On 09 Jan 2014, at 05:55, meekerdb wrote:

Bruno writes Bp & p, where "Bp" ambiguously means "Provesp" (Beweisbar?) and "Believes p".

`What is ambiguous? I said that I limit the interview to Platonist`

`*correct* machine, believing in arithmetic or in recursively`

`enumerable extension of arithmetic. And the fact that the machine`

`cannot prove Bp -> p for all p, suggest that provability obeys to the`

`axioms I gave for belief, and not for knowledge (where Bp->p is not`

`just true but believed as well).`

"Believes p and P" is then a belief that is "true".

OK. That's correct.

I put scare quotes around "true" because I think it just means "is aconsequence of some (Peano's) axioms", which is not necessarily thesame as "expresses a fact".

`At the meta-level (G*), that is true, but the machine does not know`

`that, and for correct machine, this change nothing. We have Bp -> p`

`(as a theorem of G*, not of G).`

Bruno

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'). JMOn Wed, Jan 1, 2014 at 5:50 AM, Bruno Marchal <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 inany way from belief (assumed or not). knowledge *is* belief, whenor in the world those beliefs are true, but this you can neverknow as such.Since your theory to an infinite number of semi-classical worldswith 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 (truebelief) obeys a different logic (an epistemic intuitionist logic)despite G* knows that it is the same machine, having the sameaction. The machine just dont know that, although it can infer itfrom 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 thisyou need []p -> <>p, which is ocrrect for Bp & p, though, andindeed a physics appears already there, but that is a sort ofanomaly (which confirms what I took as an anomaly in Plotinus, butthe machine agrees with him).Now, Bp, when present in the nuances, gives the logic of thecorresponding "certainty", so it is trivially a probability one. Weneed to extract the logic, and the probability different from 1 arehandled by the mathematics, and is related to the Dp (not Bp). Theprobability bears on the accessible "worlds".The interesting concept is the probability of future eventsrelative 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 relativeconsistency together with some temporal interpretation.Bruno--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To unsubscribe from this group and stop receiving emails from it,send an email to everything-list+unsubscr...@googlegroups.com.To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.

http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.