The Iterative Conception of Set
The use of tensed language and the metaphor of set 'formation' found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the...
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| Định dạng: | Journal article |
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2013
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| _version_ | 1826289411988389888 |
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| author | Studd, J |
| author_facet | Studd, J |
| author_sort | Studd, J |
| collection | OXFORD |
| description | The use of tensed language and the metaphor of set 'formation' found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the Maximality thesis, the compelling thesis that any sets can form a set. This paper seeks to save the Maximality thesis by taking the tense more seriously than has been customary (although not literally). A modal stage theory, MST, is developed in a bimodal language, governed by a tenselike logic. Such a language permits a very natural axiomatisation of the iterative conception, which upholds the Maximality thesis. It is argued that the modal approach is consonant with mathematical practice and a plausible metaphysics of sets and shown that MST interprets a natural extension of Zermelo set theory less the axiom of Infinity and, when extended with a further axiom concerning the extent of the hierarchy, interprets Zermelo-Fraenkel set theory. © 2012 Springer Science+Business Media B.V. |
| first_indexed | 2024-03-07T02:28:29Z |
| format | Journal article |
| id | oxford-uuid:a66c6b9f-1454-47fe-b5c8-0d8b95381f07 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:28:29Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:a66c6b9f-1454-47fe-b5c8-0d8b95381f072022-03-27T02:47:15ZThe Iterative Conception of SetJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a66c6b9f-1454-47fe-b5c8-0d8b95381f07Symplectic Elements at Oxford2013Studd, JThe use of tensed language and the metaphor of set 'formation' found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the Maximality thesis, the compelling thesis that any sets can form a set. This paper seeks to save the Maximality thesis by taking the tense more seriously than has been customary (although not literally). A modal stage theory, MST, is developed in a bimodal language, governed by a tenselike logic. Such a language permits a very natural axiomatisation of the iterative conception, which upholds the Maximality thesis. It is argued that the modal approach is consonant with mathematical practice and a plausible metaphysics of sets and shown that MST interprets a natural extension of Zermelo set theory less the axiom of Infinity and, when extended with a further axiom concerning the extent of the hierarchy, interprets Zermelo-Fraenkel set theory. © 2012 Springer Science+Business Media B.V. |
| spellingShingle | Studd, J The Iterative Conception of Set |
| title | The Iterative Conception of Set |
| title_full | The Iterative Conception of Set |
| title_fullStr | The Iterative Conception of Set |
| title_full_unstemmed | The Iterative Conception of Set |
| title_short | The Iterative Conception of Set |
| title_sort | iterative conception of set |
| work_keys_str_mv | AT studdj theiterativeconceptionofset AT studdj iterativeconceptionofset |