The Logic of Provability
The Logic of Provability
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USDThis 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.
- Boolos is internationally renowned philosopher of mathematics (performance of HARDBACK confirms this)
Reviews & endorsements
"The book contains an excellent combination of values: noble subject, fresh key results, and the gentle, friendly style of the author. It can be recommended as a textbook, as a handbook, or simply as high quality reading in logic." Sergei N. Artemov, Journal of Symbolic Logic
"I found it lively, lucid, and informative...Boolos' style of writing is unusually kind to the reader. When an argument becomes tricky, he breaks it down into a lot of small steps, showing the reader in detail just how to proceed. A result is that the book is remarkably easy to read." Vann McGee, Rutgers University
Product details
March 2011Adobe eBook Reader
9780511882258
0 pages
0kg
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
