Truth, Conservativeness, and Provability: Reply to Cieslinski

Mind 119 (474):423-436 (2010)
Abstract
Cieslinski has given an interesting response to Shapiro 1998 and Ketland 1999, which argued that deflationary truth theories are inadequate, since they lack the property of ‘reflective adequacy’. Cieslinski’s response, following Tennant (2002, 2005), aims to explain, without a detour using truth axioms, why someone who accepts the axioms of a theory should also accept its reflection principles. The argument is formulated very clearly (in fact, to justify a different reflection principle), and involves a couple of important assumptions, the crucial one being that the reflection scheme for a theory ‘expresses’ the acceptance of its theorems. I argue that this assumption is incorrect. For if the reflection principle for a theory expresses the claim that one is ready to accept its theorems, this latter claim should imply the reflection principle. But it does not. So, I conclude, the response fails to yield the required ‘truth-free’ method for proving or justifying reflection principles
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    Jody Azzouni (1999). Comments on Shapiro. Journal of Philosophy 96 (10):541-544.
    Solomon Feferman (1991). Reflecting on Incompleteness. Journal of Symbolic Logic 56 (1):1-49.

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