Capturing consequence
First-order formalisations are often preferred to propositional ones because they are thought to underwrite the validity of more arguments. We compare and contrast the ability of some well-known logics—these two in particular—to formally capture valid and invalid arguments. We show that there is a p...
| Main Author: | |
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| Format: | Journal article |
| Language: | English |
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Cambridge University Press
2019
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| _version_ | 1826285940206731264 |
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| author | Paseau, A |
| author_facet | Paseau, A |
| author_sort | Paseau, A |
| collection | OXFORD |
| description | First-order formalisations are often preferred to propositional ones because they are thought to underwrite the validity of more arguments. We compare and contrast the ability of some well-known logics—these two in particular—to formally capture valid and invalid arguments. We show that there is a precise and important sense in which first-order logic does not improve on propositional logic in this respect. We also prove some generalisations and related results of philosophical interest. The rest of the article investigates the results’ philosophical significance. A first moral is that the correct way to state the oft-cited superiority of first-order logic vis-à-vis propositional logic is more nuanced than often thought. The second moral concerns semantic theory; the third logic’s use as a tool for discovery. A fourth and final moral is that second-order logic’s transcendence of first-order logic is greater than first-order logic’s transcendence of propositional logic. |
| first_indexed | 2024-03-07T01:36:22Z |
| format | Journal article |
| id | oxford-uuid:9552d602-f159-4050-b096-7fce76822267 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:36:22Z |
| publishDate | 2019 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:9552d602-f159-4050-b096-7fce768222672022-03-26T23:45:26ZCapturing consequenceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9552d602-f159-4050-b096-7fce76822267EnglishSymplectic Elements at OxfordCambridge University Press2019Paseau, AFirst-order formalisations are often preferred to propositional ones because they are thought to underwrite the validity of more arguments. We compare and contrast the ability of some well-known logics—these two in particular—to formally capture valid and invalid arguments. We show that there is a precise and important sense in which first-order logic does not improve on propositional logic in this respect. We also prove some generalisations and related results of philosophical interest. The rest of the article investigates the results’ philosophical significance. A first moral is that the correct way to state the oft-cited superiority of first-order logic vis-à-vis propositional logic is more nuanced than often thought. The second moral concerns semantic theory; the third logic’s use as a tool for discovery. A fourth and final moral is that second-order logic’s transcendence of first-order logic is greater than first-order logic’s transcendence of propositional logic. |
| spellingShingle | Paseau, A Capturing consequence |
| title | Capturing consequence |
| title_full | Capturing consequence |
| title_fullStr | Capturing consequence |
| title_full_unstemmed | Capturing consequence |
| title_short | Capturing consequence |
| title_sort | capturing consequence |
| work_keys_str_mv | AT paseaua capturingconsequence |