Philosophy of Mathematics

Thomas Bedürftig; Roman Murawski

Published by De Gruyter 2018

Philosophy of Mathematics

Thomas Bedürftig and Roman Murawski

In the series De Gruyter STEM

https://doi.org/10.1515/9783110468335

Overview
Contents

About this book

The 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 readersinterested 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

Based on the third, revised German edition.

Includes recent developments.

For students, instructors and all readers interested in mathematics and philosophy.

Author / Editor information

Thomas Bedürftig, University of Hannover; Roman Murawski, AMU, Poznań, Polen.

Topics

Frontmatter Publicly Available Download PDF	I
Contents Publicly Available Download PDF	VII
Preface Requires Authentication Unlicensed Licensed Download PDF	XIII
Introduction Requires Authentication Unlicensed Licensed Download PDF	1
1. On the Way to the Reals Requires Authentication Unlicensed Licensed Download PDF	7
2. On the History of the Philosophy of Mathematics Requires Authentication Unlicensed Licensed Download PDF	27
3. On Fundamental Questions of the Philosophy of Mathematics Requires Authentication Unlicensed Licensed Download PDF	149
4. Sets and Set Theories Requires Authentication Unlicensed Licensed Download PDF	253
5. Axiomatic Approach and Logic Requires Authentication Unlicensed Licensed Download PDF	293
6. Thinking and Calculating Infinitesimally – First Nonstandard Steps Requires Authentication Unlicensed Licensed Download PDF	347
7. Retrospection Requires Authentication Unlicensed Licensed Download PDF	387
Biographies Requires Authentication Unlicensed Licensed Download PDF	403
Bibliography Requires Authentication Unlicensed Licensed Download PDF	421
Index of Names Requires Authentication Unlicensed Licensed Download PDF	437
Index of Symbols Requires Authentication Unlicensed Licensed Download PDF	443
Index of subjects Requires Authentication Unlicensed Licensed Download PDF	445

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Students and instructors of mathematics and philosophy; the interested lay public.
Pages
- Front matter: 15
- Main content: 459
Illustrations
- Illustrations: 24
Keywords: Axiomatik; Logik; Mathematik; Mengenlehre; Philosophie

eBook

Published: October 26, 2018
ISBN: 9783110468335

Paperback

Published: October 26, 2018
ISBN: 9783110468304