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Philosophy of Mathematics Today

  • Evandro Agazzi
  • György Darvas

Part of the Episteme book series (EPIS, volume 22)

Table of contents

  1. Front Matter
    Pages i-xxix
  2. General Philosophical Perspectives

    1. Front Matter
      Pages 1-1
    2. Francisco Miró Quesada
      Pages 3-37
    3. Mario Bunge
      Pages 51-71
    4. Gilles Gaston Granger
      Pages 89-100
    5. René Thom
      Pages 101-113
  3. Foundational Approaches

  4. The Applicability of Mathematics

    1. Front Matter
      Pages 233-233
    2. Giovanni M. Prosperi
      Pages 261-267
    3. Erhard Scheibe
      Pages 269-285
    4. Jacques Ricard, Käty Ricard
      Pages 299-304
    5. Jesús Mosterín
      Pages 305-317
  5. Historical Considerations

About this book

Introduction

Mathematics is often considered as a body of knowledge that is essen­ tially independent of linguistic formulations, in the sense that, once the content of this knowledge has been grasped, there remains only the problem of professional ability, that of clearly formulating and correctly proving it. However, the question is not so simple, and P. Weingartner's paper (Language and Coding-Dependency of Results in Logic and Mathe­ matics) deals with some results in logic and mathematics which reveal that certain notions are in general not invariant with respect to different choices of language and of coding processes. Five example are given: 1) The validity of axioms and rules of classical propositional logic depend on the interpretation of sentential variables; 2) The language­ dependency of verisimilitude; 3) The proof of the weak and strong anti­ inductivist theorems in Popper's theory of inductive support is not invariant with respect to limitative criteria put on classical logic; 4) The language-dependency of the concept of provability; 5) The language­ dependency of the existence of ungrounded and paradoxical sentences (in the sense of Kripke). The requirements of logical rigour and consistency are not the only criteria for the acceptance and appreciation of mathematical proposi­ tions and theories.

Keywords

experience logic mathematics philosophy of mathematics physics reason set theory

Editors and affiliations

  • Evandro Agazzi
    • 1
    • 2
  • György Darvas
    • 3
    • 4
  1. 1.University of FribourgSwitzerland
  2. 2.University of GenovaItaly
  3. 3.Symmetrion — The Institute for Advanced Symmetry StudiesBudapestHungary
  4. 4.The Hungarian Academy of SciencesBudapestHungary

Bibliographic information

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