On 18 Oct 2013, at 21:22, meekerdb wrote:

On 10/18/2013 11:45 AM, Bruno Marchal wrote:
The key result is that incompleteness makes the Theaetetus' definition of knowledge (the only one I know capable of doing justice to the metaphysical antic dream argument) given a classical theory of knowledge (S4Grz) which X1* is an important "physical" variant.

I'm not sure how to parse that sentence, but the definition of knowledge that you give seems to me just a rough approximation (like the physicists spherical cow) to knowledge people actually have.

Sure.



For example, I 'know' the four color theorem is true, but I can't prove it without a computer. And there must be infinitely many other theorems of arithmetic who's proof is would take longer than the age of the universe. So, except as rough approximation why should we identify Bp&p with Knows(p).

Because it provides the only way to associate knowledge (S4) to provability (rational belief). That it works is already a miracle made possible thanks to incompleteness and self-reference, and that it is the only way is a result by Artemov.

And the ideally self-referentially correct machine reasoning about herself cannot avoid it.

We always simplified when we do science, and when it shows that the simplification leads already to a rich theory putting some light, usually we don't complain. If you know better, please improve the situation ... But you have to understand that the UDA reduces the mind body problem into a self-referential arithmetical problem.

Bruno



http://iridia.ulb.ac.be/~marchal/



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