FOM: modeling PRA in the physical world
Stephen G Simpson
simpson at math.psu.edu
Thu Mar 11 13:06:54 EST 1999
Vladimir Sazonov 06 Mar 1999 11:23:01
> Thus, despite the physical world is bounded (finite?) it is
> concluded that it models PRA??
There is no contradiction here, because that which is finite may also
be potentially infinite. I want to seriously entertain the idea that
the real world (this is probably more than just the physical world)
may provide a model of PRA, via potential infinity.
> I would say, that potential infinity (our ability to distract from
> resource bounds) is peoples *invention*. It does no hold in our
> universe in any direct sense.
You define potential infinity subjectively as `our ability to distract
from resource bounds'. This formulation prejudges the issue by
assuming that potential infinity is a subjective phenomenon. By
contrast, Aristotle defined potential infinity objectively, as `that
which is always becoming other and other'. For instance, winter is
potentially infinite, because every winter is followed by another
winter. This is an objective fact, not a subjective matter of our
ability to distract from something.
> mathematicians, *postulate* that successor operation always gives a
> new number.
The fact that every winter is followed by another winter is a fact,
not merely a mathematical postulate.
> as Mycielski was mentioned above, I think it will be interesting to
> FOMers his short abstract ...
>
> "To FOM or not to FOM, that is the question"
Mycielski, like Sazonov, is interested in ultrafinitist ideas. I too
wish that Mycielski could be persuaded to participate more explicitly
in FOM.
-- Steve
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