Also available: Wittgenstein's Lectures: Cambridge, 1930–1932 From the Notes
of John King and Desmond Lee ... and A. C. Jackson Edited by P. T. Geach WITTGENSTEIN'S LECTURES On the Foundations of Mathematics Cambridge, 1939 F.
Author: Ludwig Wittgenstein
Publisher: University of Chicago Press
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.
Author: Assistant Professor of Philosophy Mathieu MarionPublish On: 1998
LIST OF ABBREVIATIONS Wittgenstein AWL BB LA LFM LO LWL Wittgenstein ' s Lectures , Cambridge 1932 – 1935 , from ... Wittgenstein ' s Lectures on the Foundations of Mathematics , Cambridge 1939 , from the notes of R . Bosanquet ,
Author: Assistant Professor of Philosophy Mathieu Marion
Publisher: Oxford University Press
This is a careful, historically informed study of Wittgenstein's philosophy of mathematics, tracing the work development of his thinking from the 1920s through to the 1950s, in the context of the mathematical and philosophical work of the times.
8 – 9 , 185 – 6 , 192 – 3 ; Wittgenstein ' s Lectures on the Foundations of Mathematics : Cambridge , 1939 , pp . 56ff , 86 – 9 ; The Blue and Brown Books ,
p . 41 ; Philosophical Investigations $ $ 334 , 463 ; Moore , Philosophical Papers ,
op . cit ...
Author: Alice Marguerite Crary
Publisher: Psychology Press
The New Wittgensteinoffers a major reevaluation of Wittgenstein's thinking. This stellar collection of original essays by the "third wave" of Wittgenstein critics presents a significantly different portrait of the philosopher, not as a proponent of metaphysical theories but as an advocate of philosophy as therapy--a means of helping us grasp the essence of thought and language by attending to our everyday forms of expression. Boldly criticizing standard interpretations and offering unorthodox perspectives, these controversial essays will change the way we look at Wittgenstein's entire body of work. Contributors: Stanley Cavell, David Cerbone, James Conant, Alice Crary, Cora Diamond, David Finkelstein, Juliette Floyd, P.M.S. Hacker, John McDowell, Hilary Putnam, Rupert Read, Martin Stone, Edward Witherspoon.
Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge 1939, ed.
C. Diamond (Harvester, Hassocks, Sussex, 1976). Ludwig Wittgenstein: Letters to
Russell, Keynes and Moore, ed. G. H. von Wright (Blackwell, Oxford, 1974).
Author: P. M. S. Hacker
Publisher: Oxford University Press
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.
Wittgenstein's Critique of Metaphysics and Modernity Kevin M. Cahill. ——.
Notebooks, 1914–1916. Ed. G. E. M. ... Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939. Ed. Cora Diamond. Ithaca, N.Y.:
Author: Kevin M. Cahill
Publisher: Columbia University Press
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.
... Typescript (2005) Cambridge Letters (1997) Culture and Value (1998) Lectures and Conversations on Aesthetics, Psychology, and Religious Belief (
1966) Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939 (1976) ...
Author: John G. Gunnell
Publisher: Columbia University Press
A distinctive feature of Ludwig Wittgenstein's work after 1930 was his turn to a conception of philosophy as a form of social inquiry, John G. Gunnell argues, and Thomas Kuhn's approach to the philosophy of science exemplified this conception. In this book, Gunnell shows how these philosophers address foundational issues in the social and human sciences, particularly the vision of social inquiry as an interpretive endeavor and the distinctive cognitive and practical relationship between social inquiry and its subject matter. Gunnell speaks directly to philosophers and practitioners of the social and human sciences. He tackles the demarcation between natural and social science; the nature of social phenomena; the concept and method of interpretation; the relationship between language and thought; the problem of knowledge of other minds; and the character of descriptive and normative judgments about practices that are the object of inquiry. Though Wittgenstein and Kuhn are often criticized as initiating a modern descent into relativism, this book shows that the true effect of their work was to undermine the basic assumptions of contemporary social and human science practice. It also problematized the authority of philosophy and other forms of social inquiry to specify the criteria for judging such matters as truth and justice. When Wittgenstein stated that "philosophy leaves everything as it is," he did not mean that philosophy would be left as it was or that philosophy would have no impact on what it studied, but rather that the activity of inquiry did not, simply by virtue of its performance, transform the object of inquiry.
