Bruno Marchal wrote:
> Le 09-juil.-06, à 14:26, 1Z a écrit :
>
>
>
> > So how do insubstantial numbers generate a substantial world ?
>
>
>
>
> I guess there is no substantial world and I explain in all details here
> http://iridia.ulb.ac.be/~marchal/ (and on this list) why insubstantial
> numbers generate inescapably, by the mixing of their additive and
> multiplicative structures, local coherent webs of beliefs in
> substantial worlds, and how the laws of physics must emerge (with comp)
> from those purely mathematical webs ... making "comp" testable in the
> usual Popperian sense. In that sense "comp" already succeeds some first
> tests.
Insubstantial numbers can't generate beliefs or appearances unless
they are substantial enough to generate some kind of psyhcological
reality. Standard solipsistic arguments, like the ones you use,
seek to show how the appearance of an objective , physical
world can arise given the *assumption* that there is already
some kind of psychological or subjective reality for appearances
to appear in and beliefs to be believed by.
Standard solipsists do not find that assumption problematic because
they are starting from their experience of the world. If you are
starting from
only the assumption of the existence (in some admitedly insubstantial
sense)
of mathematical objects. you cannot just assume that there are
experienceing
midns. You have to show how experiencing minds emerge from numbers
before you can show ow an apparent physical world arises out of their
experience.
And there is still the problem that your "insubstantial" mathematical
existence is still too substantial for some tastes. Claiming that
mathematical existence falls short of full physical existence
is not going to satisfy staunch anti-realists about mathematics,
for whom numbers just don't exist at all. And producing
mathematical sentences like "there exists a number such..."
is hardly likely to convince them that mathematical objects
have any real existnce, after they have spent their lives
inisting that such sentences are mere /facons de parler/.
Mathematical anti-realists might not be correct of course,
but that they are wrong is and additional assumption above
and beyond COMP. (And of course anti-realists don't think
mathematical realsim is entailed by COMP. They don't think
the fact that humans can calculate means numbers exist,
why should the fact that comuters calculate persuade them that numbers
exist) ?
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Received on Sun Jul 09 2006 - 12:27:05 PDT