A Modal Logic for Gödelian Intuition

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Abstract
This essay aims to provide a modal logic for rational intuition. Similarly to treatments of the property of knowledge in epistemic logic, I argue that rational intuition can be codified by a modal operator governed by the axioms of a dynamic provability logic, which augments GL with the modal μ-calculus. Via correspondence results between modal logic and first-order logic, a precise translation can then be provided between the notion of 'intuition-of', i.e., the cognitive phenomenal properties of thoughts, and the modal operators regimenting the notion of 'intuition-that'. I argue that intuition-that can further be shown to entrain conceptual elucidation, by way of figuring as a dynamic-interpretational modality which induces the reinterpretation of both domains of quantification and the intensions of mathematical concepts that are formalizable in monadic first- and second-order formal languages.
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First archival date: 2017-06-14
Latest version: 2 (2017-06-20)
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Reasoning About Knowledge.Fagin, Ronald; Y. Halpern, Joseph; Moses, Yoram & Vardi, Moshe

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