---------- Forwarded message ----------
From: Eric Cavalcanti <[EMAIL PROTECTED]>
Date: Aug 13, 2005 4:38 PM
Subject: Re: Modal Logic
To: Bruno Marchal <[EMAIL PROTECTED]>
On 8/13/05, Bruno Marchal <[EMAIL PROTECTED]> wrote:
> Hi Eric,
> > I am having a problem understanding this axiom:
> >> (...) Lob formula (B(Bp->p)->Bp), the main axiom of the modal logic
> > Suppose p = "it is raining today"
> > B(Bp->p) is true because I believe that if I believe it is raining
> > today
> > it IS raining today, since If I believe it is raining today it is
> > because
> > I have gone outside and seen that it is raining today, or I believe my
> > source of information for that matter.
> > But it doesn't follow from that that I do believe that it is raining
> > today.
> > It happens by the way that I don't believe it is raining today, because
> > I can see a beutiful sun outside.
> > What's wrong?
> Literaly, it means you are less modest than a Lobian machine!
> If B(Bp -> p) was true, it would mean that whatever the poof you have
> that p is true, then p is true. What about dreaming that you have look
> through the window and see it rains?
OK, I grant that I might have false beliefs. In fact, I strongly
believe that I do have many false beliefs.
> (Remember B is not the "incorrigible" first person. B is really for a
> scientific third person sharable justification). Of course it makes
> things still more unbelievable, given that you will tell me that in
> case you have a proof, it is even more amazing you can be wrong. But
> then it is like that by incompleteness.
OK, so we shouldn't read Bx as "I believe x", but as
"It is believable that x". Is that right?
But B(Bp -> p) is very different from Bp -> p.
The first is "It is believable that p is believable only if p is true".
The second is "It is believable that p only if p is true".
But if we are talking about third person justifiable beliefs,
how can we ever say B(Bp->p) is true? Couldn't we always
be sceptical about the truth of any belief?
Can you give a particular example of a sentence p such that
B(Bp->p) is true?