>Pat,
>
> You evidently have not done a course in geometry where every
>theorem starts with the assumption "if 2 not-equal-to 0". (01)
Indeed, I have not had that particular experience, though I did learn
axiomatic set theory from Quine, which may have been even more
unnerving, since we were not even allowed to assume that zero existed
until near the end of the semester. (02)
> This leaves mathematicians permanently scared with the idea (03)
Did you mean 'scared' here? If so I cannot quite follow your meaning.
Or did you mean 'scarred'? (04)
>that pure mathematics is a formal system independent of reality - "a
>game played this way" if you like - and it is the job of applied
>mathematicians to identify the formal apparatus that can be used to
>model some aspects of reality. (05)
Well, I spent 3 years at Cambridge learning parts of pure and applied
math in about equal amounts, and one of the lasting lessons I took
away with me was that they are really one subject. (06)
>This is not to say that the mathematics cannot apply to reality, but
>rather that it is sometimes tricky to work out which parts it
>applies to. (07)
There is a discipline to thinking about that, indeed. One gets into
questions of error, accuracy and dimensionality, as I dimly recall. (08)
> Perhaps the question keeps arising because there is a
>fundamental difference in assumptions/perceptions between the
>different religions of mathematics and logic (to wander into another
>thread)? (09)
I don't think that there is much to choose here (ie in this
discussion) between math and logic, as they are both concerned with
necessary truths. And of course neither of them are religions. (010)
Pat (011)
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