Re: Epistemology 201: The Science of Science

From: Mitch Harris (harrisq_at_tcs.inf.tu-dresden.de)
Date: 01/25/05 

Date: Tue, 25 Jan 2005 14:28:16 +0100

Jason wrote:
>
>>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.

> 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. 

-- 
Mitch Harris
(remove q to reply)

Relevant Pages

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