Difficult to know and impossible to forget, Ludwig Wittgenstein is remembered as the greatest philosopher of the twentieth century. He published only one book in his lifetime - a masterpiece that moulded the evolution of philosophy and baffled his teachers. Spanning most of his life, from his early encounters with Bertrand Russell in Cambridge to a final trip to New York via the Russian Front, Wittgenstein: The Crooked Roads tracks the journeys of a tortured soul.William L...

Hermeneutics is the branch of knowledge that deals with interpretation, a behaviour that is intrinsic to our daily lives. As humans, we decipher the meaning of newspaper articles, books, legal matters, religious texts, political speeches, emails, and even dinner conversations every day . But how is knowledge mediated through these forms? What constitutes the process of interpretation? And how do we draw meaning from the world around us so that we might understand our position in it? In thi...

This is a charming and insightful contribution to an understanding of the "Science Wars" between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy. It traces the root of postmodern theory to a debate on the foundations of mathematics early in the 20th century, then compares developments in mathematics to what took place in the arts and humanities, discussing issues as diverse as literary theory, arts, and artifici...

This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each...

The Cambridge Companion to Hegel and Nineteenth-Century Philosophy examines Hegel within his broader historical and philosophical contexts. Covering all major aspects of Hegel's philosophy, the volume provides an introduction to his logic, epistemology, philosophy of mind, social and political philosophy, philosophy of nature and aesthetics. It includes essays by an internationally recognised team of Hegel scholars. The volume begins with Terry Pinkard's article on Hegel's life, a conspect...

To mark the centenary of the 1910 to 1913 publication of the monumental Principia Mathematica by Alfred N. Whitehead and Bertrand Russell, this collection of fifteen new essays by distinguished scholars considers the influence and history of PM over the last hundred years.

Philosophical logic has been, and continues to be, a driving force behind much progress and development in philosophy more broadly. This collection by up-and-coming philosophical logicians deals with a broad range of topics, including, for example, proof-theory, probability, context-sensitivity, dialetheism and dynamic semantics.

This book charts the shape of future philosophical investigation by posing the question: “What is the Matrix?” Guided by the example of the Matrix film trilogy, the author examines issues ranging from simulation, proof and action to value, culture and mythology, offering a progressively deeper diagnosis of modern philosophical conditions. In contrast to the contemporary focus upon cognitive science and a commitment to the distinction between appearance and reality, this book helps readers ...

Gottlob Frege (1848–1925) was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of language and philosophical logic. Frege is generally seen (along with Russell and Wittgenstein) as one of the fathers of the ana...

Paradoxes of the Infinite presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19th century: Dr Bernard Bolzano’s Paradoxien. This volume contains an adept translation of the work itself by Donald A. Steele S.J., and in addition an historical introduction, which includes a brief biography as well as an evaluation of Bolzano the mathematician, logician and physicist.

The aim of this book is to provide an introduction to probability logic-based formalization of uncertain reasoning. The authors' primary interest is mathematical techniques for infinitary probability logics used to obtain results about proof-theoretical and model-theoretical issues such as axiomatizations, completeness, compactness, and decidability, including solutions of some problems from the literature.An extensive bibliography is provided to point to related work, and this boo...

Logic and Philosophy of Mathematics in the Early Husserl focuses on the first ten years of Edmund Husserl’s work, from the publication of his Philosophy of Arithmetic (1891) to that of his Logical Investigations (1900/01), and aims to precisely locate his early work in the fields of logic, philosophy of logic and philosophy of mathematics. Unlike most phenomenologists, the author refrains from reading Husserl’s early work as a more or less immature sketch of claims consolidated only in his...