Re: Successor Axiom: on what grounds TF?

Helene.Boucher_at_wanadoo.fr
Date: 02/06/05 

Date: 6 Feb 2005 07:11:24 -0800

Torkel Franzen wrote:
> Andrew Boucher says:
>
> > On a technical level it seems interesting that one is still able to
> > prove a large class of theorems without the Successor Axiom. If
you
> > find that "silly", well, that's okay, different tastes for
different
> > people.
>
> Right. So why associate this work with dubious philosophizing about
> the existence of successors, instead of simply stating that various
> results can be proved in a weak theory?

When did you stop beating your wife?

Anyway, it would seem that the technical results strengthens the
philosophical case. I can't really comment at this point, since I
don't know know enough about what one can prove without the SA. But
ideally one would like to produce a division of theorems into two, A
(those which don't need the SA axiom) and B (those which are equivalent
to the SA over the base theory), where the A theories are the only ones
which are necessary for science or for use in the real world.

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