Wittgenstein's Lectures on the foundations of mathematics, Cambridge, 1939: From the notes of R. G. Bosanquet, Norman Malcolm, Rush Rhees and Yorick Smythies [Hardcover]

Ludwig Wittgenstein (Author)

Book Description

Publication Date: 1976

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.

--This text refers to the Paperback edition.

Editorial Reviews

About the Author

Cora Diamond is professor of philosophy at the University of Virginia.

--This text refers to the Paperback edition.

Product Details

• Hardcover: 300 pages
• Publisher: Harvester Press (1976)
• Language: English
• ISBN-10: 085527039X
• ISBN-13: 978-0855270391
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #4,694,104 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

10 of 13 people found the following review helpful:

5.0 out of 5 stars Lucid, ... and Smells like Cookies!, November 7, 2005

By 

A. Warren "Dedalus" (Bay Village, OH USA) - See all my reviews
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This review is from: Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939 (Paperback)

In most ways I've found this book easier going than his "Remarks on the Foundations of Mathematics," though of course there is some overlap. The continuity of the examples and discussion is well worth any confusion in the presentation (these are, after all, lecture notes by his students). It's also fairly strange to see, in the middle of a lecture, Alan Turing ask a question...

The best part, however, is that this is perhaps the sweetest-smelling book I have ever read. And what, to be honest, goes better with abstract investigations into the basis of mathematics than the smell of cookies? Nothing, that's what.

3 of 5 people found the following review helpful:

4.0 out of 5 stars Wittgenstein rambles, but has powerful philosophical insights, December 21, 2010

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Joseph A. Schrock "Truth Seeker" (Starkville, MS USA) - See all my reviews
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This review is from: Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939 (Paperback)

This particular work on some of Wittgenstein's Cambridge lectures seems to me to be quite rambling in nature; however, since I've only read the first few lectures in "Wittgenstein's Lectures on the Foundations of Mathematics", I'm unprepared to offer much criticism or commendation. It appears that Wittgenstein had extraordinarily creative and brilliant insights into various aspects of philosophy, including the philosophy of mathematics. Yet, I suppose that his methods of using all sorts of circumlocutions ("beating around the bush") are characteristic of his philosophizing.

For those who enjoy delving into deep and abstract philosophical issues, such as foundations of mathematics, philosophy of language, etc., Wittgenstein's writings can be quite thought-provoking and challenging. Few 20th century philosophers have had as great an impact on the philosophy of language in the West as has Wittgenstein. So, if you're one of those individuals who enjoys having his/her imagination taken on a wild tour of complex and philosophically abstruse ideas, Wittgenstein's philosophizing (including the book currently being reviewed) is not a bad place to find them.

I include here an addendum to my earlier review of "Wittgenstein's Lectures". Now that I've finished the book, I wish to add to my original review some additional observations.

Wittgenstein discusses logic and mathematics in such ways as to give me the impression that he did not believe that logic is a realm of reality in which all "logical laws" are infallible, and did not seem to believe that any correct conclusion arrived at by application of principles of logic will necessarily agree with any other conclusion that is correctly arrived at by logic.

According to my own thinking about logic, this ground of all necessary aspects of reality (logic) is the domain of all realities that are possible, as well as all realities that do, in fact, exist. Therefore, if anything is logically possible, there exist various ways of expressing that logical possibility, and every logically correct way of expressing the possibility will exactly agree with every other logically correct way of expressing it. Maybe Wittgenstein would have agreed with this, but if so, then I don't fully understand the import of some of his arguments in the book under review here.

From my own viewpoints on Wittgenstein's philosophy, he added tremendously to our understanding of logic and language, and in areas like logic, language, and foundations of mathematics, Wittgenstein was among the very preeminent philosophers of the 20th century. His legacy in these areas of human thought will leave lasting marks.

Thus, "Wittgenstein's Lectures on the Foundations of Mathematics" is a work well worth reading and deciphering by any philosopher of logic, mathematics, or language. Much of it is tough reading, but it tends to get one's synapses firing, and it is anything but dull.