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Re: Some observations on the Peano's Axioms
Posted:
Jun 13, 2012 12:11 AM
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On Jun 13, 3:16 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> > In the meta-languagae (whether Aatu likes to refer to the rubric 'meta-
> > language' or not), he's quantifying over FORMULAS of the first order
> > object language.
>
> One of these days, we must have a little chat about this meta-language
> business...
I look forward to that!
> In this particular instance there's not much to object to,
Indeed!
> although I personally would probably have just said something along the
> lines of:
>
> There is no quantification over predicates (or formulas for that
> matter) in any of the axioms of first-order PA.
So far so good.
> Rather, in the
> presentation of the axioms of PA we find a mathematical description
> or definition (in ordinary mathematical English) of an infinite set
> of axioms.
Which amounts to quantification over formulas in the meta-language!
Moe Blee was quite right. Accurate.
-- Barracking Bill
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