Reference, paradoxes and truth

Synthese 171 (1):195 - 226 (2009)
Abstract
We introduce a variant of pointer structures with denotational semantics and show its equivalence to systems of boolean equations: both have the same solutions. Taking paradoxes to be statements represented by systems of equations (or pointer structures) having no solutions, we thus obtain two alternative means of deciding paradoxical character of statements, one of which is the standard theory of solving boolean equations. To analyze more adequately statements involving semantic predicates, we extend propositional logic with the assertion operator and give its complete axiomatization. This logic is a sub-logic of statements in which the semantic predicates become internalized (for instance, counterparts of Tarski’s definitions and T-schemata become tautologies). Examples of analysis of self-referential paradoxes are given and the approach is compared to the alternative ones.
Keywords Paradox  Self-reference  Internal theory of truth
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    References found in this work BETA
    Nuel D. Belnap (1982). Gupta's Rule of Revision Theory of Truth. Journal of Philosophical Logic 11 (1):103-116.
    Roy T. Cook (2004). Patterns of Paradox. Journal of Symbolic Logic 69 (3):767-774.
    Solomon Feferman (1991). Reflecting on Incompleteness. Journal of Symbolic Logic 56 (1):1-49.

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