RE: Platonism vs Realism WAS: ROADMAP (well, not yet really...

2006-08-22 Thread Stathis Papaioannou

Brent Meeker writes (quoting SP):

> > You might say that a computer program has a two-way interaction with its
> > environment while a recording does not, but it is easy to imagine a 
> > situation
> > where this can be perfectly reproduced by a recording. In run no. 1, you 
> > start up
> > the computer program and have a conversation with it. In run no. 2 you 
> > start up
> > the computer program and play it the recording of your voice from run no. 
> > 1. As
> > far as the program is aware, it receives exactly the same inputs and goes 
> > through
> > exactly the same responses on both runs, but one is a recording and the 
> > other is
> > not. Run no. 2 is exactly analogous to a film: a fixed input resulting in a 
> > fixed
> > output, even though if the input had been different the output would also 
> > have
> > been different. I don't see how you could say that the computer is 
> > conscious in
> > run no. 1 but not in run no. 2.
> 
> If the program is intelligent it'll be bored by 2. :-)  You seem to mixing 
> questions 
> of discovering whether a program is intelligent, with what it means for it to 
> be 
> intelligent.

No, it won't be bored because there is no way for it to know that it is going 
through the 
first or the second run. The point I was trying to make is that there is no 
real basis for 
distinguishing between a recording and a program, and hence no basis for saying 
that 
a program can be intelligent or conscious and a recording cannot. A corrolary 
to this is 
that there can be no real distinction between program and data, or computer and 
environment: they are just artificially segregated parts within a larger 
system. This 
means that in general it is not possible to say whether a physical system is or 
isn't 
implementing a computation, because the usual test of whether it handles 
counterfactuals 
will not necessarily work. This would be a trivial result *unless* we say that 
a computation 
can be conscious, in which case self-contained universes of conscious beings 
are hidden 
all around us. To avoid this conclusion you either have to drop 
computationalism or drop 
the idea that consciousness supervenes on physical activity.

Stathis Papaioannou
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Re: computationalism and supervenience

2006-08-22 Thread Russell Standish

On Tue, Aug 22, 2006 at 01:18:06PM -, 1Z wrote:
> 
> That is an interesting point. However, a computation would have to be
> associated
> with all related branches in order to bring all the counterfactuals (or
> rather
> conditionals) into a single computation.
> 
>  (IOW treating branches individually would fall back into the problems
> of the Movie approach)
> 
> If a computation is associated with all branches, consciousness will
> also be
> according to computationalism. That will bring on a White Rabbit
> problem with a vengeance.

Not really, as conscious experience is only associated with one
branch, but multiple branches are needed to have any conscious
experience at all.

The WR problem is solved by the robustness solution Alistair Malcolm
and I worked out years ago. We have good evolutionary reasons to
suppose robustness is an essential feature of consciousness.


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Re: computationalism and supervenience

2006-08-22 Thread Russell Standish

On Tue, Aug 22, 2006 at 11:50:07AM +0200, Bruno Marchal wrote:
> >
> > To be sure, this is not how I interpret Maudlin or the movie-graph
> > argument. I interpret it as NOT COMP or NOT PHYS SUP or NOT 
> > SINGLE_UNIVERSE.
> >
> > In a multiple universe (eg Everett style MWI), all counterfactuals are
> > instantiated as well, so physical supervenience (over all branches) is
> > compatible to COMP, and not equivalent to a recording.
> 
> 
> 
> 
> This is a very interesting remark, although I am not convinced. I have 
> also believed for a while that a material universe could be saved by 
> the way the quantum multiverse actualizes the counterfactuals.
> But if that were true, consciousness would not supervene on a 
> *classical* machine running deterministically an emulation of a 
> universal quantum turing itself running my brain, making comp false. 

I have put this to you in the past, but you have always responded that
the multiple universes always emerges out of the UD, leaving me most
confused as to whether I support the COMP position or not.


