Hide search box
Advanced search
(incl. VAT) Net price: PLN
Purchase form
To cart

Philosophy of Mathematics

Authors: Thomas Bedürftig, Roman Murawski Publisher: De Gruyter Publication date: 2018 Publication language: Angielski Number of pages: 476 Publication formats: EAN: 9783110468335 ISBN: 9783110468335 Category: Philosophy: epistemology & theory of knowledge Mathematical foundations History of mathematics Publisher's index: - Bibliographic note: -

Description

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

TOC

  • Contents 8
  • Preface 14
  • Introduction 18
  • 1. On the Way to the Reals 24
  • 2. On the History of the Philosophy of Mathematics 44
  • 3. On Fundamental Questions of the Philosophy of Mathematics 166
  • 4. Sets and Set Theories 270
  • 5. Axiomatic Approach and Logic 310
  • 6. Thinking and Calculating Infinitesimally – First Nonstandard Steps 364
  • 7. Retrospection 404
  • Biographies 420
  • Bibliography 438
  • Index of Names 454
  • Index of Symbols 460
  • Index of subjects 462
Show more