{"product_id":"iterative-conceptions-of-set-paperback-softback-9781009227261","title":"Iterative Conceptions of Set (Paperback \/ softback) 9781009227261","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eIterative Conceptions of Set\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis Element challenges the orthodox view of set theory as a discipline about a large hierarchy of infinite sets.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eNeil Barton (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009227261, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 13 June 2024\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e104 pages\u003cbr\u003e23 x 15 x 0.5 cm, 0.172 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'This book is a good example of a philosophy of mathematics that is historically and mathematically well informed, rigorous in its treatment of complicated and technical material, and yet still accessible enough for non-experts on the field (like myself). It should be read by any philosopher (of mathematics or otherwise) who is curious about set theory and its philosophy.' Francisco N. Martínez-Aviña, Metascience\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eMany philosophers are aware of the paradoxes of set theory (e.g. Russell's paradox). For many people, these were solved by the iterative conception of set which holds that sets are formed in stages by collecting sets available at previous stages. This Element will examine possibilities for articulating this solution. In particular, the author argues that there are different kinds of iterative conception, and it's open which of them (if any) is the best. Along the way, the author hopes to make some of the underlying mathematical and philosophical ideas behind tricky bits of the philosophy of set theory clear for philosophers more widely and make their relationships to some other questions in philosophy perspicuous.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Introduction\u003cbr\u003e 2. Why set theory?\u003cbr\u003e 3. The naive conception of set and the classic paradoxes\u003cbr\u003e 4. The logical and combinatorial conceptions of set\u003cbr\u003e 5. Iterative conceptions: first examples\u003cbr\u003e 6. Forcing as a construction method\u003cbr\u003e 7. A 'new' kind of paradox?\u003cbr\u003e 8. Countabilist conceptions of iterative set\u003cbr\u003e 9. Mathematics and philosophy under the different conceptions\u003cbr\u003e 10. Conclusions, open questions, and the future\u003cbr\u003e References.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Philosophy [\u003ca title=\"See our other books on Philosophy\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Philosophy%20%5BHP%5D%22\"\u003eHP\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52501152170264,"sku":"9781009227261","price":16.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009227261i.jpg?v=1786213019","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/iterative-conceptions-of-set-paperback-softback-9781009227261","provider":"Freshly Printed Books","version":"1.0","type":"link"}