Philip Kitcher

[aleph_0]

I just spoke with a modern philosopher, Philip Kitcher, who has published a book The Nature of Mathematical Knowledge. He is an extreme empiricist--about the closest you can get to without being a logical positivist, if indeed he isn't one. I have just ordered the book, but I wonder if anybody knows about him or empiricist mathematics. Note, he's not a constructivist. Far from it, he thinks we should be much less concerned with proof and rigor than we are today. He points out that continental mathematicians in the 17th and 18th centuries were much more experimental with their mathematical proofs and theories, and they flourished at that time. English mathematicians, however, painstakingly proved theorems that were lightyears behind their continental counterparts and as a result English mathematics at the time stagnated. He doesn't say that there is no place for proofs, but only that we should not restrict ourselves to them. He is, at heart, a pragmatist. I'm not sure whether Objectivist will object to his epistemological pragmatism in the way that they object to ethical pragmatism, but I'm curious to know if anybody is familiar with the subject.

[Seanjos]

Looks interesting... I've too many maths books to read in the coming months. Let us know how you get on!

[ctrl y]

I just spoke with a modern philosopher, Philip Kitcher, who has published a book The Nature of Mathematical Knowledge. He is an extreme empiricist--about the closest you can get to without being a logical positivist, if indeed he isn't one. I have just ordered the book, but I wonder if anybody knows about him or empiricist mathematics. Note, he's not a constructivist. Far from it, he thinks we should be much less concerned with proof and rigor than we are today. He points out that continental mathematicians in the 17th and 18th centuries were much more experimental with their mathematical proofs and theories, and they flourished at that time.

What does it mean to be "experimental" as regards a mathematical theory?

[aleph_0]

Take, for example, the exploration of infinite series pursued by the likes of Leibniz, and who famously got absurdly wrong results from his investigations--but the studies carried on, until he got better results that ultimately flourished into modern day calculus. Also note the painstakingly slow and muddled development of probability theory. In fact, mathematical proofs as we know them today didn't really exist until about the late 19th century. Instead of these rigorous proofs, mathematicians relied in intuitions about what seems true, and on seeing a system of mathematics work well enough in practice.