Anscombe (Oxford, 1967) Lectures on the Foundations of Mathematics, Cambridge, 1939 (Ithaca, NY, 1976) Culture and Value (Oxford, 1980) Wittgenstein's Lectures. Cambridge, 1930–1932 (Oxford, 1980) Philosophical
Author: Edward Kanterian
Publisher: Reaktion Books
Ludwig Wittgenstein is generally considered as the greatest philosopher since Immanuel Kant, and his personal life, work, and his historical moment intertwined in a fascinating, complex web. Noted scholar Edward Kanterian explores these intersections in Ludwig Wittgenstein, the newest title in the acclaimed Critical Lives series. Wittgenstein’s works—from Tractatus Logico-Philosophicus to the posthumously published Philosophical Investigations—are notoriously dense, and Kanterian carefully distills them here, proposing thought-provoking new interpretations. Yet the philosopher’s passions were not solely confined to theoretical musings, and the book explores Wittgenstein’s immersion in art and music and his social position as a member of the sophisticated Viennese upper class at the turn of the century. His personal and professional relationships also offer insights into his thoughts, as he was friends with the greatest thinkers of the twentieth century, including John Maynard Keynes, George Edward Moore, Bertrand Russell, and Gilbert Royle. The philosopher was also deeply tormented by ethical and religious questions, and his internal turmoil, Kanterian argues, gives us a deeper understanding of the important conflicts and tensions of his age. Ultimately, the author contends, Wittgenstein’s life reveals insights into the ethical quandaries of our own time. A readable and concise account, Ludwig Wittgenstein is an informative, accessible introduction to the one of the greatest thinkers of our age.
THE FOUNDATIONS OF MATHEMATICS In order to obtain an overview of Wittgenstein's thinking about mathematics it is ... notes taken by four of Wittgenstein's students who attended his lectures at Cambridge in 1939, skilfully
edited by Cora ...
Author: Gordon Hunnings
Publisher: SUNY Press
This book explores the interrelated concepts of representation and grammar in the philosophy of Ludwig Wittgenstein. Throughout his life, Wittgenstein was obsessed with the problem of the nature of language and the relationship between language and the world. His intellectual journey, one of the most compelling in twentieth century thought, is the detailed adventure told by Gordon Hunnings in The World and Language in Wittgensteins Philosophy. This book surveys Wittgensteins elucidation of how the world is represented in language, including the posthumously published material of his middle period. Early in his career, Wittgensteins answer to the problem explored the representational connection between language and the world through the analogy of propositions as logical pictures of facts. Later, his mature answer elucidated the concept of the world as a construction of logical grammar. Hunnings shows how these shifting images of reality reflected in language also mirror the changes in Wittgensteins philosophy.
I ,ud wig Wittgenstein, Wittgenstein's Lectures on the Foundations of Mathematics
, Cambridge 1939, 1 row the Notes of R. G. Bosanqnet, Norman Malcolm, Rush
Rhees, and Yorick Smythies, ed. Cora Diamond (New York: Cornell University ...
Author: Janna Levin
Kurt Gödel’s Incompleteness Theorems sent shivers through Vienna’s intellectual circles and directly challenged Ludwig Wittgenstein’s dominant philosophy. Alan Turing’s mathematical genius helped him break the Nazi Enigma Code during WWII. Though they never met, their lives strangely mirrored one another—both were brilliant, and both met with tragic ends. Here, a mysterious narrator intertwines these parallel lives into a double helix of genius and anguish, wonderfully capturing not only two radiant, fragile minds but also the zeitgeist of the era. From the Trade Paperback edition.
Keynote lecture at the Philosophy of Education Society of Great Britain Annual
Conference, Oxford, 28–30 March. Wittgenstein, L., 1922. ... Wittgenstein's Lectures on the Foundations of Mathematics: Cambridge 1939. Chicago, IL:
University of ...
Author: William H. Kitchen
Publisher: Bloomsbury Publishing
Authority and the Teacher seeks to overturn the notion that authority is a restrictive force within education, serving only to stifle creativity and drown out the voice of the student. William H. Kitchen argues that any education must have, as one of its cornerstones, a component which encourages the fullest development of knowledge, which serves as the great educational emancipator. In this version of knowledge-driven education, the teacher's authority should be absolute, so as to ensure that the teacher has the scope to liberate their pupils. The pupil, in the avoidance of ignorance, can thus embrace what is rightfully theirs; the inheritance of intellectual riches passed down through time. By invoking the work of three major philosophers – Polanyi, Oakeshott and Wittgenstein – as well as contributions from other key thinkers on authority, this book underpins previous claims for the need for authority in education with the philosophical clout necessary to ensure these arguments permeate modern mainstream educational thinking.
