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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.
This edition of G. E. Moore's notes taken at Wittgenstein's seminal Cambridge lectures in the early 1930s provides, for the first time, an almost verbatim record of those classes. The presentation of the notes is both accessible and faithful to their original manuscripts, and a comprehensive introduction and synoptic table of contents provide the reader with essential contextual information and summaries of the topics in each lecture. The lectures form an excellent introduction to Wittgenstein's middle-period thought, covering a broad range of philosophical topics, ranging from core questions in the philosophy of language, mind, logic, and mathematics, to illuminating discussions of subjects on which Wittgenstein says very little elsewhere, including ethics, religion, aesthetics, psychoanalysis, and anthropology. The volume also includes a 1932 essay by Moore critiquing Wittgenstein's conception of grammar, together with Wittgenstein's response. A companion website offers access to images of the entire set of source manuscripts.

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