On 14 December 2011 07:49, Eelco <hoogendoorn.ee...@gmail.com> wrote: > On Dec 14, 4:18 am, Steven D'Aprano <steve > +comp.lang.pyt...@pearwood.info> wrote: >> > They might not be willing to define it, but as soon as we programmers >> > do, well, we did. >> >> > Having studied the contemporary philosophy of mathematics, their concern >> > is probably that in their minds, mathematics is whatever some dead guy >> > said it was, and they dont know of any dead guy ever talking about a >> > modulus operation, so therefore it 'does not exist'. >> >> You've studied the contemporary philosophy of mathematics huh? >> >> How about studying some actual mathematics before making such absurd >> pronouncements on the psychology of mathematicians? > > The philosophy was just a sidehobby to the study of actual > mathematics; and you are right, studying their works is the best way > to get to know them. Speaking from that vantage point, I can say with > certainty that the vast majority of mathematicians do not have a > coherent philosophy, and they adhere to some loosely defined form of > platonism. Indeed that is absurd in a way. Even though you may trust > these people to be perfectly functioning deduction machines, you > really shouldnt expect them to give sensible answers to the question > of which are sensible axioms to adopt. They dont have a reasoned > answer to this, they will by and large defer to authority.
Please come down from your vantage point for a few moments and consider how insulting your remarks are to people who have devoted most of their intellectual energy to the study of mathematics. So you've studied a bit of mathematics and a bit of philosophy? Good start, keep working at it. You think that every mathematician should be preoccupied with what axioms to adopt, and why? Mathematics is a very large field of study and yes, some mathematicians are concerned with these issues (they are called logicians) but for most it isn't really about axioms. Mathematics is bigger than the axioms that we use to formalise it. Most mathematicians do not need to care about what precise axiomatisation underlies the mathematics that they practise because they are thinking on a much higher level. Just like we do not worry about what machine language instruction actually performs each step of the Python program we are writing. You say that mathematicians defer to authority, but do you really think that thousands of years of evolution and refinement in mathematics are to be discarded lightly? I think not. It's good to have original ideas, to pursue them and to believe in them, but it would be foolish to think that they are superior to knowledge which has been accumulated over so many generations. You claim that mathematicians have a poor understanding of philosophy. It may be so for many of them, but how is this a problem? I doesn't prevent them from having a deep understanding of their field of mathematics. Do philosophers have a good understanding of mathematics? Cheers, -- Arnaud -- http://mail.python.org/mailman/listinfo/python-list
