Is there a countable omega-universal logic?
Some informal arguments are valid, others are invalid. A core application of logic is to tell us which is which by capturing these validity facts. Philosophers and logicians have explored how well a host of logics carry out this role, familiar examples being propositional, rst-order and second-order...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Cambridge University Press
2025
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| _version_ | 1826317716847329280 |
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| author | Paseau, A Weitkämper, F |
| author_facet | Paseau, A Weitkämper, F |
| author_sort | Paseau, A |
| collection | OXFORD |
| description | Some informal arguments are valid, others are invalid. A core application of logic is to tell us which is which by capturing these validity facts. Philosophers and logicians have explored how well a host of logics carry out this role, familiar examples being propositional, rst-order and second-order logic. Since natural language and standard logics are countable, a natural question arises: is there a countable logic guaranteed to capture the validity patterns of any language fragment? That is, is there a countable omega-universal logic? Our article philosophically motivates this question, makes it precise, and then answers it. It is a self-contained concise sequel to `Capturing Consequence' by A.C. Paseau (RSL vol. 12, 2019). |
| first_indexed | 2025-03-11T16:58:20Z |
| format | Journal article |
| id | oxford-uuid:96adf153-f120-4c8c-bba5-4a4a23ab524b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-03-11T16:58:20Z |
| publishDate | 2025 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:96adf153-f120-4c8c-bba5-4a4a23ab524b2025-03-03T10:29:33ZIs there a countable omega-universal logic?Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:96adf153-f120-4c8c-bba5-4a4a23ab524bEnglishSymplectic ElementsCambridge University Press2025Paseau, AWeitkämper, FSome informal arguments are valid, others are invalid. A core application of logic is to tell us which is which by capturing these validity facts. Philosophers and logicians have explored how well a host of logics carry out this role, familiar examples being propositional, rst-order and second-order logic. Since natural language and standard logics are countable, a natural question arises: is there a countable logic guaranteed to capture the validity patterns of any language fragment? That is, is there a countable omega-universal logic? Our article philosophically motivates this question, makes it precise, and then answers it. It is a self-contained concise sequel to `Capturing Consequence' by A.C. Paseau (RSL vol. 12, 2019). |
| spellingShingle | Paseau, A Weitkämper, F Is there a countable omega-universal logic? |
| title | Is there a countable omega-universal logic? |
| title_full | Is there a countable omega-universal logic? |
| title_fullStr | Is there a countable omega-universal logic? |
| title_full_unstemmed | Is there a countable omega-universal logic? |
| title_short | Is there a countable omega-universal logic? |
| title_sort | is there a countable omega universal logic |
| work_keys_str_mv | AT paseaua isthereacountableomegauniversallogic AT weitkamperf isthereacountableomegauniversallogic |