Logic is a field studied mainly by researchers and students of philosophy, mathematics and computing. Inductive logic seeks to determine the extent to which the premisses of an argument entail its conclusion, aiming to provide a theory of how one should reason in the face of uncertainty. It has applications to decision making and artificial intelligence, as well as how scientists should reason when not in possession of the full facts. In this book, Jon Williamson embarks on a quest to find...

This book is open access under a CC BY license.This book is the first to develop explicit methods for evaluating evidence of mechanisms in the field of medicine. It explains why it can be important to make this evidence explicit, and describes how to take such evidence into account in the evidence appraisal process. In addition, it develops procedures for seeking evidence of mechanisms, for evaluating evidence of mechanisms, and for combining this evaluation with evidence of associ...

In "Some Remarks on Logical Form," Ludwig Wittgenstein revisits and substantially qualifies the austere picture of language developed in the Tractatus Logico-Philosophicus. The essay examines the relation between propositions, elementary propositions, and the structures of reality they represent, with particular attention to the difficulty of analyzing systems of color exclusion and other forms of incompatibility. Its compressed, argumentative prose retains the Tractatus's architectonic am...

Perhaps the most important work of philosophy written in the twentieth century, Tractatus Logico-Philosophicus was the only philosophical work that Ludwig Wittgenstein published during his lifetime. Written in short, carefully numbered paragraphs of extreme brilliance, it captured the imagination of a generation of philosophers. For Wittgenstein, logic was something we use to conquer a reality which is in itself both elusive and unobtainable. He famously summarized the book in the...

A brief account of philosophical logic from one of the world's leading authoritiesPhilosophical Logic is a clear and concise critical survey of nonclassical logics of philosophical interest written by one of the world's leading authorities on the subject. After giving an overview of classical logic, John Burgess introduces five central branches of nonclassical logic (temporal, modal, conditional, relevantistic, and intuitionistic), focusing on the sometime...

In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value?This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of ...

'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...

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...

If you keep removing single grains of sand from a heap, when is it no longer a heap? From discussions of the heap paradox in classical Greece, to modern formal approaches like fuzzy logic, Timothy Williamson traces the history of the problem of vagueness. He argues that standard logic and formal semantics apply even to vague languages and defends the controversial, realist view that vagueness is a form of ignorance - there really is a grain of sand whose removal turns a heap into a non-hea...

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...

Paraconsistent logic is a theory of reasoning in philosophy that studies inconsistent data. The discipline has several different schools of thought, including preservationism, which responds to the problems that arise when human beings continue to reason when faced with inconsistent data. On Preserving is the first complete account of the Preservationist School, which developed in Canada out of the early work of Raymond Jennings, Peter Schotch, and their students.Assemblin...