Re: Name the thesis: "Formal sentences capture informal ones"

Helene.Boucher_at_wanadoo.fr
Date: 01/30/05 

Date: 30 Jan 2005 08:22:55 -0800

Torkel Franzen wrote:
> Helene.Boucher@wanadoo.fr writes:
>
> > Presumably you would mean by 'ordinary mathematics'
> > something which includes the truth of the successor axiom, so your
> > additional phrase answers the question "Why is it trivially
true...?"
> > in a trivial way (the answer being, "because it's true by the
> > definition of 'ordinary' mathematics") or turns the question into
one
> > of causality instead of grounds ("why has ordinary mathematics come
to
> > include the successor axiom?").
>
> It's not an answer at all to the question why it is trivially true.
> It is merely the observation that since you put in question trivial
> theorems of ordinary mathematics, your regarding Con(PA) as not being
> a faithful translation of "PA is consistent" becomes a side issue.

You appear to be replying to my remarks about your inclusion of "in
ordinary mathematics" after "is trivially true." I therefore do not
understand your comments, since they do not appear to have any
relevance.

>
> > Except (again!) the faithfulness of the translation was the issue
of
> > the thread. And the intensional equivalence of two sentences
should
> > not turn on whether something else is true or not.
>
> Naturally it turns on whether we take other things to be true.

I think you misunderstood what I meant, so I must have been unclear.
What I meant was: if S1 and S2 are only equivalent supposing that some
other proposition is true, then they cannot be intensionally
equivalent.

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