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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2411.16994 |
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| _version_ | 1866909053044654080 |
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| author | Dorr, Cian Mandelkern, Matt |
| author_facet | Dorr, Cian Mandelkern, Matt |
| contents | In the course of proving a tenability result about the probabilities of conditionals, van Fraassen (1976) introduced a semantics for conditionals based on omega-sequences of worlds, which amounts to a particularly simple special case of ordering semantics for conditionals. On that semantics, 'If p, then q' is true at an omega-sequence just in case q is true at the first tail of the sequence where p is true (if such a tail exists). This approach has become increasingly popular in recent years. However, its logic has never been explored. We axiomatize the logic of omega-sequence semantics, showing that it is the result of adding two new axioms to Stalnaker's logic C2: one, Flattening, which is prima facie attractive, and, and a second, Sequentiality, which is complex and difficult to assess, but, we argue, likely invalid. But we also show that when sequence semantics is generalized from omega-sequences to arbitrary (transfinite) ordinal sequences, the result is a more attractive logic that adds only Flattening to C2. We also explore the logics of a few other interesting restrictions of ordinal sequence semantics. Finally, we address the question of whether sequence semantics is motivated by probabilistic considerations, answering, pace van Fraassen, in the negative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16994 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sequence and Consequence Dorr, Cian Mandelkern, Matt Logic In the course of proving a tenability result about the probabilities of conditionals, van Fraassen (1976) introduced a semantics for conditionals based on omega-sequences of worlds, which amounts to a particularly simple special case of ordering semantics for conditionals. On that semantics, 'If p, then q' is true at an omega-sequence just in case q is true at the first tail of the sequence where p is true (if such a tail exists). This approach has become increasingly popular in recent years. However, its logic has never been explored. We axiomatize the logic of omega-sequence semantics, showing that it is the result of adding two new axioms to Stalnaker's logic C2: one, Flattening, which is prima facie attractive, and, and a second, Sequentiality, which is complex and difficult to assess, but, we argue, likely invalid. But we also show that when sequence semantics is generalized from omega-sequences to arbitrary (transfinite) ordinal sequences, the result is a more attractive logic that adds only Flattening to C2. We also explore the logics of a few other interesting restrictions of ordinal sequence semantics. Finally, we address the question of whether sequence semantics is motivated by probabilistic considerations, answering, pace van Fraassen, in the negative. |
| title | Sequence and Consequence |
| topic | Logic |
| url | https://arxiv.org/abs/2411.16994 |