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Types, Tableaus, and Gödel’s God

  • Book
  • © 2002

Overview

Authors:
  1. Melvin Fitting

    1. Lehman College and the Graduate Center, City University of New York, USA

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Part of the book series: Trends in Logic (TREN, volume 12)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xv
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  2. Classical Logic

    1. Front Matter

      Pages 1-1
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    2. Classical Logic—Syntax

      • Melvin Fitting
      Pages 3-10

    3. Classical Logic—Semantics

      • Melvin Fitting
      Pages 11-32

    4. Classical Logic—Basic Tableaus

      • Melvin Fitting
      Pages 33-42

    5. Soundness And Completeness

      • Melvin Fitting
      Pages 43-68

    6. Equality

      • Melvin Fitting
      Pages 69-76

    7. Extensionality

      • Melvin Fitting
      Pages 77-79

  3. Modal Logic

    1. Front Matter

      Pages 81-81
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    2. Modal Logic Syntax And Semantics

      • Melvin Fitting
      Pages 83-104

    3. Modal Tableaus

      • Melvin Fitting
      Pages 105-114

    4. Miscellaneous Matters

      • Melvin Fitting
      Pages 115-130

  4. Ontological Arguments

    1. Front Matter

      Pages 131-131
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    2. Gödel’s Argument, Background

      • Melvin Fitting
      Pages 133-143

    3. Gödel’s Argument, Formally

      • Melvin Fitting
      Pages 145-172

  5. Back Matter

    Pages 173-181
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Keywords

About this book

Gödel's modal ontological argument is the centrepiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and the Prawitz/Takahashi completeness proof is given. Then modal machinery is added, semantically and through tableau rules, to produce a modified version of Montague/Gallin intensional logic. Extensionality, rigidity, equality, identity, and definite descriptions are investigated. Finally, various ontological proofs for the existence of God are discussed informally, and the Gödel argument is fully formalized. Objections to the Gödel argument are examined, including one due to Howard Sobel showing Gödel's assumptions are so strong that the modal logic collapses. It is shown that this argument depends critically on whether properties are understood intensionally or extensionally.
Parts of the book are mathematical, parts philosophical. A reader interested in (modal) type theory can safelyskip ontological issues, just as one interested in Gödel's argument can omit the more mathematical portions, such as the completeness proof for tableaus. There should be something for everybody (and perhaps everything for somebody).

Authors and Affiliations

  • Lehman College and the Graduate Center, City University of New York, USA

    Melvin Fitting

Bibliographic Information

  • Book Title: Types, Tableaus, and Gödel’s God

  • Authors: Melvin Fitting

  • Series Title: Trends in Logic

  • DOI: https://doi.org/10.1007/978-94-010-0411-4

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2002

  • Hardcover ISBN: 978-1-4020-0604-3Published: 31 May 2002

  • Softcover ISBN: 978-94-010-3912-3Published: 11 October 2012

  • eBook ISBN: 978-94-010-0411-4Published: 06 December 2012

  • Series ISSN: 1572-6126

  • Series E-ISSN: 2212-7313

  • Edition Number: 1

  • Number of Pages: XV, 181

  • Topics: Logic, Ontology, Philosophy of Religion, Metaphysics

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