The Logic of Provability

George S. Boolos (Autor)

Buch | Hardcover

314 Seiten

1994
Cambridge University Press (Verlag)
978-0-521-43342-6 (ISBN)

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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.

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.

Erscheint lt. Verlag	25.2.1994
Verlagsort	Cambridge
Sprache	englisch
Maße	166 x 236 mm
Gewicht	558 g
Themenwelt	Geisteswissenschaften ► Philosophie ► Philosophie der Neuzeit
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	0-521-43342-8 / 0521433428
ISBN-13	978-0-521-43342-6 / 9780521433426
Zustand	Neuware