For several terms at Cambridge in 1939, Ludwig Wittgenstein lectured on the philosophical foundations of mathematics. A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.

The book is a first detailed discussion of Ludwig Wittgenstein’s Remarks on Colour, a compilation of writings on the subject from the last fifteen months of his life. The origin and significance of the remarks are explained along with a remark-by-remark guide to what Wittgenstein says. In addition to serving as an account of the thought recorded in the text, the book provides an interpretation of Wittgenstein’s treatment of colour concepts and an account of his distinctive philosophical style. Remarks on Colour is shown to be a good way into the philosophy, to reveal a great deal about how Wittgenstein approaches philosophy, and to bring out features of his thought elided, if not missed, by more general studies, especially those that focus on more finished work.

The application of standard measurement is a cornerstone of modern science. In this collection of essays, standardization of procedure, units of measurement and the epistemology of standardization are addressed by specialists from sociology, history and the philosophy of science.

Offers a comprehensive and accessible exploration of the scope and importance of Gottlob Frege's work.

This volume discusses some crucial ideas of the founders of the analytic philosophy: Gottlob Frege, Bertrand Russell and Ludwig Wittgenstein, or the ‘golden trio’. The book shows how these ‘old’ ideas are still present and influential in the current philosophical debates and to what extent these debates echo the original ideas. The collection aim is twofold: to better understand these fruitful ideas by placing them in the original setting, and to systematically examine these ideas in the context of the current debates animating philosophical discussions today. Divided into five sections, the book first sets the stage and offers a general introduction to the background influences, as well as delimitations of the initial foundational positions. This first section contains two papers dedicated to the discussion of realism and the status of science at that time, followed by two papers that tackle the epistemic status of logical laws. The next three sections constitute the core of the volume, each being dedicated to the most important figures in the early analytic tradition: Frege, Russell, and Wittgenstein. The last section gathers several essays that discuss either the relation between two or more analytic thinkers, or various important concepts such as ‘predicativism’ and ‘arbitrary function’, or the principles of abstraction and non-contradiction.​

This book explores the intricate and multi-dimensional conception of clarity and obscurity in the law. It presents and examines the most recent research and theories, giving practical guidance on how to avoid obscurity in legal drafting and its impact on legal interpretation. The book is aimed at a multidisciplinary audience and seeks to promote an interdisciplinary debate on clarity, law and language, calling for the moving of clarity beyond the study of plain language. The aims of the book are thus two fold. The first is to critically reach a nexus between the disciplines of law and language with respect to the debates on clarity in legal discourse. The second is to achieve an international perspective on the issue, drawing from a wide range of legal and political contexts.

Answering the question 'How is fruitful discussion possible?', this book addresses the central philosophical issue of how reason shall be understood and how it is limited. This study argues that the understanding of discussion according to which it necessarily starts from putative universal norms and rules for argumentation is problematic, among other reasons since such rules are unfruitful in contexts where there are vast disagreements such as religion. Inspired by Wittgensteinian ideas, Strandberg develops instead a new way of understanding discussion, truth and rationality which escapes these problems, and shows how this solution can be used to answer the accusation against Wittgensteinian philosophy for being conservative and resulting in fideism.

Modern European Criticism and Theory offers the reader a comprehensive critical overview of the widespread and profound contest of ideas within European 'theory'. The book focuses primarily on the thought of major voices in poetics, philosophy, linguistics, and psychoanalysis, as well as in literary and cultural studies from the Enlightenment to the present day. Examining how conceptions of subjectivity, identity and gender have been questioned, the more than 50 essays written by acknowledged experts in their fields critically assess the ways in which we think, see, and act in the world, as well as the ways in which we represent such thought psychologically, politically, and culturally. A further reading list accompanies each chapter.

This monograph examines the private annotations that Ludwig Wittgenstein made to his copy of G.H. Hardy’s classic textbook, A Course of Pure Mathematics. Complete with actual images of the annotations, it gives readers a more complete picture of Wittgenstein’s remarks on irrational numbers, which have only been published in an excerpted form and, as a result, have often been unjustly criticized. The authors first establish the context behind the annotations and discuss the historical role of Hardy’s textbook. They then go on to outline Wittgenstein’s non-extensionalist point of view on real numbers, assessing his manuscripts and published remarks and discussing attitudes in play in the philosophy of mathematics since Dedekind. Next, coverage focuses on the annotations themselves. The discussion encompasses irrational numbers, the law of excluded middle in mathematics and the notion of an “improper picture," the continuum of real numbers, and Wittgenstein’s attitude toward functions and limits.

Wittgenstein’s Whewell’s Court Lectures contains previously unpublished notes from lectures given by Ludwig Wittgenstein between 1938 and 1941. The volume offers new insight into the development of Wittgenstein’s thought and includes some of the finest examples of Wittgenstein’s lectures in regard to both content and reliability. Many notes in this text refer to lectures from which no other detailed notes survive, offering new contexts to Wittgenstein’s examples and metaphors, and providing a more thorough and systematic treatment of many topics Each set of notes is accompanied by an editorial introduction, a physical description and dating of the notes, and a summary of their relation to Wittgenstein’s Nachlass Offers new insight into the development of Wittgenstein’s ideas, in particular his ideas about certainty and concept-formation The lectures include more than 70 illustrations of blackboard drawings, which underline the importance of visual thought in Wittgenstein’s approach to philosophy Challenges the dating of some already published lecture notes, including the Lectures on Freedom of the Will and the Lectures on Religious Belief