Modern Logic ― A Survey: Historical, Philosophical and Mathematical Aspects of Modern Logic and its Applications (Synthese Library, 149)

Logic has attained in our century a development incomparably greater than in any past age of its long history, and this has led to such an enrichment and proliferation of its aspects, that the problem of some kind of unified recom­ prehension of this discipline seems nowadays unavoidable. This splitting into several subdomains is the natural consequence of the fact that Logic has intended to adopt in our century the status of a science. This always implies that the general optics, under which a certain set of problems used to be con­ sidered, breaks into a lot of specialized sectors of inquiry, each of them being characterized by the introduction of specific viewpoints and of technical tools of its own. The first impression, that often accompanies the creation of one of such specialized branches in a diSCipline, is that one has succeeded in isolating the 'scientific core' of it, by restricting the somehow vague and redundant generality of its original 'philosophical' configuration. But, after a while, it appears that some of the discarded aspects are indeed important and a new specialized domain of investigation is created to explore them. By follOwing this procedure, one finally finds himself confronted with such a variety of independent fields of research, that one wonders whether the fact of labelling them under a common denomination be nothing but the contingent effect of a pure historical tradition. Front Matter....Pages i-viii Front Matter....Pages 1-1 The General Sense and Character of Modern Logic....Pages 3-14 The Growth of Logic Out of the Foundational Research in Mathematics....Pages 15-33 Front Matter....Pages 35-35 Proof Theory....Pages 37-43 Model Theory....Pages 45-65 Constructivist Approaches to Logic....Pages 67-91 Infinitary Logics....Pages 93-112 Many-Valued Logics....Pages 113-129 Modal and Relevance Logics: 1977....Pages 131-151 Front Matter....Pages 153-153 Logic and the Foundations of Mathematics....Pages 155-166 Logic and Set Theory....Pages 167-171 Recursion Theory....Pages 173-195 The Interplay Between Logic and Mathematics: Intuitionism....Pages 197-221 Logic and Probability....Pages 223-233 Logic and Category Theory....Pages 235-252 Front Matter....Pages 253-253 Logic and the Methodology of Empirical Sciences....Pages 255-282 Standard vs. Nonstandard Logic: Higher-Order, Modal, and First-Order Logics....Pages 283-296 Logic and Computers....Pages 297-309 Logic and Linguistics....Pages 311-329 Logical Foundations of Quantum Mechanics....Pages 331-351 Inductive Logic 1945–1977....Pages 353-375 Front Matter....Pages 377-377 Logic and Ontology....Pages 379-398 Problems and Prospects of Deontic Logic a Survey....Pages 399-423 Report on Tense Logic....Pages 425-438 Logical Semiotic....Pages 439-456 Logic and Rhetoric....Pages 457-463 Back Matter....Pages 465-483