Re: Vimalakirti Machines
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: >> 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 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 ) 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. 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 machi
Re: Vimalakirti Machines
Bruno wrote: > So the divine intellect of the Vimalakirti Machine will contains all proposition of the form: > ~B: > 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 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 ) and so can take the complement of the terrestrial intellect to get all of the things that the terrestrial intellect cannot know. Right? 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. I am uncomfortable taking the complement of something when I don?t know what the Universal Set is. 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". This is what the "divine soul" has, Bp & p. > 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. 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. > ... > 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? 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. :) Tom --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Vimalakirti Machines
Solution: The terrestrial hypostases correspond to discourses of the Vimalakirty machine, where a discourse is defined by the set of propositions asserted by the machine. Now the machine says nothing, so that each terrestrial hypostases are empty. The divine hypostases are given by some "omniscient true discourse" on the machine (that is: on its intellect, on its souls, on its intelligible matter and on its sensible matters (see below)). Let us look at the "divine intellect". Well, the machine says nothing, so it is true that the machine didn't say that 1+1 = 2, all right? So ~B(1+1 = 2) is true. So ~B(1+1 = 2) belongs to the divine intellect of the Vimalakirti machine. OK, but the machine didn't say that 1+1 ≠ 2 either. So ~B(1+1 ≠ 2) is also true, and also belongs to the divine intellect. More generally, given that the machine does not utter any proposition, all proposition saying that the machine does not say will be true. So the divine intellect of the Vimalakirti Machine will contains all proposition of the form: ~B: 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 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? I let you find the divine soul, defined by the logic of Cp with Cp defined from the intellect (Bp) by Bp & p. It is the "true opinion" proposed by Theaetetus. BTW I was saying that Plotinus did use the Theaetetus' trick in its approach to the soul, and I have discovered recently that Emile Brehier confirms this in a footnote in its (first) translation of the V Enneads of Plotinus (1931). Note that the corresponding diamond for the soul can be defined by ~C~. Remark. In which world could the divine intellect lives? We have there that D is always true, and B is always false. In the alethic reading: everything is possible, and nothing is necessary. Is it cool? Do we have met such world? Those who remember our trip in the "Pappaioannou multiverse" does remember that from each world there, you can access to a dead end (cul-de-sac world), and by Kripke semantics, in a dead end everything is necessary but nothing is possible (brrr...). Now it looks like the divine intellect of a Vimalakirti machine/entity lives in an "anti-dead end world", where everything is possible and nothing is necessary. Is it cooler than a dead end? And could such a world exist in a Kripke Multiverse. Certainly not. In a Kripkean Multiverse Dp is true at world alpha if there is a world beta accessible from alpha, and such that p is true in beta. But in the "divine intellect" of a Vimalakirti machine even Df (f = false) is true, so that if such a world was Kripkean, f would be true in some world! Well, that is not the case in any Kripkean multiverse. Curiously enough Kripke himself will met such "non-normal" anti-cul-de-sac worlds in his study of the system S1 S2 S3 of C.I. Lewis, that is the first modern modal theories; and we will see (soon or later) that the intelligible and sensible matter, both terrestrial and divine, will introduce those "Vimalakirti weirdness". 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. Bon week-end, Bruno Le 01-mars-06, à 16:42, Bruno Marchal a écrit : 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
Re: Vimalakirti Machines
g people's background and my philosophy is that
all question can and should be asked).
Tomorrow I give the solution for the "divine" hypostases. Those
contains all the propositions which are true *ABOUT* the Vimalakirti
machine. I let you guess ...
Bruno
(*)GÖDEL K., 1933, Eine Interpretation des Intuitionistischen
Aussagenkalküls, Ergebnisse eines Mathematischen Kolloquiums, Vol 4,
pp. 39-40, also in FEFERMAN & Al. 1986.
> 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 <[EMAIL PROTECTED]>
> To: everything-list@googlegroups.com
> 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 & Dpagain 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/
>
>
>
>
>
>
http://iridia.ulb.ac.be/~marchal/
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Re: Vimalakirti Machines
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 <[EMAIL PROTECTED]>
To: everything-list@googlegroups.com
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 & Dpagain 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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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 & Dpagain 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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