At 08:52 04/10/04 +0000, Brent Meeker wrote:
-----Original Message----- From: Bruno Marchal [mailto:[EMAIL PROTECTED] Sent: Monday, October 04, 2004 11:52 AM To: Everything List Subject: Re: Use of Three-State Electronic Level to Express Belief .... You can always try, but let us be sure we agree on the "intuitive" meaning of Bp, in the case of the Smullyan's "self- rererential" interpretation of the "B".
So we have a machine M. The machine M print propositions from time to time. Bp means that the machine M print p. The machine could print Bp.
"Could" is a slippery word. Is it required that M actually print Bp within a finite number of printings?
Just remember that Bp means the machine has print, or prints, or
will print, sooner or later the proposition p.
From "Bp is true" you cannot infer that the machine will print Bp, only that she
will print p.
Even a self-referentially correct machine is not obliged to print Bp when she
prints (has printed, will print, ...) p.
But a correct machine will never print Bp when she will never print p.
Note that a machine can remain consistent and print Bp without ever printing p (this follows from Godel). But here I anticipate perhaps.
Now we will say (with Smullyan and the modal logicians) that a machine is normal if the machine prints (has printed, will ...) Bp when she prints (has printed, will ...) p. That machine has some "introspective power": when she prints p, she acknowledges the fact: she prints Bp. Obviously such a normal machine will in that case also prints BBp, BBBp, BBBBp, BBBBBp, BBBBBBp, BBBBBBBp, ... You can describe a normal machine by saying that the propositions, Bp->BBp, with p being any propositions, are true about the machine. Again this does not mean the machine will print Bp->BBp for all p. This follows again from the fact that a machine can be normal without printing (communicating, believing, ...) she is normal. OK?