The logic of provability

Bibliographic Information

The logic of provability

George Boolos

Cambridge University Press, 1993

Available at  / 28 libraries

Search this Book/Journal

Note

Includes bibliographical references (p. [262]-269) and index

Description and Table of Contents

Description

This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency (1979). Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos does is to show how the concepts, techniques, and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Godel and the 'self-referential' sentences constructed in their proof. The book explores the effects of reinterpreting the notions of necessity and possibility to mean provability and consistency.

Table of Contents

  • 1. GL and other systems of propositional modal logic
  • 2. Peano arithmetic
  • 3. The box as Bew(x)
  • 4. Semantics for GL and other modal logics
  • 5. Completeness and decidability of GL and K, K4, T, B, S4, and S5
  • 6. Canonical models
  • 7. On GL
  • 8. The fixed point theorem
  • 9. The arithmetical completeness theorems for GL and GLS
  • 10. Trees for GL
  • 11. An incomplete system of modal logic
  • 12. An S4 -preserving proof-theoretical treatment of modality
  • 13. Modal logic within set theory
  • 14. Modal logic within analysis
  • 15. The joint provability logic of consistency and w-consistency
  • 16. On GLB: the fixed point theorem, letterless sentences, and analysis
  • 18. Quantified provability logic with one one-place predicate letter
  • Notes
  • Bibliography
  • Index.

by "Nielsen BookData"

Details

  • NCID
    BA22373311
  • ISBN
    • 0521433428
  • LCCN
    92043610
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cambridge [England] ; New York, NY, USA
  • Pages/Volumes
    xxxvi, 275 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
Page Top