Preface to the Second Edition

Michael Dummett, in the preface to his anthology Truth and Other Enigmas (London: Duckworth, 1978), writes as follows about his decision to reprint the essays without any changes, other than trivial corrections of misprints and the like:

It is not because I am wholly satisfied with everything contained in these essays that I have adopted this policy of not attempting to improve them: it is, conversely, because, once the process of emendation had been initiated, it would have been hard to bring it to an end… Any attempt by [a] writer, years later, to convert [one of his essays]…into an expression of his present way of looking at the topic will produce only a mutilated object, representing neither his former nor his present view: he must either leave it as it stands, or write a completely new essay on the subject (pages ix-x).

That is not unlike how I feel about the second edition of this book. To adapt an old joke: in order to get to where I want to be from here, I would not start from here. As a result, and given also the logistics of the publication process, this second edition is substantially the same as the first, and certainly more like the first than anything I would aim to produce if I were starting the project afresh. That said, I still regard the first edition as a representation of my basic views on this subject—which means, ironically and conversely, that I have felt able to revise it much more extensively than Dummett did his essays. Thus, I have not only removed typographical errors and corrected faulty references; I have amended what I now take to be various simple philosophical and exegetical mistakes. And I have introduced many changes of a more cosmetic nature.

The second edition has also given me a welcome opportunity to make some general comments about the organization of the book, to respond to certain worries that reviewers and other readers had about the first edition, and to say a little more, in amplification and clarification, about one or two of the book’s main themes. Such is the purpose of this preface. (Actually, ‘preface’ is something of a misnomer. It is really more of an epilogue. But I have tried to write it in such a way as to provide useful orientation for anyone who chooses to read it before the rest of the book. )

-xi-

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The Infinite
Table of contents

Table of contents

  • Title Page iii
  • Contents vii
  • Preface to the Second Edition xi
  • Preface xx
  • Introduction: Paradoxes of the Infinite 1
  • Part One - The History 15
  • Chapter 1 - Early Greek Thought 17
  • Chapter 2 - Aristotle 34
  • Chapter 3 - Medieval and Renaissance Thought 45
  • Chapter 4 - The Calculus 57
  • Chapter 5 - The Rationalists and the Empiricists 75
  • Chapter 6 - Kant 84
  • Chapter 7 - Post-Kantian Metaphysics of the Infinite 96
  • Chapter 8 - The Mathematics of the Infinite, and the Impact of Cantor 110
  • Chapter 9 - Reactions 131
  • Part Two - Infinity Assessed 145
  • Chapter 10 - Transfinite Mathematics 147
  • Chapter 11 - The Löwenheim-Skolem Theorem 159
  • Chapter 12 - Gödel's Theorem 172
  • Chapter 13 - Saying and Showing 186
  • Chapter 14 - Infinity Assessed. the History Reassessed 201
  • Chapter 15 - Human Finitude 218
  • Glossary 234
  • Bibliography 250
  • Index 261
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