ISBN:
9789401728669
Language:
English
Pages:
Online-Ressource (XII, 395 p)
,
digital
Edition:
Springer eBook Collection. Humanities, Social Sciences and Law
Series Statement:
Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science 286
Parallel Title:
Erscheint auch als
Parallel Title:
Erscheint auch als
Parallel Title:
Erscheint auch als
Keywords:
Philosophy (General)
;
Science Philosophy
;
Information theory
;
Logic, Symbolic and mathematical
;
Logic
;
Mathematical logic.
;
Science—Philosophy.
;
Computer science.
Abstract:
Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science
DOI:
10.1007/978-94-017-2866-9
URL:
Volltext
(lizenzpflichtig)
