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Philosophy of Mathematics Today

  • Book
  • © 1997

Overview

Editors:
  1. Evandro Agazzi

    1. University of Fribourg, Switzerland
      University of Genova, Italy

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    You can also search for this editor in PubMed   Google Scholar

  2. György Darvas

    1. Symmetrion — The Institute for Advanced Symmetry Studies, Budapest, Hungary
      The Hungarian Academy of Sciences, Budapest, Hungary

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

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

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xxix
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  2. General Philosophical Perspectives

    1. Front Matter

      Pages 1-1
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    2. Logic, Mathematics, Ontology

      • Francisco Miró Quesada
      Pages 3-37

    3. From Certainty to Fallibility in Mathematics?

      • Marco Borga
      Pages 39-50

    4. Moderate Mathematical Fictionism

      • Mario Bunge
      Pages 51-71

    5. Language and Coding-Dependency of Results in Logic and Mathematics

      • Paul Weingartner
      Pages 73-87

    6. What is a Profound Result in Mathematics?

      • Gilles Gaston Granger
      Pages 89-100

    7. The Hylemorphic Schema in Mathematics

      • René Thom
      Pages 101-113

  3. Foundational Approaches

    1. Front Matter

      Pages 115-115
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    2. Categorical Foundations of the Protean Character of Mathematics

      • Saunders Mac Lane
      Pages 117-122

    3. Category Theory and Structuralism in Mathematics: Syntactical Considerations

      • Jean-Pierre Marquis
      Pages 123-136

    4. Reflection in Set Theory the Bernays-Levy Axiom System

      • Gert H. Müller
      Pages 137-169

    5. Structuralism and the Concept of Set

      • Charles Parsons
      Pages 171-194

    6. Aspects of Mathematical Experience

      • Wilfried Sieg
      Pages 195-217

    7. Logicism Revisited in the Propositional Fragment of Leśniewski’s Ontology

      • Arata Ishimoto
      Pages 219-232

  4. The Applicability of Mathematics

    1. Front Matter

      Pages 233-233
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    2. The Relation of Mathematics to the Other Sciences

      • Evandro Agazzi
      Pages 235-259

    3. Mathematics and Physics

      • Giovanni M. Prosperi
      Pages 261-267

    4. The Mathematical Overdetermination of Physics

      • Erhard Scheibe
      Pages 269-285

    5. Gödel’s Incompleteness Theorem and Quantum Thermodynamic Limits

      • Daniele Mundici
      Pages 287-298
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Keywords

About this book

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.

Editors and Affiliations

  • University of Fribourg, Switzerland

    Evandro Agazzi

  • University of Genova, Italy

    Evandro Agazzi

  • Symmetrion — The Institute for Advanced Symmetry Studies, Budapest, Hungary

    György Darvas

  • The Hungarian Academy of Sciences, Budapest, Hungary

    György Darvas

Bibliographic Information

  • Book Title: Philosophy of Mathematics Today

  • Editors: Evandro Agazzi, György Darvas

  • Series Title: Episteme

  • DOI: https://doi.org/10.1007/978-94-011-5690-5

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1997

  • Hardcover ISBN: 978-0-7923-4343-1Published: 30 November 1996

  • Softcover ISBN: 978-94-010-6400-2Published: 14 October 2012

  • eBook ISBN: 978-94-011-5690-5Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XXIX, 361

  • Topics: Mathematical Logic and Foundations, Logic, Philosophy of Science, Epistemology

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