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From Dedekind to Gödel

Essays on the Development of the Foundations of Mathematics

  • Book
  • © 1995

Overview

Editors:
  1. Jaakko Hintikka

    1. Boston University, USA

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Part of the book series: Synthese Library (SYLI, volume 251)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-ix
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  2. Tracking Contradictions in Geometry: The Idea of a Model from Kant to Hilbert

    • Judson Webb
    Pages 1-20

  3. Standard vs. Nonstandard Distinction: A Watershed in the Foundations of Mathematics

    • Jaakko Hintikka
    Pages 21-44

  4. Kronecker on the Foundations of Mathematics

    • Harold M. Edwards
    Pages 45-52

  5. The Mysteries of Richard Dedekind

    • David Charles McCarty
    Pages 53-96

  6. Frege’s Letters

    • Claire Ortiz Hill
    Pages 97-118

  7. Frege’s Principle

    • Richard G. Heck Jr.
    Pages 119-142

  8. Husserl and Hilbert on Completeness

    • Claire Ortiz Hill
    Pages 143-163

  9. Hahn’s Über die Nichtarchimedischen Grössensysteme and the Development of the Modern Theory of Magnitudes and Numbers to Measure Them

    • Philip Ehrlich
    Pages 165-213

  10. The Origins of Russell’s Paradox: Russell, Couturat, and the Antinomy of Infinite Number

    • Gregory H. Moore
    Pages 215-239

  11. The Emergence of Descriptive Set Theory

    • Akihiro Kanamori
    Pages 241-262

  12. Chance Against Constructibility

    • Jan Von Plato
    Pages 263-281

  13. Thoralf Skolem, Hermann Weyl and “Das Gefühl der Welt als Begrenztes Ganzes”

    • William Boos
    Pages 283-329

  14. On Tarski’s Background

    • Jan Woleński
    Pages 331-341

  15. Wittgenstein and Ramsey on Identity

    • Mathieu Marion
    Pages 343-371

  16. On Saying What You Really Want to Say: Wittgenstein, Gödel, and the Trisection of the Angle

    • Juliet Floyd
    Pages 373-425

  17. Gödel and Husserl

    • Dagfinn Føllesdal
    Pages 427-446

  18. Back Matter

    Pages 447-472
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Keywords

About this book

Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Gödel are not entirely neglected, either.
Audience: Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.

Editors and Affiliations

  • Boston University, USA

    Jaakko Hintikka

About the editor

Jaakko Hintikka is the author or co-author of thirty volumes and of some 300 scholarly articles in mathematical and philosophical logic, epistemology, language theory, philosophy of science, history of ideas and history of philosophy, including Aristotle, Descartes, Leibniz, Kant, Peirce, The Bloomsbury Group, Husserl and Wittgenstein. He has also been active in international scholarly organizations, most recently as the First Vice-President of FISP, Vice-President of IIP and Co-Chair of the American Organizing Committee of the Twentieth World Congress of Philosophy. He has been Editor-in-Chief of the International Journal Synthese and the Managing Editor of Synthese Library since 1965.

Bibliographic Information

  • Book Title: From Dedekind to Gödel

  • Book Subtitle: Essays on the Development of the Foundations of Mathematics

  • Editors: Jaakko Hintikka

  • Series Title: Synthese Library

  • DOI: https://doi.org/10.1007/978-94-015-8478-4

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media B.V. 1995

  • Hardcover ISBN: 978-0-7923-3484-2Published: 30 November 1995

  • Softcover ISBN: 978-90-481-4554-6Published: 16 November 2010

  • eBook ISBN: 978-94-015-8478-4Published: 09 March 2013

  • Series ISSN: 0166-6991

  • Series E-ISSN: 2542-8292

  • Edition Number: 1

  • Number of Pages: X, 460

  • Topics: Logic, Mathematical Logic and Foundations, History of Mathematical Sciences, Modern Philosophy

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