On 29 Jan 2014, at 18:12, John Clark wrote:
On Tue, Jan 28, 2014 at 3:20 AM, Bruno Marchal <[email protected]>
wrote:
>> A proof is a FINITE number of statements establishing the truth
or falsehood of something;
> Not establishing the truth, but establishing the theoremhood.
I stand corrected; although it would be true if the axioms in the
logical system you're using are true, and that's why you need to be
very very careful before adding new axioms to your system.
A case like that can be made for arithmetic, but despite I do believe
that indeed 17 is prime, in serious theology, it is wiser and simpler
to put even that as an hypothesis. Sure, it is provable in PA, and in
RA, but I take those axioms of PA and RA as hypotheses too. That is
what we assume. Better to keep our personal conviction for ourselves,
or for the pause-café.
That helps also for the model theory, which theorizes on semantic and
truth, in relation with theories, as a subject matter.
Bruno
John K Clark
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