FOM: modeling PRA in the physical world

Stephen G Simpson simpson at
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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