SUO: Re: The Winners Of Our Dis-Contents
Pat Hayes wrote:
>
> [Jon Awbrey wrote:]
> >
> > The problem is not writing the axioms --
> > the problem is drawing the consequences.
> >
> > Jon Awbrey
>
> They are *both* very hard problems. Drawing the consequences
> is traditionally thought of as the problem of theorem-proving,
> and there is a lot known about it (and how hard it indeed is).
> But just writing the axioms is also a very hard problem, as
> some of the greatest minds of the last century have found;
> and this, which Jon is wrong to dismiss quite so casually,
> is the main problem which the SUO has to address.
>
> Pat
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Pat,
I am not sure how much in the way of philosophical
completeness you expected out of a bumper sticker
or a Burma Shave punchline -- as you very well
comprehend, my intellectual life is largely
pastiched together from the likes of such
jingles -- but this remark was extracted
by another from its initial context,
where the discussion began with
a request for textbook cases
of axiom sets, and where I
instanced the example of
the axioms for a group,
which as "tri-vial" as
they are, rather try
our powers to draw
their consequence,
the ease at issue
being only that
of looking in
textbooks to
discover
them.
Fear not! As no one has to usher into the theatre of my imagination
the idea that our modern mathematics was not created in modern times,
I am very well aware of just what it cost us to buy our Galois shoes!
Cheers,
Jon
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