The open-endedness of the set concept and the semantics of set theory
Some philosophers have argued that the open-endedness of the set concept has revisionary consequences for the semantics and logic of set theory. I consider (several variants of) an argument for this claim, premissed on the view that quantification in mathematics cannot outrun our conceptual abilitie...
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| Format: | Journal article |
| Language: | English |
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2003
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| _version_ | 1797088899639541760 |
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| author | Paseau, A |
| author_facet | Paseau, A |
| author_sort | Paseau, A |
| collection | OXFORD |
| description | Some philosophers have argued that the open-endedness of the set concept has revisionary consequences for the semantics and logic of set theory. I consider (several variants of) an argument for this claim, premissed on the view that quantification in mathematics cannot outrun our conceptual abilities. The argument urges a non-standard semantics for set theory that allegedly sanctions a non-classical logic. I show that the views about quantification the argument relies on turn out to sanction a classical semantics and logic after all. More generally, this article constitutes a case study in whether the need to account for conceptual progress can ever motivate a revision of semantics or logic. I end by expressing skepticism about the prospects of a so-called non-proof-based justification for this kind of revisionism about set theory. © 2003 Kluwer Academic Publishers. |
| first_indexed | 2024-03-07T02:56:44Z |
| format | Journal article |
| id | oxford-uuid:af8decec-2863-40eb-9813-291b2b253f21 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:56:44Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | oxford-uuid:af8decec-2863-40eb-9813-291b2b253f212022-03-27T03:50:18ZThe open-endedness of the set concept and the semantics of set theoryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:af8decec-2863-40eb-9813-291b2b253f21EnglishSymplectic Elements at Oxford2003Paseau, ASome philosophers have argued that the open-endedness of the set concept has revisionary consequences for the semantics and logic of set theory. I consider (several variants of) an argument for this claim, premissed on the view that quantification in mathematics cannot outrun our conceptual abilities. The argument urges a non-standard semantics for set theory that allegedly sanctions a non-classical logic. I show that the views about quantification the argument relies on turn out to sanction a classical semantics and logic after all. More generally, this article constitutes a case study in whether the need to account for conceptual progress can ever motivate a revision of semantics or logic. I end by expressing skepticism about the prospects of a so-called non-proof-based justification for this kind of revisionism about set theory. © 2003 Kluwer Academic Publishers. |
| spellingShingle | Paseau, A The open-endedness of the set concept and the semantics of set theory |
| title | The open-endedness of the set concept and the semantics of set theory |
| title_full | The open-endedness of the set concept and the semantics of set theory |
| title_fullStr | The open-endedness of the set concept and the semantics of set theory |
| title_full_unstemmed | The open-endedness of the set concept and the semantics of set theory |
| title_short | The open-endedness of the set concept and the semantics of set theory |
| title_sort | open endedness of the set concept and the semantics of set theory |
| work_keys_str_mv | AT paseaua theopenendednessofthesetconceptandthesemanticsofsettheory AT paseaua openendednessofthesetconceptandthesemanticsofsettheory |