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arXiv · 2409.08243

Reasoning Around Paradox with Grounded Deduction

Bryan Ford
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Abstract

How can we reason around logical paradoxes without falling into them? This paper introduces grounded deduction or GD, a Kripke-inspired approach to first-order logic and arithmetic that is neither classical nor intuitionistic, but nevertheless appears both pragmatically usable and intuitively justifiable. GD permits the direct expression of unrestricted recursive definitions -- including paradoxical ones such as 'L := not L' -- while adding dynamic typing premises to certain inference rules so that such paradoxes do not lead to inconsistency. This paper constitutes a preliminary development and investigation of grounded deduction, to be extended with further elaboration and deeper analysis of its intriguing properties.

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Bryan Ford. 2024-09-12. Reasoning Around Paradox with Grounded Deduction. https://arxiv.org/abs/2409.08243

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