Re: How to tell if a theory is a good one

From: Torkel Franzen (torkel_at_sm.luth.se)
Date: 10/04/04 

Date: 04 Oct 2004 09:06:26 +0200

D.McAnally@i'm_a_gnu.uq.net.au (David McAnally) writes:

> On the other hand, assuming the consistency of ZF Set Theory, it becomes a
> trivial exercise to demonstrate the consistence of PA, i.e. if ZF is
> consistent, then PA is consistent.

  Invoking ZF is absurd overkill. Only a very modest amount of set
theory is needed. Specifically, the theory ACA will suffice.

> Torkel was presumably talking from the point of viewof taking the
> consistency of ZF a given.

  No, I was talking from the point of view of ordinary mathematics. If
you don't accept the trivial proof as proving the consistency of PA,
then you have no reason to accept any other mathematical result proved
at a similar level of mathematical abstraction. So just what are you
(not you personally, but somebody who doesn't accept the consistency
proof for PA as proving anything) prepared to accept in mathematics?

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