{"product_id":"the-logic-of-provability-paperback-9780521483254","title":"The Logic of Provability (Paperback) 9780521483254","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Logic of Provability\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eBoolos, a pre-eminent philosopher of mathematics, investigates the relationship between provability and modal logic.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eGeorge S. Boolos (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521483254, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 28 April 1995\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e316 pages\u003cbr\u003e22.9 x 15.3 x 1.7 cm, 0.447 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\"I found it lively, lucid, and informative...Boolos' style of writing is unusually kind to the reader.  When an argument becomes tricky, he breaks it down into a lot of small steps, showing the reader in detail just how to proceed.  A result is that the book is remarkably easy to read.\"   Vann McGee, Rutgers University\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency (1979). Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos does is to show how the concepts, techniques, and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Godel and the 'self-referential' sentences constructed in their proof. The book explores the effects of reinterpreting the notions of necessity and possibility to mean provability and consistency.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. GL and other systems of propositional modal logic\u003cbr\u003e 2. Peano arithmetic\u003cbr\u003e 3. The box as Bew(x)\u003cbr\u003e 4. Semantics for GL and other modal logics\u003cbr\u003e 5. Completeness and decidability of GL and K, K4, T, B, S4, and S5\u003cbr\u003e 6. Canonical models\u003cbr\u003e 7. On GL\u003cbr\u003e 8. The fixed point theorem\u003cbr\u003e 9. The arithmetical completeness theorems for GL and GLS\u003cbr\u003e 10. Trees for GL\u003cbr\u003e 11. An incomplete system of modal logic\u003cbr\u003e 12. An S4 -preserving proof-theoretical treatment of modality\u003cbr\u003e 13. Modal logic within set theory\u003cbr\u003e 14. Modal logic within analysis\u003cbr\u003e 15. The  joint provability logic of consistency and w-consistency\u003cbr\u003e 16. On GLB: the fixed point theorem, letterless sentences, and analysis\u003cbr\u003e 18. Quantified provability logic with one one-place predicate letter\u003cbr\u003e Notes\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Philosophy: logic [\u003ca title=\"See our other books on Philosophy: logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Philosophy:%20logic%20%5BHPL%5D%22\"\u003eHPL\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46002821529880,"sku":"9780521483254","price":29.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521483254i_66efb9b7-9328-4b6f-a962-8f600baaa0c1.jpg?v=1691383010","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-logic-of-provability-paperback-9780521483254","provider":"Freshly Printed Books","version":"1.0","type":"link"}