>-----Original Message----- >From: Bruno Marchal [mailto:[EMAIL PROTECTED] >Sent: Monday, June 06, 2005 12:36 PM >To: Brent Meeker >Cc: EverythingList list >Subject: Re: Observer-Moment Measure from Universe Measure > > > >Le 06-juin-05, à 01:40, Brent Meeker a écrit : > >> What do you take to be the standard definition of "knows"? Is it "X >> knows Y" >> iff "X believes Y is true" and "Y is true"? > >That's the one by Theaetetus. > >> Or do you include Gettier's >> amendment, "X knows Y" iff "X believes Y is true" and "Y is true" and >> "There is >> a causal chain between the fact that makes Y true and X's belief that >> Y"? > >It could depend of the axiom chosen to describe belief. > >For knowability I take the S4 axioms and rules: > >1) axioms: > ><all classical tautologies> > >BX -> X >BX -> BBX >B(X->Y) -> (BX -> BY) > >2) Rule: > >X X -> Y X >----------- ----- (Modus ponens, necessitation) > Y BX > >But in the interview of the Lobian machine I recover the S4 axioms + >Grz, from >defining "knowing X" by "proving X formally and X true" (I apply the >Theaetetus on >formal provability). > >I cannot use Gettier's given that I have no notion of causality to >start with. (Recall >I don't have any physical notion to start with). > >Bruno

In that case, how does "true" differ from "provable"? If it is simply a formal system, with no facts which can make a proposition true by reference, then it seems that there is no separate notion of "true" apart from "provable". Brent Meeker