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> > Peter_Smith wrote:
> >> PRA allows [the equivalent of] initial universal quantifiers).
I later asked,
> > If this is really true, then why did I get so savagely attacked
> > (by DMC of all people!) for alleging that the schematic
> > variables in your axiom schemata were in fact [an equivalent of]
> > these selfsame [equivalents of] initial universal quantifiers????!?!????
AK replies:
> Because you were wrong.
No, I wasn't, and I'm still not, and YOU HERE *are*.
> Peter was then talking about a different theory
Shit.
We are all always talking about PRA.
And PRA, whatever it may be, IS NOT merely "a theory".
We haven't yet even been able to agree on what ORDER of theory
it is, or over what language, or whether that language does or doesn't
allow "[an equivalent of]" universal quantification.
If you want to present 3 different definitions of PRA, fine, but at
least
be able to say something coherent about how they relate.
> - one in which (the language of) the consistency of no theory can be
> expressed, incidentally.
Well, that WAS the OP's ORIGINAL question, namely,
"How can you express consistency in PRA, given that it is
quantifier-free?"
> You get it from my formulation by dropping
> variables as terms,
Well, are variables-as-terms in YOUR formulation implicitly
universally-quantified over? Were THEY meta-language variables?
I repeat, there IS such a thing as a distinction without a difference.
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