INTRODUCTION MATHEMATICAL logic differs from the traditional formal logic so markedly in method, and so far surpasses it in power and subtlety, ...

Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of (...) philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gode1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Godel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.". (shrink)

A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

This volume tackles the slippery subject of 'meaning'.

Bringing together powerful new tools from set theory and the philosophy of language, this book proposes a solution to one of the few unresolved paradoxes from antiquity, the Paradox of the Liar. Treating truth as a property of propositions, not sentences, the authors model two distinct conceptions of propositions: one based on the standard notion used by Bertrand Russell, among others, and the other based on J.L. Austin's work on truth. Comparing these two accounts, the authors show that while the (...) Russellian conception of the relation between sentences, propositions, and truth is crucially flawed in limiting cases, the Austinian perspective has fruitful applications to the analysis of semantic paradox. In the course of their study of a language admitting circular reference and containing its own truth predicate, Barwise and Etchemendy also develop a wide range of model-theoretic techniques--based on a new set-theoretic tool, Peter Aczel's theory of hypersets--that open up new avenues in logical and formal semantics. (shrink)

This dissertation is a critical examination of three truth-gap theories as resolutions to the semantical paradoxes and a comparison of these theories with Tarski's classical resolution. Chapter I sets forth the semantical paradoxes and represents them in a simple and elegant language in which self-reference is possible. Several obvious solutions to the paradoxes are then discussed and dismissed in order to develop criteria for a good resolution of the semantical paradoxes. We then critically examine Tarski's philosophical solution to the semantical (...) paradoxes and model his formal solution to the antinomy of the liar in our self-referential language. Chapter II presents Robert L. Martin's "Category Solution" to the paradox of the liar. The language developed in Chapter I is modified to model Martin and Woodruff's result that a formal language L can contain its own truth predicate 'true-in-L'. We then critically evaluate the "Category Solution". Chapter III presents Bas van Fraassen's "Presupposition Solution" to the paradox of the liar. Again, the language developed in Chapter I is modified to model van Fraassen's solution, and then we critically evaluate van Fraassen's solution to the liar. Chapter IV is a critical exposition and evaluation of Saul Kripke's theory of truth based on the concept of "semantic grounding". As in the previous chapters, the language of Chapter I is modified to model Kripke's truth-gap theory and Kripke's application of fixed-point theorems to semantics. Both Kripke's resolution of the antinomy of the liar within his formal language and Kripke's theory of truth are critically evaluated. Chapter V presents a synopsis of our argument against the truth-gap theories as resolutions to the semantical paradoxes and provides a diagnosis why the truth-gap solutions fail. We reaffirm a Tarskian approach to the semantical paradoxes. (shrink)

The present volume collects some of Barwise's papers written since then, those directly concerned with relations among logic, situation theory, and situation semantics. Several papers appear here for the first time.

Keine ausführliche Beschreibung für "Die Wahrheit über den Lügner" verfügbar.