Le 10-mars-06, à 01:43,  Tom  ([EMAIL PROTECTED])  a écrit :

>
> Bruno wrote:
>> So the divine intellect of the Vimalakirti Machine will contains all
> proposition of the form:
>> ~B<whatever>:
>> more example:
>> ~B(an asteroid will not hurt earth in 2102)
>> ~B(an asteroid will hurt earth in 2102)
>> ~B(1+1 = 4)
>> ~B(1+1 ? 4)
>> ~B(PI is rational)
>> ~B(PI is not rational)
>> etc.
>> This gives an infinite set of true propositions *about* the machine,
>> all beginning by "~B". The modalist will recall that "~B" is
> equivalent
>> with "D~", and <whatever> is of course the same as <~whatever>,
>> so the divine intellect can be characterized by saying it contains
>> all "possibilities" (the alethic reading of the diamond "D").
>>
>> This was simple enough, no?
>
> So when you say that the divine is the set of propositions that are
> true about the entity, what you are really saying is that the divine
> knows about all of the elements in the Universal Set (your <whatever>)


He knows only all the truth about the Vimalakirti machines.




> and so can take the complement of the terrestrial intellect to get all
> of the things that the terrestrial intellect cannot know.   Right?


Not really. For example B"1+1=2"  is neither in the "terrestrial 
intellect", nor in the divine one, which will indeed contains 
~B"1+1=2". It is not a complement.



> For
> the Vimalakirti Machine (and also for me today, too, whether I am a
> machine or not) this includes both of the following.
>
> An asteroid will not hit the earth in 2102.
> An asteroid will hit the earth in 2102.


Anything including those two sentences would be inconsistent, I guess 
you are right and really menas that the divine intellect contains the 
two sentences preceding by "~B", that is

~B"An asteroid will not hit the earth in 2102"
~B"An asteroid will hit the earth in 2102"



>
> I am uncomfortable taking the complement of something when I don?t know
> what the Universal Set is.


Me too. Here there is no complement. I just assume I have some 
language, so that I have some propositions p, q, r, ... together with 
the usual connectives, + the connective B, where "Bp" means the entity 
asserts p. (Always false for the Vimalakirti machine given that she is 
eternally mute!).
That set is well defined, and latter, with the lobian machine we will 
have the choice between the language of first order arithmetic, or set 
theory, or second order arithmetic, etc. Lobianity is rather 
independent of the language chosen.



> This is akin to the Something vs. Nothing
> problem.  Everything and Nothing are equally mysterious.  Doesn?t
> taking the complement of a discourse by a machine provide no more
> information than the discourse itself?  It seems that you would have to
> have access to the truth (p) for the "divine intellect" to be any
> smarter than the "terrestrial intellect".


The divine intellect of the Vimalakirti machine is already more 
powerful than its terrestrial intellect.
The late is empty, and the divine is the set of all sentences having 
the shape ~B<sentences>.
The case of the lobian machine will be less trivial, although there 
will be similarities.



> This is what the "divine
> soul" has, Bp & p.


The intellect *and* the "divine" truth participate in the soul, yes.



>
>> I let you find the divine soul...
>
> For the Vimalakirti Machine, since "Bp" is empty, and thus "Bp & p" is
> empty, then by your "taking the complement" argument above it would
> seem to me that you would say that the divine soul "contains all
> possibilities" also.  The fact that p is anded with Bp to begin with
> shouldn?t make a difference in this case, since the result is empty.


OK. The terrestrial soul is empty too.



> The divine soul cannot have access to all truth p, but only the portion
> of truth covered by Bp, which is empty since Bp is empty.  The divine
> soul is the propositions which are true *about the entity*, not all
> true propositions.


OK. Precisely let B'p be Bp & p. Then the corresponding diamond is D'p, 
that is ~B'~p, which is then ~(B~p & ~p), which is ~B~p v ~p. This 
works for any p, So D'p is really Dp v p, and from this it follows by 
your reasoning that the divine Soul is not empty and equal to the 
divine intellect, for the Vimalakirti machine/entity (This will not be 
the case for the lobian machine where the divine and terrestrial soul 
are identical).



>
>> ...
>> I hope this helps you to distinguish a discourse made
>> BY a machine/entity from a discourse made ABOUT
>> the machine/entity. This is a key to understand the
>> difference between terrestrial and divine in the
>> mathematical interpretation of Plotinus.
>
> The difference seems to bank on taking the complement.  What is your
> Universal Set?  Is it only things that can be expressed by numbers?


The universal sets is determined by the use of some language. But, if 
the universal set is the set of all propositions, the terrestrial 
intellect and the divine one are not complement. If the universal set 
is the set of the true propositions, then, in the special case of the 
mute Vimalakirti machine the two intellect-hypostases are indeed 
complementary.



> By
> the way, I saw that in the Wall Street Journal today there is an
> article about a man who sold his soul on eBay for $504.  I guess his
> Universal Set is just numbers.  :)


If soul means some third person description encoding some possible 
personal subjective state, then $504 is very cheap, given the risk of 
being reconstituted in some unknown possible hell. The guy would be mad 
in that case, imo. I would suggest to wait solid quantum security 
protocols before doing *classical teleportation*, if not, it is at your 
risk and peril.


Bruno


http://iridia.ulb.ac.be/~marchal/


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