Re: Epistemology 201: The Science of Science

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

Date: Tue, 25 Jan 2005 23:08:36 +1300

> >The four colour map problem was finally 'proved' by computer. That is, every
> >possible combination of neighbouring map shapes were tried and tested. This
is
> >empirical. There is (or at least was at the time) no know formal method to
> >prove it.
>
> This is a misunderstanding.
>
> If you are able to prove that a problem reduces to a finite number of
> cases, and if you are able to verify those cases, that amounts to
> formal proof. Empirical "proof" would involve actually coloring maps
> and counting how many colors. It would not be accepted as proof by
> mathematicians.

Well, they verified the cases by computer. But how do you prove an algorithm is
correct? If there is an effective method to prove that an algorithm is correct
then what can prove this effective method is correct? The 'proof' of the four
colour problem is partially inductive. Empiricism has leaked into mathematics
via computers.

The computer literally did the colouring of maps and counting of the colours.
It was accepted after they tried it on other computers with different
programmes. But again, this is inductive evidence. That it is a legitimate
proof is controversial.

Relevant Pages

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