The Logic of Provability

ISBN-13: 9780521483254 / Angielski / Miękka / 1995 / 316 str.

George S. Boolos

Opis

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.

Recenzje

"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

Spis treści

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.