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...

The intuitive concept of consequence, the notion that one sentence follows logically from another, has driven the study of logic for more than two thousand years. But logic has moved forward dramatically in the past century - largely as a result of bringing mathematics to bear on the field. The infusion of mathematically precise definitions and techniques has turned a field dominated by homely admonitions into one characterized by illuminating theorems. The aim of this book is to correct a common misunderstanding of one of the most widely used techniques of mathematical logic. Central to the...

The Logical Reasoning with Diagrams and Sentences courseware package teaches the principles of analytical reasoning and proof construction using a carefully crafted combination of textbook, desktop, and online materials. This package is sure to be an essential resource in a range of courses incorporating logical reasoning, including formal linguistics, philosophy, mathematics, and computer science.

Unlike traditional formal treatments of reasoning, this package uses both graphical and sentential representations to reflect common situations in everyday reasoning where information...