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Interpreting Gödel
Critical Essays

Juliette Kennedy, John Burgess, Janet Folina, Michael Detlefsen, Curtis Franks, Charles Parsons, John Steel, Jouko Väänänen, Bjorn Poonen, Saharon Shelah
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  • Date Published: August 2014
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781139989435

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  • The logician Kurt Gödel (1906–1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Gödel's work on the foundations and philosophy of mathematics. Their essays explore almost every aspect of Godel's intellectual legacy including his concepts of intuition and analyticity, the Completeness Theorem, the set-theoretic multiverse, and the state of mathematical logic today. This groundbreaking volume will be invaluable to students, historians, logicians and philosophers of mathematics who wish to understand the current thinking on these issues.

    • Includes contributions from a range of experts in Gödel's work on the foundations and philosophy of mathematics
    • Topics covered include almost every aspect of Gödel's intellectual legacy - emphasis is alternatively historical, philosophical, mathematical and set theoretical
    • The themes discussed are relevant to current concerns in philosophy, exposing readers to state-of-the-art thinking on many issues in contemporary philosophy of mathematics
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    Reviews & endorsements

    'These essays explore most aspects of Gödel's legacy, including his conceptions of intuition and analyticity, the Completeness theorem, the set-theoretic multiverse and the current state of mathematical logic.' Graham Hoare, The Mathematical Gazette

    'In sum, this is a collection of stimulating essays, mathematically as well as philosophically. They are not exactly easy reading and require familiarity, at least in broad strokes, with Gödel's mathematical work and his central philosophical ideas (as well as their evolution and historical context). The patient reader will be rewarded by a deeper understanding of both.' Wilfried Sieg, Isis

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    Product details

    • Date Published: August 2014
    • format: Adobe eBook Reader
    • isbn: 9781139989435
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    1. Introduction: Gödel and analytic philosophy: how did we get here? Juliette Kennedy
    Part I. Gödel on Intuition:
    2. Intuitions of three kinds in Gödel's views on the continuum John Burgess
    3. Gödel on how to have your mathematics and know it too Janet Folina
    Part II. The Completeness Theorem:
    4. Completeness and the ends of axiomatization Michael Detlefsen
    5. Logical completeness, form, and content: an archaeology Curtis Franks
    Part III. Computability and Analyticity:
    6. Gödel's 1946 Princeton bicentennial lecture: an appreciation Juliette Kennedy
    7. Analyticity for realists Charles Parsons
    Part IV. The Set-Theoretic Multiverse:
    8. Gödel's program John Steel
    9. Multiverse set theory and absolutely undecidable propositions Jouko Väänänen
    Part V. The Legacy:
    10. Undecidable problems: a sampler Bjorn Poonen
    11. Reflecting on logical dreams Saharon Shelah.

  • Editor

    Juliette Kennedy, University of Helsinki
    Juliette Kennedy is an Associate Professor in the Department of Mathematics and Statistics at the University of Helsinki.

    Contributors

    Juliette Kennedy, John Burgess, Janet Folina, Michael Detlefsen, Curtis Franks, Charles Parsons, John Steel, Jouko Väänänen, Bjorn Poonen, Saharon Shelah

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