國立高雄大學圖資館 |

Introduction to the philosophy of mathematics

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Introduction to the philosophy of mathematicsby Jörg Neunhäuserer.
作者:	Neunhäuserer, Jörg.
出版者:	Berlin, Heidelberg :Springer Berlin Heidelberg :2025.
面頁冊數:	viii, 155 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	MathematicsPhilosophy.
電子資源:	https://doi.org/10.1007/978-3-662-72179-7
ISBN:	9783662721797$q(electronic bk.)

Introduction to the philosophy of mathematics
Neunhäuserer, Jörg.

Introduction to the philosophy of mathematics[electronic resource] /by Jörg Neunhäuserer. - Berlin, Heidelberg :Springer Berlin Heidelberg :2025. - viii, 155 p. :ill., digital ;24 cm. - Mathematics study resources,v. 222731-3832 ;. - Mathematics study resources ;Band 2..

1 Introduction -- 2 Pythagoreanism -- 3 Platonism -- 4 Rationalism -- 5 Kantianism -- 6 Mathematics in German Idealism -- 7 Logicism -- 8 Intuitionism -- 9 Formalism -- 10 Constructivism -- 11 Structuralism -- 12 Naturalism -- 13 Further Developments -- 14 Appendix: Set Theory.

What kind of objects does mathematics investigate, and in what sense do these objects exist? Why are we justified in considering mathematical statements as part of our knowledge, and how can they be validated? A philosophy of mathematics seeks to answer such questions. In this introduction, we present the major positions in the philosophy of mathematics and formulate their core ideas into clear, accessible theses. Readers will learn which philosophers developed each position and the historical context in which they emerged. Drawing on fundamental intuitions and scientific findings, one can argue for or against these theses - such arguments form the second focus of this book. The book aims to encourage readers to reflect on the philosophy of mathematics, to develop their own stance, and to learn how to argue for it. This book is a translation of the original German 2nd edition. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book may read stylistically differently from a conventional translation. The Author Jörg Neunhäuserer earned his doctorate in mathematics at Freie Universität Berlin. He has published numerous articles in academic journals and has taught mathematics lectures in various bachelor's and master's programs at the universities of Berlin, Brunswick, Clausthal, Dresden, Hanover, Göttingen and Lüneburg. His German-language books on Mathematical Concepts and Beautiful Theorems of Mathematics are also available from Springer Spektrum.

ISBN: 9783662721797$q(electronic bk.)

Standard No.: 10.1007/978-3-662-72179-7doiSubjects--Topical Terms:

187658
Mathematics
--Philosophy.

LC Class. No.: QA8.4

Dewey Class. No.: 510.1

Introduction to the philosophy of mathematics
LDR:03057nmm a2200373 a 4500 001 690457
003 DE-He213
005 20251011130407.0
006 m d
007 cr nn 008maaau
008 260409s2025 gw s 0 eng d
020 $a 9783662721797$q(electronic bk.)
020 $a 9783662721780$q(paper)
024 7 $a 10.1007/978-3-662-72179-7 $2 doi
035 $a 978-3-662-72179-7
040 $a GP $c GP
041 1 $a eng $h ger
050 4 $a QA8.4
072 7 $a PB $2 bicssc
072 7 $a PB $2 bicssc
072 7 $a MAT000000 $2 bisacsh
072 7 $a PB $2 thema
072 7 $a PB $2 thema
082 0 4 $a 510.1 $2 23
090 $a QA8.4 $b .N494 2025
100 1 $a Neunhäuserer, Jörg. $3 1005969
240 1 0 $a Einführung in die Philosophie der Mathematik. $l English
245 1 0 $a Introduction to the philosophy of mathematics $h [electronic resource] / $c by Jörg Neunhäuserer.
260 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Springer, $c 2025.
300 $a viii, 155 p. : $b ill., digital ; $c 24 cm.
490 1 $a Mathematics study resources, $x 2731-3832 ; $v v. 22
505 0 $a 1 Introduction -- 2 Pythagoreanism -- 3 Platonism -- 4 Rationalism -- 5 Kantianism -- 6 Mathematics in German Idealism -- 7 Logicism -- 8 Intuitionism -- 9 Formalism -- 10 Constructivism -- 11 Structuralism -- 12 Naturalism -- 13 Further Developments -- 14 Appendix: Set Theory.
520 $a What kind of objects does mathematics investigate, and in what sense do these objects exist? Why are we justified in considering mathematical statements as part of our knowledge, and how can they be validated? A philosophy of mathematics seeks to answer such questions. In this introduction, we present the major positions in the philosophy of mathematics and formulate their core ideas into clear, accessible theses. Readers will learn which philosophers developed each position and the historical context in which they emerged. Drawing on fundamental intuitions and scientific findings, one can argue for or against these theses - such arguments form the second focus of this book. The book aims to encourage readers to reflect on the philosophy of mathematics, to develop their own stance, and to learn how to argue for it. This book is a translation of the original German 2nd edition. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book may read stylistically differently from a conventional translation. The Author Jörg Neunhäuserer earned his doctorate in mathematics at Freie Universität Berlin. He has published numerous articles in academic journals and has taught mathematics lectures in various bachelor's and master's programs at the universities of Berlin, Brunswick, Clausthal, Dresden, Hanover, Göttingen and Lüneburg. His German-language books on Mathematical Concepts and Beautiful Theorems of Mathematics are also available from Springer Spektrum.
650 0 $a Mathematics $x Philosophy. $3 187658
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Philosophy of Mathematics. $3 745264
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Mathematics study resources ; $v Band 2. $3 939447
856 4 0 $u https://doi.org/10.1007/978-3-662-72179-7
950 $a Mathematics and Statistics (SpringerNature-11649)