry Field (2003). A Revenge-Immune Solution to the Semantic Paradoxes. Journal of Philosophical Logic 32 (2):139-177.
Hannes Leitgeb (2007). What Theories of Truth Should Be Like (but Cannot Be). Philosophy Compass 2 (2):276–290.
Leon Horsten (2009). Levity. Mind 118 (471):555-581.
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