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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.
Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than any other indicates its centrality in his thought. Marion traces the development of Wittgenstein's thinking from the 1920s through to the 1950s, in the context of themathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. He shows that study of Wittgenstein's writings on mathematics is essential to a proper understanding of his philosophy,and also that it can do much to illuminate current debates about the foundations of mathematics.
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.
Wittgenstein’s Whewell’s Court Lectures contains previously unpublished notes from lectures given by Ludwig Wittgenstein between 1938 and 1941.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
Kevin M. Cahill reclaims one of Ludwig Wittgenstein's most passionately pursued endeavors: to reawaken a sense of wonder around human life and language and its mysterious place in the world. Following the philosopher's spiritual and cultural criticism and tying it more tightly to the overall evolution of his thought, Cahill frames an original interpretation of Wittgenstein's engagement with Western metaphysics and modernity, better contextualizing the force of his work. Cahill synthesizes several approaches to Wittgenstein's life and thought. He stresses the nontheoretical aspirations of the philosopher's early and later writings, combining key elements from the so-called resolute readings of the Tractatus with the "therapeutic" readings of Philosophical Investigations. Cahill shows how continuity in Wittgenstein's cultural and spiritual concerns informed if not guided his work between these texts, and in his reading of the Tractatus, Cahill identifies surprising affinities with Martin Heidegger's Being and Time—a text rarely associated with Wittgenstein's early formulations. In his effort to recapture wonder, Wittgenstein both avoided and undermined traditional philosophy's reliance on theory. As Cahill relates the steps of this bold endeavor, he forms his own innovative, analytical methods, joining historicist and contextualist approaches to text-based, immanent readings. The result is an original, sustained examination of Wittgenstein's thought.
Wittgenstein: Comparisons and Context is a collection of P. M. S. Hacker's papers on Wittgenstein and Wittgensteinian themes written over the last decade. It presents Hacker's own (Wittgensteinian) conception of philosophy, and defends it against criticisms. Subjects explored include Wittgenstein and Kant on transcendental arguments; Quine's epistemological naturalism; and Wittgenstein's philosophy of psychology, anthropological and ethnologicalapproaches, and philosophy of language. Hacker's final essay offers a synoptic view of analytic philosophy and its history, in which Wittgenstein played so notable a part.

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