Hi Eric,
Le 11-août-05, à 01:34, Eric Cavalcanti a écrit :
Hi Bruno,
On 8/11/05, Bruno Marchal <[EMAIL PROTECTED]> wrote:
I am having a problem understanding this axiom:
(...) Lob formula (B(Bp->p)->Bp), the main axiom of the modal logic
of self-reference (G)
can be interpreted as showing that some form of honest placebo effect
works! But this is something I am still taking with some grain of
salt.
See the book "Forever Undecided" to see Smullyan exploiting the
working
of some self-fulfilling beliefs.
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?
(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.
Now, another remark is that I don't think the B can be used at all for
everyday belief which are much more complex due to the long social
interaction between us. The everyday beliefs are probably mixture of
the logics I described in comp, and which concerns sound machines. But
to get physics, this is enough.
Bruno
http://iridia.ulb.ac.be/~marchal/
