A Formal Background to Mathematics

Logic, Sets and Numbers

  • Robert Edwards

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XXXIV
  2. Robert Edwards
    Pages 1-134
  3. Robert Edwards
    Pages 135-276
  4. Robert Edwards
    Pages 277-339
  5. Robert Edwards
    Pages 340-467
  6. Robert Edwards
    Pages 468-637
  7. Robert Edwards
    Pages 638-721
  8. Back Matter
    Pages 722-935

About this book

Introduction

§1 Faced by the questions mentioned in the Preface I was prompted to write this book on the assumption that a typical reader will have certain characteristics. He will presumably be familiar with conventional accounts of certain portions of mathematics and with many so-called mathematical statements, some of which (the theorems) he will know (either because he has himself studied and digested a proof or because he accepts the authority of others) to be true, and others of which he will know (by the same token) to be false. He will nevertheless be conscious of and perturbed by a lack of clarity in his own mind concerning the concepts of proof and truth in mathematics, though he will almost certainly feel that in mathematics these concepts have special meanings broadly similar in outward features to, yet different from, those in everyday life; and also that they are based on criteria different from the experimental ones used in science. He will be aware of statements which are as yet not known to be either true or false (unsolved problems). Quite possibly he will be surprised and dismayed by the possibility that there are statements which are "definite" (in the sense of involving no free variables) and which nevertheless can never (strictly on the basis of an agreed collection of axioms and an agreed concept of proof) be either proved or disproved (refuted).

Keywords

Differentialgleichung Differentialrechnung Finite Integralrechnung equation mathematics proof theorem variable

Authors and affiliations

  • Robert Edwards
    • 1
  1. 1.Institute of Advanced StudiesThe Australian National UniversityCanberraAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-9984-4
  • Copyright Information Springer-Verlag New York 1979
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90431-3
  • Online ISBN 978-1-4612-9984-4
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book
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