On 08 Jun 2015, at 06:31, LizR wrote (to Brent)
Note that Bruno rejects the conditioning on "justified". Plato's
Theaetetus dialogue defines "knowledge" as "true belief". I think
that's a deficiency in modal logic insofar as it's supposed to
formalize good informal reasoning. But I can see why it's done;
it's difficult if not impossible to give formal definition of
"justified".
Yes.
See my answer to brent. The whole AUDA is made possible because we do
have an excellent axiomatisation of justification. The theory applies
to all consistent continuations of anyone believing in RA or PA axioms.
Then INFORMAL justification, is obtained by the move []p to []p & p,
made possible by the fact that incompleteness implies they obey quite
different logics.
There is no modal logic. Only arithmetical machine self-reference
logics. It just happens that modal logic simplifies a lot the
calculus. Like tensor analysis simplifies general relativity, but is
not part of the theory itself which is concerned with space-time and
gravity.
Bruno
http://iridia.ulb.ac.be/~marchal/
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