FOM: RE: Re: Ontology in Logic and Mathematics

[Matt Insall]

Roger:
(e.g. fix the domain of discourse as the collection of everything which
"really" exists)


Matt:
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
http://www.umr.edu/~insall