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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