{"product_id":"mathematics-and-its-logics-philosophical-essays-paperback-9781108714006","title":"Mathematics and Its Logics; Philosophical Essays (Paperback \/ softback) 9781108714006","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eMathematics and Its Logics\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003ePhilosophical Essays\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eThe essays in this volume present a sustained case for a healthy pluralism in mathematics and its logics.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eGeoffrey Hellman (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781108714006, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 10 November 2022\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e294 pages\u003cbr\u003e22.9 x 15.2 x 1.6 cm, 0.431 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eIn these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extendability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e Part I. Structuralism, Extendability, and Nominalism: 1. Structuralism without Structures?\u003cbr\u003e 2. What Is Categorical Structuralism?\u003cbr\u003e 3. On the Significance of the Burali-Forti Paradox\u003cbr\u003e 4. Extending the Iterative Conception of Set: A Height-Potentialist Perspective\u003cbr\u003e 5. On Nominalism\u003cbr\u003e 6. Maoist Mathematics? Critical Study of John Burgess and Gideon Rosen, A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics (Oxford, 1997)\u003cbr\u003e Part II. Predicative Mathematics and Beyond: 7. Predicative Foundations of Arithmetic (with Solomon Feferman)\u003cbr\u003e 8. Challenges to Predicative Foundations of Arithmetic (with Solomon Feferman)\u003cbr\u003e 9. Predicativism as a Philosophical Position\u003cbr\u003e 10. On the Gödel-Friedman Program\u003cbr\u003e Part III. Logics of Mathematics: 11. Logical Truth by Linguistic Convention\u003cbr\u003e 12. Never Say 'Never'! On the Communication Problem between Intuitionism and Classicism\u003cbr\u003e 13. Constructive Mathematics and Quantum Mechanics: Unbounded Operators and the Spectral Theorem\u003cbr\u003e 14. If 'If-Then' Then What?\u003cbr\u003e 15. Mathematical Pluralism: The Case of Smooth Infinitesimal Analysis.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Philosophy of mathematics [\u003ca title=\"See our other books on Philosophy of mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Philosophy%20of%20mathematics%20%5BPBB%5D%22\"\u003ePBB\u003c\/a\u003e], 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], 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":"Default Title","offer_id":46266396016920,"sku":"9781108714006","price":24.48,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781108714006i.jpg?v=1696717926","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/mathematics-and-its-logics-philosophical-essays-paperback-9781108714006","provider":"Freshly Printed Books","version":"1.0","type":"link"}