During these years at Cambridge - he was elected Professor there in 1939 — Wittgenstein lectured on language, logic, the foundation of mathematics and the
philosophy of psychology. Some of this lecture material is now published in the
form both of Wittgenstein's own notes for lectures and of lecture notes taken by
his students. Throughout his life, Wittgenstein constantly wrote down his ideas in
Author: Marie McGinn
Wittgenstein is one of the most important and influential twentieth-century philosophers in the western tradition. In his Philosophical Investigations he undertakes a radical critique of analytical philosophy's approach to both the philosophy of language and the philosophy of mind. The Routledge Guidebook to Wittgenstein's Philosophical Investigations introduces and assesses: Wittgenstein's life The principal ideas of the Philosophical Investigations Some of the principal disputes concerning the interpretation of his work Wittgenstein's philosophical method and its connection with the form of the text. With further reading included throughout, this guidebook is essential reading for all students of philosophy, and all those wishing to get to grips with this masterpiece.
I first saw Wittgenstein in the Michaelmas term of 1938, my first term at Cambridge. At a meeting of the ... I attended Wittgenstein's lectures, which were
on the philosophical foundations of mathematics, in the Lent term of 1939. He
continued on ...
Author: Norman Malcolm
Publisher: Oxford University Press
Wittgenstein was one of the most powerful influences on contemporary philosophy, yet he shunned publicity and was essentially a private man. This remarkable, vivid, personal memoir is written by one of his friends, the eminent philosopher Norman Malcolm. Reissued in paperback, this edition includes the complete text of fifty-seven letters which Wittgenstein wrote to Malcolm over a period of eleven years. Also included is a concise biographical sketch by another of Wittgenstein's philosopher friends, Georg Henrik von Wright.'A reader does not need to care about philosophy to be excited by Mr Malcolm's book; it is about Wittgenstein as a man, and its interest is human interest'. (From a review of the first edition in the Manchester Guardian)
Ludwig Wittgenstein selbst hielt seine Überlegungen zur Mathematik für seinen bedeutendsten Beitrag zur Philosophie. So beabsichtigte er zunächst, dem Thema einen zentralen Teil seiner Philosophischen Untersuchungen zu widmen.
1912 1926 1931 1934 1935 1936 1937 1938 1939 1942 1943 1944 1945 1947
1948 1950 1951 1952 1954 Born 23 ... Delivers undergraduate lecture-course in Cambridge and attends Wittgenstein's class on Foundations of Mathematics 4 ...
Author: R.O. Gandy
Mathematical Logic is a collection of the works of one of the leading figures in 20th-century science. This collection of A.M. Turing's works is intended to include all his mature scientific writing, including a substantial quantity of unpublished material. His work in pure mathematics and mathematical logic extended considerably further; the work of his last years, on morphogenesis in plants, is also of the greatest originality and of permanent importance. This book is divided into three parts. The first part focuses on computability and ordinal logics and covers Turing's work between 1937 and 1938. The second part covers type theory; it provides a general introduction to Turing's work on type theory and covers his published and unpublished works between 1941 and 1948. Finally, the third part focuses on enigmas, mysteries, and loose ends. This concluding section of the book discusses Turing's Treatise on the Enigma, with excerpts from the Enigma Paper. It also delves into Turing's papers on programming and on minimum cost sequential analysis, featuring an excerpt from the unpublished manuscript. This book will be of interest to mathematicians, logicians, and computer scientists.
Resnik, Michael (1997) Mathematics as a Science of Patterns, Oxford: Oxford
University Press. ... In S. Shapiro (ed.) ... (1939) Greek Mathematical Works, i.
Thales to Euclid, Greek text with facing English translation, Loeb Classical
Library, 335, Cambridge, MA: Harvard University Press. ... Whitehead, Alfred
North (1925) Science and the Modern World: The Lowell Lectures, 1925, New
York: Macmillan. Wittgenstein, Ludwig (1978) Remarks on the Foundations of Mathematics, revised.
Author: John P. Burgess
Publisher: OUP Oxford
While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the rise of experimental mathematics on the one hand and computerized formal proofs on the other hand. The main theses of Rigor and Structure are that the features of mathematical practice that a large group of philosophers of mathematics, the structuralists, have attributed to the peculiar nature of mathematical objects are better explained in a different way, as artefacts of the manner in which the ancient ideal of rigor is realized in modern mathematics. Notably, the mathematician must be very careful in deriving new results from the previous literature, but may remain largely indifferent to just how the results in the previous literature were obtained from first principles. Indeed, the working mathematician may remain largely indifferent to just what the first principles are supposed to be, and whether they are set-theoretic or category-theoretic or something else. Along the way to these conclusions, a great many historical developments in mathematics, philosophy, and logic are surveyed. Yet very little in the way of background knowledge on the part of the reader is presupposed.