Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939

...Then don't buy this. However, if you are interested in information science (or more precisely the theory of it) then this book is for you.

Anyone interested in mathematics and culture need to read this book. It gives a new way of looking at mathematics as a language game. I especially like the idea of following a rule in the grammatical construction of a sentence and following a rule in a mathematical calculation as being essentially the same.

You don't have to like math to enjoy this; but you do have to enjoy being challenged.

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.

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.