The Nineteenth Century [Routledge History of Philosophy, V. 7]

By C. L. Ten | Go to book overview

CHAPTER 9

Logic and the philosophy of mathematics in the nineteenth century

John Stillwell


INTRODUCTION

In its history of over two thousand years, mathematics has seldom been disturbed by philosophical disputes. Ever since Plato, who is said to have put the slogan ‘Let no one who is not a geometer enter here’ over the door of his academy, mathematics has been the standard of exact truth against which other philosophical discourse is measured. Descartes’ Discourse on Method grew out of his Geometry. Spinoza wrote his Ethics in the style of Euclid’s Elements. And Leibniz dreamed of a Characteristica Universalis by means of which ‘we should be able to reason in metaphysics and morals in much the same way as in geometry and analysis’.

Mathematics is not only supremely logical, it is also astonishingly powerful. Here is how it struck Thomas Hobbes, according to Aubrey’s Brief Lives:

He was 40 yeares old before he looked on Geometry; which happened accidentally. Being in a Gentleman’s Library, Euclid’s Elements lay open, and ‘twas the 47 El. libri I. He read the Proposition. By G——, sayd he (he would now and then sweare an emphaticall Oath by way of emphasis) this is impossible! So he reads the Demonstration of it, which referred him back to such a Proposition; which proposition he read. That referred him back to another, which he also read…that at last he was demonstratively convinced of that trueth. This made him in love with Geometry.

([9.1], 230)

-242-

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The Nineteenth Century [Routledge History of Philosophy, V. 7]
Table of contents

Table of contents

  • Title Page iii
  • Contents v
  • General Editors' Preface vii
  • Acknowledgements x
  • Chronology xiv
  • Introduction 1
  • Chapter 1 - The Early Utilitarians 5
  • Chapter 2 - Whewell's Philosophy of Science and Ethics 32
  • Chapter 3 - J. S. Mill 62
  • Bibliography 96
  • Chapter 4 - J. S. Mill 98
  • Chapter 5 - Sidgwick 122
  • Chapter 6 - Comte and Positivism 148
  • Bibliography 174
  • Chapter 7 - Nietzsche 177
  • Chapter 8 - Dilthey 206
  • Bibliography 235
  • Chapter 9 - Logic and the Philosophy of Mathematics in the Nineteenth Century 242
  • Chapter 10 - Philosophy of Biology in the Nineteenth Century 272
  • Bibliography 296
  • Chapter 11 - The Separation of Psychology from Philosophy 297
  • Chapter 12 - American Pragmatism 357
  • Chapter 13 - American Pragmatism 381
  • Bibliography 405
  • Chapter 14 - Green, Bosanquet and the Philosophy of Coherence 408
  • Bibliography 434
  • Chapter 15 - Bradley 437
  • Bibliography 458
  • Glossary 459
  • Index 461
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