Noncommutative Analysis

Following up on my commitment from the last post, I am coming back with a final report of the Brown’s Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures. I wrote midway through the book that I recommend it, because I felt that by reading it I was working myself up into debates with the author, which made reading very active. Having read the book, I feel even more enthusiastic than before to study philosophy of mathematics, so I still feel that this book should be recommended. However, I must say that I did not find it to be a well written book. Fun, yes. Enticing, sure. Entertaining even. But it doesn’t feel like any justice has been done to the subject, and I am not sure what I have learned. What bothers me is most is not that the author concentrated on his own view, not doing justice to other points of view and debunking them in a shallow way – it is actually refreshing to read a book with an opinion. What bothers me most is that the various approaches and schools are simply not explained in sufficient detail and depth (even the author’s). The author name-drops various philosophers or thinkers or various approaches, and goes into a discussion before the reader has a chance to understand really what it is about. Like a child telling his parent about a daydream, he just starts in the middle as if we can see his thoughts. In earlier parts of the books it worked fine for me, because the main characters (Russel, Hilbert, etc.) were familiar to me. Later in the book, when he discussed Lakatos, I was very happy, because I happened to read Lakatos with attention, so I could follow the hints and complete the argument using my memory. But later on in the book, for example when discussing Wittgenstein, it became harder to enjoy, since the presentation seems to assume that the reader knows who the philosopher is, recognizes his main works and understands what they are about. And when the author came to discuss Freiling’s “refutation” of the continuum hypothesis, he was writing as if we have already discussed it, without even putting it into a time frame, so it felt as if the text was not intended to be read by me.