Turning the Liar paradox into a metatheorem of Basic logic

Paola A. Zizzi

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arXiv · quant-ph/0701171

Turning the Liar paradox into a metatheorem of Basic logic

Paola A. Zizzi

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Abstract

We show that self-reference can be formalized in Basic logic by means of the new connective @, called "entanglement". In fact, the property of non-idempotence of the connective @ is a metatheorem, which states that a self-entangled sentence loses its own identity. This prevents having self-referential paradoxes in the corresponding metalanguage. In this context, we introduce a generalized definition of self-reference, which is needed to deal with the multiplicative connectives of substructural logics.

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quant-ph cs.LO math.LO

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Paola A. Zizzi. 2007-03-28. Turning the Liar paradox into a metatheorem of Basic logic. https://arxiv.org/abs/quant-ph/0701171

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