Reasoning Around Paradox with Grounded Deduction
Bryan Ford
arXiv preprint 2409.08243
September 12, 2024 (first version)
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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