Reasoning Around Paradox with Grounded Deduction
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910902841769984 |
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| author | Ford, Bryan |
| author_facet | Ford, Bryan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_08243 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reasoning Around Paradox with Grounded Deduction Ford, Bryan Logic Logic in Computer Science 03B60 F.4.1 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. |
| title | Reasoning Around Paradox with Grounded Deduction |
| topic | Logic Logic in Computer Science 03B60 F.4.1 |
| url | https://arxiv.org/abs/2409.08243 |