{"product_id":"varieties-of-continua-from-regions-to-points-and-back-9780198712749","title":"Varieties of Continua: From Regions to Points and Back","description":"\u003cem\u003eVarieties of Continua\u003c\/em\u003e explores the development of the idea of the continuous. Hellman and Shapiro begin with two historical episodes. The first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view, that a true continuum cannot be\u003cbr\u003ecomposed of points, to the now standard, point-based frameworks for analysis and geometry found in modern mainstream mathematics (stemming from the work of Bolzano, Cauchy, Weierstrass, Dedekind, Cantor, et al.). The second is the mid-tolate-twentieth century revival of pre-limit methods in analysis\u003cbr\u003eand geometry using infinitesimals including non-standard analysis (due to Abraham Robinson), and the more radical smooth infinitesimal analysis that uses intuitionistic logic. Hellman and Shapiro present a systematic comparison of these and related alternatives (including constructivist and\u003cbr\u003epredicative conceptions), weighing various trade-offs, helping articulate a modern pluralist perspective, and articulate a modern pluralist perspective on continuity. The main creative work of the book is the development of rigorous regions-based theories of classical continua, including Euclidean\u003cbr\u003eand non-Euclidean geometries, that are mathematically equivalent (inter-reducible) to the currently standard, point-based accounts in mainstream mathematics.\u003cem\u003e\u003c\/em\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Geoffrey Hellman, Stewart Shapiro\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Oxford University Press, USA\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 04\/15\/2018\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 224\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.00lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.30h x 6.10w x 0.80d\u003cbr\u003e\u003cb\u003eISBN:\u003c\/b\u003e 9780198712749\u003cbr\u003e\u003cbr\u003e\u003cb\u003eReview Citation(s): \u003c\/b\u003e\u003cbr\u003e\u003ci\u003eChoice\u003c\/i\u003e 10\/01\/2018\u003cbr\u003e\u003cp\u003e\u003cb\u003eAbout the Author\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cstrong\u003eGeoffrey Hellman\u003c\/strong\u003e received his BA and PhD from Harvard (1973). Having published widely in analytic philosophy and philosophy of science, he has, since the 1980s, concentrated on philosophy of quantum mechanics and philosophy and foundations of mathematics. Following the lead of his adviser, Hilary Putnam, Hellman has developed modal-structural interpretations of mathematical theories, including number theory, analysis, and set theory. He has also worked on predicative foundations of arithmetic (with Solomon Feferman) and pluralism in mathematics (with J.L. Bell). In 2007 he was elected as a fellow of the American Academy of Arts and Sciences. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cstrong\u003eStewart Shapiro\u003c\/strong\u003e received an MA in mathematics in 1975, and a PhD in philosophy in 1978, both from the State University of New York at Buffalo. He is currently the O'Donnell Professor of Philosophy at The Ohio State University, and he serves as Distinguished Visiting Professor at the University of Connecticut, and as Professorial Fellow at the University of Oslo. He has contributed to the philosophy of mathematics, philosophy of language, logic, and philosophy of logic, publishing monographs on higher-order logic, structuralism, vagueness, and pluralism in logic.\u003cbr\u003e\u003cbr\u003e","brand":"Oxford University Press, USA","offers":[{"title":"Hardcover","offer_id":39932101361779,"sku":"9.78E+12","price":77.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0555\/9255\/0515\/products\/img_0d58fd7f-8953-4d0c-aedf-16535a1c8c22.jpg?v=1647789907","url":"https:\/\/bookstorenmore.com\/products\/varieties-of-continua-from-regions-to-points-and-back-9780198712749","provider":"Bookstore N More","version":"1.0","type":"link"}