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.
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Sjur Dyrkolbotn deserves thanks for discussions concerning several aspects presented in this article.
Anonymous referees provided valuable comments and drew our attention to pointer structures of which we were not aware when writing the first version of this article.
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Walicki, M. Reference, paradoxes and truth. Synthese 171, 195–226 (2009). https://doi.org/10.1007/s11229-008-9392-9
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DOI: https://doi.org/10.1007/s11229-008-9392-9