000			01905nam a22001937a 4500
999			_c4304 _d4304
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008			221216b ||||| |||| 00| 0 eng d
020			_a9780262542234
082			_a510.1 _bHAM
100			_aHamkins, Joel David _99499
245			_aLectures on the philosophy of mathematics
260			_bMIT Press _aCambridge _c2020
300			_axviii, 329 p.
365			_aUSD _b45.00
520			_aAn introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes—numbers, rigor, geometry, proof, computability, incompleteness, and set theory—that give rise again and again to philosophical considerations. Hamkins shows, for example, how number systems set the stage for discussions of such philosophical issues as platonism, logicism, and the nature of abstraction. Consideration of the rise of rigor in the calculus leads to a discussion of whether the indispensability of mathematics in science offers grounds for mathematical truth. Sophisticated technical developments in set theory give rise to a necessary engagement with deep philosophical concerns, including the criteria for new mathematical axioms. Throughout, Hamkins offers a clear and engaging exposition that is both accessible and sophisticated, intended for readers whose mathematical backgrounds range from novice to expert.
650			_aMathematics - Philosophy _910970
650			_aMathematics _91140
942			_2ddc _cBK