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".


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').


On Wed, Jan 1, 2014 at 5:50 AM, Bruno Marchal < <>> 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 
    are true, but this you can never know as such.

    Since your theory to an infinite number of semi-classical worlds with 
    events (and even different physics) it seems that "true belief" is not a 
    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 
    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 
    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 
    temporal interpretation.


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