Lectures on the Foundations of Mathematics, Cambridge 1939

by Ludwig Wittgenstein, Cora Diamond (Editor)

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.

Genres: Philosophy, Mathematics, Nonfiction, Theory, Physics, Computer Science

300 pages, paper

Published October 15, 1989

About the author

Ludwig Josef Johann Wittgenstein (Ph.D., Trinity College, Cambridge University, 1929) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language.

Described by Bertrand Russell as "the most perfect example I have ever known of genius as traditionally conceived, passionate, profound, intense, and dominating", he helped inspire two of the twentieth century's principal philosophical movements: the Vienna Circle and Oxford ordinary language philosophy. According to an end of the century poll, professional philosophers in Canada and the U.S. rank both his Tractatus Logico-Philosophicus and Philosophical Investigations among the top five most important books in twentieth-century philosophy, the latter standing out as "...the one crossover masterpiece in twentieth-century philosophy, appealing across diverse specializations and philosophical orientations". Wittgenstein's influence has been felt in nearly every field of the humanities and social sciences, yet there are widely diverging interpretations of his thought.

Reviews

[Erik Graff · Rating 3 out of 5]

While at Loyola University Chicago I served as a teaching assistant for a number of their philosophy faculty and one member of the linguistics department, but mostly I worked for Father Bill Ellos either full- or, if shared with someone else, part-time. Since there were so many Jesuit collegians at the school, the position was almost entirely research oriented, teaching positions being reserved for them. My only experience teaching there was in logic.

Bill's own dissertation was on Wittgenstein, so one of the first things he had me do was to edit it. Meanwhile, he very strongly encouraged me to read Wittgenstein on my own and, I believe, counted some of this reading towards an independent study credit. As a consequence, I became pretty familiar with the philosopher and even wrote a paper entitled "Wittgenstein's 'World-Picture' in On Certainty' which was delivered at a philosophy conference and ultimately published. A copy of that is included here, in GoodReads.

Wittgenstein's Lectures on the Foundations of Mathematics were read in the midst of all reading one book "by" (he actually published very little) him after another. There's been a real Wittgenstein industry involving the creation of books "by" him from the notes of former students and this is one of them.

[Harry · Rating 4 out of 5]

A great treat for all Wittgenstein enthusiasts. Alan Turing, who had also taught a course with the same title (but not the same subject, it turns out) is present at most of the lectures, and their disagreements form a large part of the book. In page 95 Turing says "I see your point", to which Wittgenstein replies (in an exasperated manner, one would assume) "I have no point." Beautiful.

[stephen]

it is hard to make one of these reviews about these lectures.
a chatty wittgenstein is very interesting to read.
if you've read much of his work, you'll know where this is heading, and it heads to those places--but you get some of the riffing, which is not present in the same way in even the more expansive of his written works.

probably not the best way in to wittgenstein, but if you're already in, a lovely and entertaining part of the pool to swim about in---the places where he'll say "all that is bosh" for example are like those little plastic castles that fish seem to like, for some reason. so you are now like a fish.

[Zedder · Rating 4 out of 5]

If you want to understand the basis for the resolute reading of Wittgenstein, just read these lectures, edited (or some might say "composed") by Cora Diamond. It's an easy read, and much more clear than Witters' own "Remarks on the Foundations of Mathematics".

[Haley · Rating 3 out of 5]

this was actually impossible for me to read. i understood maybe three concepts, and that’s only because i was helped. i think i’d have to read it at least three more times for my pea brain to wrap around what’s going on

[Quiver · Rating 5 out of 5]

We are inclined to imagine numbers as structures. We could think of a tune as as a structure of notes. If we think of a triangle—the number 3 stands for a structure.

Mind-blowing, yet accessible to those curious about mathematics without being professional mathematicians. Highly recommended especially for aspiring philosophers (of science).

[Slimbo · Rating 4 out of 5]

p nice to follow along w i. think th way its presented as discursive dialogue makes it easy to follow along w and a bit mor engagin, doesnt feel like it draws to a conclusion or anything but does leav me w feeling of. a different understanding in how math/logic related

[Henrik · Rating 4 out of 5]

'"p.p→q → q" = tautological'=~tautological

[Ege]

"I think this also doubles up as one of the best introductions to his later philosophical method/approach as a whole."

[Neal McDonald · Rating 5 out of 5]

W taught a class. Turing took it. Shit got deep: you don’t math the way you think you do.

[Andrea · Rating 4 out of 5]

Cambridge 1939, Wittgenstein tiene un ciclo di trentuno lezioni sulla filosofia della matematica, a cui prende parte, tra gli spettatori, il matematico Alan Turing. Questo testo rientra a pieno diritto in quello che viene definito il "Secondo Wittgenstein", ed è un'interessante testimonianza della proposta didattica del filosofo austriaco che è stata ricostruita attraverso gli appunti di quattro differenti uditori.

Se Wittgenstein nel suo Tractatus Logico-Philosophicus aveva ridotto spietatamente la matematica alla logica, in queste lezioni ripensa radicalmente le proprie posizioni e affronta il problema delle ambiguità del linguaggio in relazione alla struttura della comunicazione matematica (che a differenza di come Russell o Frege ritenevano non può essere interamente spiegata con le proposizioni logiche) e, soprattutto, confronta i risultati dei matematici con la realtà empirica.

Seppur frutto di interpretazioni, il lavoro è attendibile ed interessante, e chi avrà letto di Wittgenstein non faticherà a riconoscere tra le righe di questi appunti tutto il suo tormento e il suo desiderio di risposte, nonché il suo affascinante modo di porsi dinanzi alle questioni.

[David · Rating 5 out of 5]

I got this when our County Library system still had inter-library loan before the budget cuts took that perk away. The book looked as though it had never been opened, and I suspect it may be the only copy in the entire State, having come from a small college library collection. The interchanges between Turing and Wittgenstein are some of the most interesting parts of the Q/A during these lectures. This is one book I need to acquire for another look. It has been almost twenty years since my first read. I may try to get Wittgenstein's other book on the subject which apparently covers the subject in more detail.

[Nick Black]

Started reading this in March or so, but put it down and can't find it now...argh!

[Jerusha Crone · Rating 4 out of 5]

delight