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On Oct 30, 8:59 pm, "george" <gree...@xxxxxxxxxx> wrote:
> I'm still waiting for somebody (preferably Peter Smith) to put up
> or shut up on THIS theory. Peter is being too broadly disagreeable
> here. First he disagreed with the original poster by insisting that
> "PRA allows [the equivalent of] initial universal quantifers."
> Then, the only version of PRA that he actually presented was one
> that was completely quantifier-free and appeared NOT to allow
> anything vaguely equivalent to quantifiers, and he disagreed with
> me about whether the variables in his axiom-schemata were "an
> equivalent" of initial universal quantifiers. Peter can't have this
> one both ways unless he presents two theories and explains
> why they are both PRA.
Of course PRA is to be presented either explicitly with quantifiers or
at least free variables (" [the equivalent of] initial universal
quantifers") in the object-language.
The other theory I described wasn't PRA and I never said it was. Rather
it was a *different*, weaker, theory which I mentioned in response to a
remark of yours, in order to show that there could be a theory which is
quantifier free in the object language, but which defines the p.r.
functions, at least in the sense of allowing us to calculate the values
of any p.r. function for any argument(s).
So as others have already plainly said, there are two different
theories in play in this thread (and I'm not the one who is confusing
them).
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