FOM: RE: Re: Ontology in Logic and Mathematics
montez at rollanet.org
Mon Sep 25 21:04:43 EDT 2000
(e.g. fix the domain of discourse as the collection of everything which
I have a few questions because of this statement.
1. Who gets to decide what ``really'' exists?
2. Apparently, there are some who are ontologically committed to the
existence of ``something'' that is infinite that ``really exists'', and
there are others who are ontologically committed to the denial of the
existence of an ``infinite thing''. Who gets to decide which is correct?
3. As I understand it, the belief in a theory T like (ZFC-AxInf)+not(AxInf)
would include an ontological commitment that there is in some sense
``unboundedly many'' integers, but that there is no ``collection''
consisting exactly of all integers. Now, if this means that ontological
commitment to T involves an ontological commitment that ``unboundedly many''
integers ``really'' exist, what does each one ``exist as''?
4. Does every integer have a realization in the physical universe,
according to the person who is ontologically committed to the theory T? And
if every integer has such a realization, is the person who is ontologically
committed to T also ontologically committed to believe that ``the physical
universe'' ``does not exist''?
Dr. Matt Insall
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