000			03705nam a22004335i 4500
999			_c36946 _d36946
001			20538892
003			OSt
005			20200707104607.0
007			ta
008			200707b2018 gw ||||| |||| 00| 0 eng d
010			_a 2018947914
020			_a9783110468304 (alk. paper)
020			_a9783110468335 (ebk. (pdf) : alk. paper)
020			_a9783110470772 (ebk. (epub)
040			_aDLC _beng _erda _cHNU
042			_apcc
082			_223 _3GC _a510.1 B39 2018
100	1		_aBeduerftig, Thomas.
245	1	0	_aPhilosophy of mathematics / _cThomas Beduerftig, Roman Murawski.
250			_a1st edition.
263			_a1810
264		1	_aBerlin, Germany ; _aBoston, Massachusetts, USA : _bDe Gruyter, _c©2018.
300			_axv, 457 pages ; _c24 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	0		_aDe Gruyter Stem
504			_aIncludes bibliographical references and index.
505			_aIntro; Contents; Preface; Introduction; 1. On the Way to the Reals; 2. On the History of the Philosophy of Mathematics; 3. On Fundamental Questions of the Philosophy of Mathematics; 4. Sets and Set Theories; 5. Axiomatic Approach and Logic; 6. Thinking and Calculating Infinitesimally -- First Nonstandard Steps; 7. Retrospection; Biographies; Bibliography; Index of Names; Index of Symbols; Index of subjects.
520			_aThe present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today's mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readers interested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally - First nonstandard steps Retrospection.
521			_aCoED _bBachelor of Secondary Education major in Mathematics
546			_aText in English
650			_aMathematics -- Philosophy.
700			_aMurawski, Roman.
906			_a0 _bibc _corignew _d2 _eepcn _f20 _gy-gencatlg
942			_2ddc _cBK _h500-599