(September 12, 2015 at 12:34 pm)Faith No More Wrote:(September 12, 2015 at 12:21 pm)Pyrrho Wrote: This reminds me of an idea I encountered long ago (so long ago that it hardly matters now if it was true then) that most mathematicians were platonists with respect to mathematics. The Internet Encyclopedia of Philosophy states "Mathematical platonism enjoys widespread support and is frequently considered the default metaphysical position with respect to mathematics." But it would be interesting to see a poll of mathematicians.
Thinking back on the expressed attitudes of my mathematics teachers, I do not recall any of them saying they had any other position, though I do not recall all of them talking about this.
My dad bought me a book a while back that was a bunch of short essays from different people about the nature of math, and it's been a bit since I've read it, but I remember seeing a fairly good mix between people that felt it was Platonic and others that weren't really convicned at all. Maybe that was a purposeful selection by the editor, though. The biggest impression I got from the book, however, was that no one really knows what math actually is.
I think books like that typically do strive to give representations of a variety of opinions rather than try to represent just what is most popular.
"A wise man ... proportions his belief to the evidence."
— David Hume, An Enquiry Concerning Human Understanding, Section X, Part I.
