Re: Real world and mathematics

On Jul 25, 4:37 pm, Angus Rodgers <twir...@xxxxxxxxxxx> wrote:


V. I. Arnol'd, What is mathematics?, (MCCME, Moscow), 2002, Russian

So, when you wrote of Arnol'd, ``See his book "What is mathematics".'',
just what did you mean? I'm puzzled.



I guess that's what I've meant. ISBN 5-94057-090-9. I'm not sure if
it's translated into English, though. :-)

I was browsing through that book, than took a break, checked the
usenet and saw *that* posting.

The book deals with the question whether mathematics is the "bunch of
consequences of some arbitrary axioms or it is a branch of natural
sciences and theoretical physics" (quoting Arnold). IMHO, the axioms
of maths are not as arbitrary as Arnold's straw man - pure
mathematician claims, and yet that does not follow that maths is a
branch of physics. Rather both math and physics (and other natural
sciences) are part of human activities (or human intelligence);
roughly speaking, the humans that produce both maths and natural
sciences are the same humans, with the same limitations and the same
way of reasoning, hence no one should claim that math and natural
sciences are completely insulated from each other. There is always
some interaction going on. Yet it does not necessarily follow that
maths is a branch of physics or natural sciences in general.

The book, by the way, *is* fun to read, and in fact Arnold gives
substantially complex picture than one can guess by reading just the
first couple of paragraphs from his book.
.

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