Bruno,
In this context, what are you taking to be the truth value of the empty
set?
In other words, how can you say that {Empty set} & p = {Empty set} ?
I thought that you were taking "&" to operate on propositions, not sets.
Doesn't {Empty set} & p mean "saying nothing" in conjunction with "the
truth value of p"?
Going even further back in your statements, how can Bp = {Empty set}
when Bp corresponds to a truth value?
The Dharm-Door of Non-Duality states that {Empty set} is neither true
nor false.
[If this doesn't show up on the list, could you post it there for me.
I have been having trouble registering.]
Tom
-----Original Message-----
From: Bruno Marchal <marchal.domain.name.hidden>
To: everything-list.domain.name.hidden
Sent: Wed, 1 Mar 2006 16:42:25 +0100
Subject: Vimalakirti Machines
Vimalakirti Machines.
Before going back to the lobian hypostases (point of views) and their
associated possible multiverses (the geometrical structure organizing
the possible collection of the observer-moments, states, worlds,
situations, etc.) it could help to study the same hypostases in the
case of a machine or entity much simpler than a lobian one.
Now there is a machine, reasoner, entity (whatever) which is even
simpler than the type 1 reasoner of Smullyan. You can consider it as a
the wisest of all machine, or the dumbest one (your choice). It has
some relationship with some of Hal Ruhl's intution, I think, and
actually, even the lobian talk will lead us to special sort of non
Kripkean world related to the Vimalakirti machine. The machine just say
nothing. Pure total and eternal silence. It is hard to imagine a
simpler discourse than this one. I call it "Vimalakirti' in honnor of a
buddhist who famously said nothing at the right time and place(**).
I recall the 8 hypostases (as I interpret it in the context of the
interview of some machine or entity):
First there are the four primary hypostases:
p (Truth, the One)
Bp (the Intellect, which splits into two: the terrestrial one, and
the divine one, described by G and G* respectively, in the case you
interview a lobian machine)
Bp & p (The Soul, which miraculously doesn't split, in the loebian
case)
Then there are the four secondary hypostases:
Bp & Dp ("Intelligible Matter", which splits in the loebian case)
Bp & Dp & p ("Sensible Matter", which also splits in the loebian
case)
Now, in the interview context, Bp means simply: the machine or entity
will print, or believe, or assert p, if she has not already done so. I
could write B(p) for the sake of readability. For example B(Alice likes
puzzles) means that the machine will assert that Alice likes puzzles,
and B(Bp), = BBp, means the machine will assert Bp, or, given that Bp
means that the machine will assert p, BBp means that the machine will
assert that the machine will assert p. Obviously ~Bp means that the
machine does not asserts p, and B~p means that the machine does assert
~p, and ~B~p means that the machine does not assert ~p. Like always I
will abbreviate ~B~p by Dp.
Now, given the triviality of the discourse of the Vimalakirti machine
(she says nothing), the hypostases will be rather simple too.
p (The truth does not change except for some mundane propositions
concerning perhaps the Vimalakirti machine itself)
Bp terrestrial: this is the discourse of the machine, it can only be
the empty set, given that the machine says nothing.
Bp & p, at the terrestrial level this is again the empty set. OK?
Bp & Dp again empty
Bp & Dp & p empty again.
So all the terrestrial hypostases are empty!
What can we say about the divine one. I recall that they are defined by
all the propositions which are true *about* the entity, independently
of the fact that the entity asserts them or not.
I let you think before giving the answer tomorrow.
Bruno
(**) Googelizing a little bit I realize that the entire teaching of
Vimalakirti is in english on the net:
http://www.buddhistinformation.com/vimalakirti_nirdesa_sutra.htm
See the end of the section 9 for his famous silence. search on the
dharma-door or on non-duality or on the full title of the 9 section:
9. The Dharma-Door of Non-duality
http://iridia.ulb.ac.be/~marchal/
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Received on Wed Mar 01 2006 - 19:07:40 PST