This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, ...

'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.' – The GuardianIn 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The impo...

A Dictionary of Logic expands on Oxford's coverage of the topic in works such as The Oxford Dictionary of Philosophy, The Concise Oxford Dictionary of Mathematics, and A Dictionary of Computer Science. Featuring more than 450 entries primarily concentrating on technical terminology, the history of logic, the foundations of mathematics, and non-classical logic, this dictionary is an essential resource for both undergraduates and postgraduates studying phi...

The main purpose of this book is the development of a new method for the semantical analysis of meaning, that is, a new method for analyzing and describing the meanings of linguistic expressions. This method, called the method of extension and intension, is developed by modifying and extending certain customary concepts, especially those of class and property. The method will be contrasted with various other semantical methods used in traditional philosophy or by contemporary authors. Thes...

This is the first English translation of Causalite´ et Lois de La Nature, and is an important contribution to the theory of causation*.* Max Kistler reconstructs a unified concept of causation that is general enough to adequately deal with both elementary physical processes, and the macroscopic level of phenomena we encounter in everyday life.This book will be of great interest to philosophers of science and metaphysics, and also to students and scholars of philosophy of m...

Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premises have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even i...

This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression.The materials in this book are based on A Hildebrand's 1991 lectures delivered at the University of Illinois at Urbana-Champaign and the author's course conducted at the National University of Singapore from 2001 to 2008.

Join original Vienna Circle member Victor Kraft in his discussion of the movement for an exclusive insider’s view of this important point in philosophical history. In this in-depth philosophical study, Victor Kraft explores the role the Vienna Circle had on the international philosophical movement. The Vienna Circle constituted a point of departure for the reawaking, rebirth, and reformation of positivism and empiricism, leading to the creation of the Neo-positivism movement. At the time o...

Examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II. This book provides a selective, critical hist...

The logician Kurt Gödel (1906–1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspect...

Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book...

Written by a leading expert, this is the ideal guide to the only book Wittgenstein published during his lifetime, the Tractatus Logico-Philosophicus. Michael Morris makes sense of Wittgenstein’s brief but often cryptic text, highlighting its key themes. He introduces and analyzes:Wittgenstein’s life and the background to the Tractatusthe ideas and text of the Tractatusthe continuing importance of Wittgenstein's work to philosophy...