Re: Epistemology 201: The Science of Science

From: The Sophist (sophist_at_brown.edu)
Date: 01/25/05 

Date: Tue, 25 Jan 2005 11:44:46 -0500

Jason wrote:

> If maths develops according to the way we see the world working, then the notion
> of mathematical 'truth' can be extended from the limited formal system notion of
> 'truth', to our every day understanding. I believe there are mathematical
> statements that are true in our world, but are not provable by the current
> axioms of maths. These statements are the ones I am referring to. They need to
> be empirically verified, which might then provide impetus for the axioms to
> change.

Could you provide an example of such statements? The only truths not
provable in the current axioms of math that come to my mind are
artificial examples like Goedel sentences, which we believe to be true
for theoretical reasons (they'd better be true, or arithmetic is
inconsistent), not on the basis of anything in our experience.

> Exhaustion and testing by algorithm is not so formal. The computer has to be
> trusted to be doing the right task. I don't know about yours, but my computer
> is not to be trusted at the best of times. Let alone the software I write...

So a method is only formal if it is applied by an infallible reasoner?
Well, that's an easy way to rule out anything from being formally
proven, but it's quite a non-standard use of the term. 

-- 
Aaron Boyden
The main division between the so-called Continental and Analytic 
traditions has been disputes over whether the task of being unclear 
should be carried out in natural language or in a formal system.

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