Mathematics : Logic

Gli insegnanti si trovano in difficoltA a proposito dello spazio e della (TM)enfasi da dare agli argomenti di teoria degli insiemi, nella propria preparazione e nel proprio lavoro, perchA(c) all'universitA non A] stata loro fornita una conoscenza adeguata. Si puA tranquillamente affermare, sulla base di molta esperienza, che il matematico medio, anche chi fa ricerca, non sa cosa sia la teoria degli insiemi. Due pregiudizi si frappongono a una buona conoscenza della teoria: uno, di tipo minimalista, A] la sua identificazione con una non meglio precisata "insiemistica," un linguaggio austero fin troppo impegnativo ove lo si voglia imporre prematuramente; la (TM)altro A] di tipo massimalista e consiste nel supposto, ed effettivo legame con le questioni piA sottili dei fondamenti della matematica. Ma la teoria ha un contenuto matematico importante, e con molti risvolti di interesse didattico. Si puA dire in una parola che A] lo studio della (TM)infinito, il che comporta anche per complemento che sia uno studio del finito. Attraverso gli insiemi numerabili ed effettivamente generati si stabilisce anche un collegamento con la piA concreta teoria della calcolabilitA . Il libro A] solo una guida, non un manuale: sono indicati gli argomenti di maggior rilievo; sono offerti commenti sui risultati piA significativi; sono segnalati anche temi da non approfondire, pur conoscendone la (TM)esistenza; sono presentate con dettagli formali poche dimostrazioni, tipiche dello stile della materia; sono proposti, come istruzioni per la (TM)uso, alcuni esercizi che potrebbero essere presentarti anche a studenti delle scuole secondarie. more...

Price: $29.95

This Handbook documents the main trends in current research between logic and language, including its broader influence in computer science, linguistic theory and cognitive science. The history of the combined study of Logic and Linguistics goes back a long way, at least to the work of the scholastic philosophers in the Middle Ages. At the beginning of this century, the subject was revitalized through the pioneering efforts of Gottlob Frege, Bertrand Russell, and Polish philosophical logicians such as Kazimierz Ajdukiewicz. Around 1970, the landmark achievements of Richard Montague established a junction between state-of-the-art mathematical logic and generative linguistic theory. Over the subsequent decades, this enterprise of Montague Grammar has flourished and diversified into a number of research programs with empirical and theoretical substance. This appears to be the first Handbook to bring logic-language interface to the fore. Both aspects of the interaction between logic and language are demonstrated in the book i.e. firstly, how logical systems are designed and modified in response to linguistic needs and secondly, how mathematical theory arises in this process and how it affects subsequent linguistic theory. The Handbook presents concise, impartial accounts of the topics covered. Where possible, an author and a commentator have cooperated to ensure the proper breadth and technical content of the papers. The Handbook is self-contained, and individual articles are of the highest quality. more...

Price: $185.00

This is the first book to collect essays from philosophers, mathematicians and computer scientists working at the exciting interface of algorithmic learning theory and the epistemology of science and inductive inference. Readable, introductory essays provide engaging surveys of different, complementary, and mutually inspiring approaches to the topic, both from a philosophical and a mathematical viewpoint. Building upon this base, subsequent papers present novel extensions of algorithmic learning theory as well as bold, new applications to traditional issues in epistemology and the philosophy of science. The volume is vital reading for students and researchers seeking a fresh, truth-directed approach to the philosophy of science and induction, epistemology, logic, and statistics. more...

Price: $179.00

Logic is the backbone of Western civilization, holding its systems of philosophy, science and law. Yet despite logic's widely acknowledged importance, it remains an unbroken seal for many, due to its heavy use of jargon and mathematical symbolism. more...

Price: $12.95

Clearly introduces the major topics in logic and their relation to current philosophical issues. more...

Price: $28.00