[FOM] Choice of new axioms 1 (reply to Friedman)

[Eray Ozkural]

On 2/13/06, Harvey Friedman <friedman at math.ohio-state.edu> wrote:
> Certainly under the idea that space is not infinitely divisible, real
> numbers then lose their physical significance. But I was just referring
> earlier to "naïve physics", which does have a strong intuitive appeal, and
> is inescapably tied up with real numbers.

Assuming that the space is infinitely divisible, real numbers are
not the single model of that concept. If we say that the physical
space is only finitely divisible as Shipman suggests, then that is a
physical idea, and it is a case already covered by theory. However,
if we try to imagine an infinite division of space, we find many
compelling models: rational numbers, real numbers,
many subsets of real numbers (such as Turing-computable etc.),
hyperreals, surreals, superreals. On the other hand, if we limit ourselves to
"computable mathematics", it seems that we are not so free in
realizing the same concept; then we would have to pick very
specific definitions.

In addition, since "naive" or folk physics is almost exclusively
concerned with simple calculation of trajectories, dynamics
and such, stronger systems may not be needed. And it is
arguable by several technical papers mentioned before that
it is the case for the science of physics (i.e., on the sufficiency
of computable mathematics for physics).

Regards,

--
Eray Ozkural (exa), PhD candidate.  Comp. Sci. Dept., Bilkent University, Ankara
http://www.cs.bilkent.edu.tr/~erayo  Malfunct: http://www.malfunct.com
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