FOM: modeling PRA in the physical world
Stephen G Simpson
simpson at math.psu.edu
Wed Mar 17 18:29:38 EST 1999
Raatikainen Panu A K 16 Mar 1999 14:01:45 writes:
> My point about Robinson Arithmetic was that your eariler claim ("
> nested quantification over a domain ... requires an ontological
> commitment to the (actual) existence of that domain") is problematic -
Well, I want to retreat from that claim. What I really intended to
say was: In order to justify induction with respect to properties
defined by nested quantification over a domain, we seem to need an
ontological commitment to the actual existence of that domain, as a
completed totality. The thought behind this is that induction only
makes sense for `definite' properties, and how can we expect
quantification over an incomplete totality to give rise to a
`definite' property?
Robinson's arithmetic is a good example of a theory where you have
quantification over N but you are not commiting yourself to the actual
existence of N as a completed totality. Another example is PRA
formulated in predicate calculus with quantifiers over N -- this is
conservative over the quantifier-free version of PRA.
-- Steve
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