Arithmetic and Combinatorics: Kant and His Contemporaries

By Gottfried Martin; Judy Wubnig | Go to book overview

Introduction

THE QUESTION about the foundations of mathematics is caught in a hopeless quarrel between formalism and intuitionism, at best bogged down in an equally hopeless attempt to mediate between the two ostensibly opposed theories.

There will be no improvement until we recognize that the problem is philosophical, that is, that in questions about the foundations of mathematics purely systematic considerations must be unfruitful from the very outset and that progress can be made only by the closest combination of systematic and historical methods.

Edmund Husserl ( 1859- 1938) holds that geometry is a field in which the theorems of geometry can be derived from axioms in a purely formal, analytic way. Oskar Becker ( 1889- 1964) continues with this approach and goes into it more deeply in his 1923 "Beiträge zur phänomenologischen Begründung der Geometrie." This approach is almost universally accepted. This dominant view, however, contradicts the ordinary sensibility of working mathematicians. I will content myself with citing the 1816 book review Carl Friedrich Gauss ( 1777- 1855) wrote of the commentary written in 1814 by Johann C. Schwab ( 1743- 1821) on Book I of Euclid Elements:

Much of the work revolves around arguing against Kant that the certainty of geometry does not depend on perception but on definition and the Principium identitas and the Principium contradictionis. Kant certainly did not want to deny that these logical devices are continually being used for expressing and relating the truths of geometry to each other; but no one who is confident about the nature of geometry can fail to recognize that these principles can produce nothing in themselves and only sterile blossoms bloom when the fertile living perception of the object itself is not in control.1

It is often asserted with unbelievable glibness that mathematical theorems are analytic. The following was even published in a Kantfestschrift:

-xvii-

Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Note: primary sources have slightly different requirements for citation. Please see these guidelines for more information.

Cited page

Bookmark this page
Arithmetic and Combinatorics: Kant and His Contemporaries
Table of contents

Table of contents

  • Title Page iii
  • Contents v
  • Foreword vii
  • Translator's Preface xi
  • Preface [1938] xv
  • Introduction xvii
  • Part I 1
  • Chapter One - The Axiomatics and Logic of Mathematics 3
  • Chapter Two - The Analytic Principles 11
  • Chapter Three - The Axioms of Arithmetic 34
  • Part II 51
  • Chapter Four - Problems About Classes of Numbers 53
  • Chapter Five - Combinatorics and the Idea of A Systematic Ontology 59
  • Chapter Six - Synthetic Judgment in Arithmetic 85
  • Appendix - Examination of Kant's "Critique of Pure Reason," Part I, Section 4 129
  • Notes 141
  • Bibliography 165
  • Name Index 185
  • Subject Index 191
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this book
  • Bookmarks
  • Highlights & Notes
  • Citations
/ 206

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    Buy instant access to save your work.

    Already a member? Log in now.

    Search by... Author
    Show... All Results Primary Sources Peer-reviewed

    Oops!

    An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.