Re: Epistemology 201: The Science of Science

From: Jason (jasonstevensNOSPAM_at_free.net.nz)
Date: 01/25/05 

Date: Wed, 26 Jan 2005 11:11:50 +1300

> >>So, yes, there most certainly *was* a formal method to prove it,
> >>consisting of reducing the problem to a finite number of cases.
> >
> > They key to the proof being empirical is that a computer is used. So if the
> > algorithm can be deductively proven to be correct, then I'll concede.
Otherwise
> > all that can be done is to test it on different computers with different
> > programmes until we're satisfied, which is inductive.
>
> How are noncomputer proofs tested? By having lots of people test them
> out. That process (of checking the proof) is just as inductive.

Yep :)

>
> > My contention is not that the four colour problem is not formally provable.
It
> > may well be by someone with a lot of time on their hands. But unless the
> > referees are prepared to spend the same amount of time, then they can only
> > appeal to a computer proof.
> >
> > BTW, this is not to say that it is not admissible as a proof. I think it
should
> > be. It is just another argument for quasi-empirical mathematics.
>
> For reference, see:
>
> http://www.math.gatech.edu/~thomas/FC/fourcolor.html
>
> The proof of 4CT is not quasi-empirical. No random sampling was made.
> The cases are exhaustive. Yes, you need to prove that the algorithm
> checking the cases is correct, and that the set of cases is
> exhaustive. But that's not more empirical than any noncomputer proof.

The sampling was in the algorithms, their implementations and the instances they
were run.

Relevant Pages

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