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

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

Date: 30 Jan 2005 07:38:29 -0800

Torkel Franzen wrote:
> Helene.Boucher@wanadoo.fr writes:
>
> > So your elucidation why something raises basic
> > questions (such as "Why is it trivially true that 2^n exists for
every
> > n?") is the statement that "Because it is trivially true that 2^n
> > exists for every n."
>
> Right.

!

> Perhaps this will be clearer if I say "trivially true in
> ordinary mathematics".

I don't think so. 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?").

> Hence, when you question whether 2^n exists
> for every n, you raise a basic question, and the question of the
> faithfulness of the translation Con(PA) becomes a side issue.

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. And ... well I
won't repeat myself !