Reference, paradoxes and truth

Synthese 171 (1):195 - 226 (2009)
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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DOI 10.2307/40495992
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References found in this work BETA
Saul A. Kripke (1975). Outline of a Theory of Truth. Journal of Philosophy 72 (19):690-716.
Anil Gupta (1982). Truth and Paradox. Journal of Philosophical Logic 11 (1):1-60.
Solomon Feferman (1991). Reflecting on Incompleteness. Journal of Symbolic Logic 56 (1):1-49.

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