Essays on the Foundations of Mathematics by Moritz Pasch

  • Stephen Pollard

Part of the The Western Ontario Series in Philosophy of Science book series (WONS, volume 83)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Stephen Pollard
    Pages 1-43
  3. Stephen Pollard
    Pages 45-49
  4. Stephen Pollard
    Pages 51-54
  5. Stephen Pollard
    Pages 55-93
  6. Stephen Pollard
    Pages 109-116
  7. Stephen Pollard
    Pages 117-138
  8. Stephen Pollard
    Pages 139-147
  9. Stephen Pollard
    Pages 149-151
  10. Stephen Pollard
    Pages 153-173
  11. Stephen Pollard
    Pages 183-203
  12. Stephen Pollard
    Pages 205-213
  13. Stephen Pollard
    Pages 221-242
  14. Back Matter
    Pages 243-245

About this book

Introduction

Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science; he provides axioms for the combinatorial reasoning essential to Hilbert’s program of consistency proofs; he explores "implicit definition" (a generalization of definition by abstraction) and indicates how this technique yields an "empiricist" reconstruction of set theory; he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties; he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles; and much more. This volume will:

    • Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics.
    • Help us look beyond the familiar triad of formalism, intuitionism, and logicism.
    • Show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities.

The book will be of interest to graduate students and researchers in logic and the foundations of mathematics.

Keywords

Arithmetic Axiomatics Decidability Empiricism Geometry History of Mathematics mathematics

Editors and affiliations

  • Stephen Pollard
    • 1
  1. 1.Dept. Philosophy & ReligionTruman State UniversityKirksvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-90-481-9416-2
  • Copyright Information Springer Science+Business Media B.V. 2010
  • Publisher Name Springer, Dordrecht
  • eBook Packages Humanities, Social Sciences and Law
  • Print ISBN 978-90-481-9415-5
  • Online ISBN 978-90-481-9416-2
  • Series Print ISSN 1566-659X
  • About this book