Re: Epistemology 201: The Science of Science

From: Mitch Harris (harrisq_at_tcs.inf.tu-dresden.de)
Date: 01/26/05 

Date: Wed, 26 Jan 2005 11:17:25 +0100

Jason wrote:

>>> 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.

But that is not "empirical" sampling.

The sampling made for Pons Asinorum (Euclid I.5) is every school child
  ever required to read it. (which I suppose means that it hasn't been
proved very well :) )

All I'm saying is that your use of "sampling" makes computer proofs
just as empirical as human ones. 

-- 
Mitch Harris
(remove q to reply)

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