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Propositions, Boolean Functions, and Paradoxes, 15 pages.

Abstract

To negate logical connectives such as implication, or gates such as AND and OR in computer science, we flip the output entries of the original function’s truth table. The present paper explores whether a similar approach to negation can apply to paradoxes such as the liar, the truth-teller, the card paradox, and Yablo’s paradox. The two main ideas are that the liar and the truth-teller are negations of each other, and a general approach to determining the truth of systems of sentences that refer to each other.

Notes

This paper is a follow-up to my previous paper on self-reference and paradoxes.