David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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References found in this work BETA
Saul A. Kripke (1975). Outline of a Theory of Truth. Journal of Philosophy 72 (19):690-716.
Stephen Yablo (1993). Paradox Without Self--Reference. Analysis 53 (4):251-252.
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.
Citations of this work BETA
Sjur Dyrkolbotn & Michał Walicki (2013). Propositional Discourse Logic. Synthese 191 (5):1-37.
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