Re: Epistemology 201: The Science of Science

From: Albert (albertwagner_at_cox.net)
Date: 01/25/05 

Date: Tue, 25 Jan 2005 12:13:01 -0600

Lester Zick wrote:
> On Tue, 25 Jan 2005 08:46:17 -0600, Albert <albertwagner@cox.net> in
> comp.ai.philosophy wrote:
>
>
>>Jason wrote:
>>
>>>>>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.
>>
>>Indeed. It is, as you pointed out, only evidence. Proof is only
>>possible in mathematics.
>
>
> Surely also in logic, Albert, through finite tautological regression
> on which mathematics would have to be based if proof is possible.

'Also in logic' implies mathematics is something other than
logic. Axioms and postulates are statements that are *accepted*
as true in order to study the consequences that follow from them.
Are you sure that you are not confusing 'proof' with 'truth'? 

-- 
"Don't you see that the whole aim of Newspeak is to narrow the 
range of thought? In the end we shall make thoughtcrime literally 
impossible, because there will be no words in which to express it."
     -- George Orwell as Syme in "1984"

Relevant Pages

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