What is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Gödel, Benacerraf, up to the most recent debate on mathematical platonism.

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...

This collection of classic and contemporary essays in philosophy of language offers a concise introduction to the field for students in graduate and upper-division undergraduate courses. It contains some of the most important basic sources in philosophy of language, including a number of classic essays by philosophers such as Frege, Russell, Wittgenstein, Kripke, Grice, Davidson, Strawson, Austin, and Putnam, as well as more recent contributions by scholars including John McDowell, Stephen...

First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic.

'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...

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...

Ludwig Wittgenstein (1889-1951) is considered by most philosophers - even those who do not share his views - to be the most influential philosopher of the 20th century. His contributions to the philosophy of language, mind, meaning and psychology - as well as to logic, mathematics and epistemology - permanently altered the philosophical landscape, and his Tractatus Logico Philosophicus and Philosophical Investigations continue to be studied in philosophy departments aroun...

Published in 1953, Wittgenstein's Philosophical Investigations had a deeply unsettling effect upon our most basic philosophical ideas concerning thought, sensation and language. Its claim that philosophical questions of meaning necessitate a close analysis of the way we use language continues to influence Anglo-American philosophy today. However, its compressed and dialogic prose is not always easy to follow. This collection of essays deepens but also challenges our understanding of the wo...

This book is concerned with the history of metaphysics since Descartes. Taking as its definition of metaphysics 'the most general attempt to make sense of things', it charts the evolution of this enterprise through various competing conceptions of its possibility, scope, and limits. The book is divided into three parts, dealing respectively with the early modern period, the late modern period in the analytic tradition, and the late modern period in non-analytic traditions. In its unusually...

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...

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...

Gottlob Frege (1848-1925) is considered the father of modern logic and one of the founding figures of analytic philosophy. He was first and foremost a mathematician, but his major works also made important contributions to the philosophy of language.Frege’s writings are difficult and deal with technical, abstract concepts. The Routledge Philosophy Guidebook to Frege On Sense and Reference helps the student to get to grips with Frege’s thought, and introduces and assesses: