Modern Logic -- A Survey: Historical, Philosophical and Mathematical Aspects of Modern Logic and Its Applications

ISBN-13: 9789400990586 / Angielski / Miękka / 2012 / 483 str.

E. Agazzi

Opis

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.

Spis treści

1: Introduction.- The General Sense and Character of Modern Logic.- The Growth of Logic Out of the Foundational Research in Mathematics.- 2: Pure Logic.- Proof Theory.- Model Theory.- Constructivist Approaches to Logic.- Inflnitary Logics.- Many-Valued Logics.- Modal and Relevance Logics: 1977.- 3: The Interplay Between Logic and Mathematics.- Logic and the Foundations of Mathematics.- Logic and Set Theory.- Recursion Theory.- The Interplay Between Logic and Mathematics: Intuitionism.- Logic and Probability.- Logic and Category Theory.- 4: The Relevance of Logic to Other Scientific Disciplines.- Logic and Methodology of Empirical Sciences.- Standard Vs. Nonstandard Logic: Higher-Order, Modal, and First-Order Logics.- Logic and Computers.- Logic and Linguistics.- Logical Foundations of Quantum Mechanics.- Inductive Logic 1945–1977.- 5: Logic and Philosophical Topics.- Logic and Ontology.- Problems and Prospects of Deontic Logic — A Survey.- Report on Tense Logic.- Logical Semiotic.- Logic and Rhetoric.- Index of Names.- Index of Subjects.