Bruno writes Bp & p, where "Bp" ambiguously means "Proves p" (Beweisbar?) and "Believes
p". "Believes p and P" is then a belief that is "true". I put scare quotes around "true"
because I think it just means "is a consequence of some (Peano's) axioms", which is not
necessarily the same as "expresses a fact".
Brent
On 1/8/2014 2:11 PM, John Mikes wrote:
Bruno and Brent:
did you agree whether *"TRUE BELIEF*" means in your sentences
1. one's belief that is TRUE, (not likely), or
2. the TRUTH that one believes in it (a maybe)?
(none of the two may be 'true').
JM
On Wed, Jan 1, 2014 at 5:50 AM, Bruno Marchal <marc...@ulb.ac.be
<mailto:marc...@ulb.ac.be>> wrote:
On 31 Dec 2013, at 21:09, meekerdb wrote:
On 12/31/2013 1:07 AM, Bruno Marchal wrote:
only rules to extract knowledge from assumed beliefs.
?
I answered "no" to your question. Knowledge is not extracted in any way from
belief (assumed or not). knowledge *is* belief, when or in the world those
beliefs
are true, but this you can never know as such.
Since your theory to an infinite number of semi-classical worlds with
different
events (and even different physics) it seems that "true belief" is not a
very
useful concept.
It is, because by incompleteness, we will have that Bp & p (true belief)
obeys a
different logic (an epistemic intuitionist logic) despite G* knows that it
is the
same machine, having the same action. The machine just dont know that,
although it
can infer it from comp + a sort of faith in herself.
Every belief is going to have probability zero of being true.
neither Bp nor Bp & p is a priori related to probability. For this you need
[]p ->
<>p, which is ocrrect for Bp & p, though, and indeed a physics appears
already
there, but that is a sort of anomaly (which confirms what I took as an
anomaly in
Plotinus, but the machine agrees with him).
Now, Bp, when present in the nuances, gives the logic of the corresponding
"certainty", so it is trivially a probability one. We need to extract the
logic, and
the probability different from 1 are handled by the mathematics, and is
related to
the Dp (not Bp). The probability bears on the accessible "worlds".
The interesting concept is the probability of future events relative to
one's
current state.
That's exactly why we need to go from Bp to Bp & Dt (or Bp & Dt & p, or
actually Bp
& p). This gives the relevant notion of relative consistency together with
some
temporal interpretation.
Bruno
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