> Your move could belong to what I will perhaps eventually call "the 
> magical use of matter for explaining (away) consciousness". That move 
> is subtler with respect to the movie-graph, than with respect to the 
> seven first step of UDA.
> But I think you are correct, and it could be a pedagogical clever idea 
> to show first clearly that the movie graph entails (not-comp OR 
> not-phys-sup OR many-world), and then to show the perhaps less easy 
> point that the concrete primitively material many-world is a red 
> herring in this setting.

Physical supervenience is not equivalent to assuming a concrete
primitive material world. The latter is an additional assumption.

> We should come back on this in a "the 8th step" (movie graph) thread.
> 
> Bruno
> 
> 
> http://iridia.ulb.ac.be/~marchal/
> 
> 
> 
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Re: Platonism vs Realism WAS: ROADMAP (well, not yet really...

2006-08-22 Thread Brent Meeker

Bruno Marchal wrote:
> 
> Le 22-août-06, à 15:26, Stathis Papaioannou a écrit :
> 
> 
>>OK, I suppose you could say "I'm intelligent" but not "I + my 
>>environment are intelligent".
>>That still allows that an inputless program might contain intelligent 
>>beings, and you are left
>>with the problem of how to decide whether a physical system is 
>>implementing such a program
>>given that you can't talk to it.
> 
> 
> 
> People who believes that inputs (being either absolute-material or 
> relative-platonical) are needed for consciousness should not believe 
> that we can be conscious in a dream, given the evidence that the brain 
> is almost completely cut out from the environment during rem sleep. 

Almost is not completely.  In any case, I don't think consciousness is 
maintained 
indefinitely with no inputs.  I think a "brain-in-a-vat" would go into an 
endless 
loop without external stimulus.

>I 
> guess they have no problem with comatose people either.

Comatose people are generally referred to as "unconscious".

> Of course they cannot be even just troubled by the UD, which is a 
> program without inputs and without outputs.

As I understood the UD the program itself was not conscious, but rather that 
some 
parts are supposed to be, relative to a simulated environment.

> 
> Now, without digging in the movie-graph, I would still be interested if 
> someone accepting "standard comp" (Peter's expression) could explain 
> how a digital machine could correctly decide that her environment is 
> "real-physical". 

"Decide" is ambiguous.  She could very well form that hypothesis and find much 
confirming and no contrary evidence.  What are you asking for?  a proof from 
some 
axioms?  Which axioms?

>If such machine and reasoning exist, it will be done 
> in Platonia, and, worst, assuming comp, it will be done as correctly as 
> the real machine argument. This would lead to the fact that in 
> Platonia, there are (many) immaterial machines proving *correctly* that 
> they are immaterial. Contradiction.

Suppose a physical machine implements computation and proves relative to some 
axioms 
that physical machines don't exist.  Contradiction?

Brent Meeker


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Re: Are First Person prime?

2006-08-22 Thread Brent Meeker

Stathis Papaioannou wrote:
> Brent meeker writes (quoting SP):
> 
> 
>>> Every physical system contains if-then statements. If the grooves on the
>>> record were different, then the sound coming out of the speakers would also 
>>> be
>>> different.
>> 
>> That's not a statement contained in the physical system; it's a statement 
>> about
>> other similar physical systems that you consider possible. You could as well
>> say, (print "Hello world.") contains an if-then because if the characters in 
>> the
>> string were different the output would be different.
> 
> 
> I don't see how you could make the distinction well-defined. 

That's my point.  Counterfactuals are defined relative to some 
environment/data/input 
which we suppose to be possibly different.  It's not so much that it's not well 
defined, but that it's aribtrarily defined.  So I think lz's point about 
intelligence 
requiring counterfactuals is the same as saying intelligence is relative to 
some 
environment - a view with which I agree.  In the case of reproducing organisms 
the 
organism/environment distinction is clear.  In a simulation it's not.

Brent Meeker


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Re: ROADMAP (well, not yet really...

2006-08-22 Thread jamikes

- Original Message -
From: "Bruno Marchal" <[EMAIL PROTECTED]>
To: 
Sent: Tuesday, August 22, 2006 6:04 AM
Subject: Re: ROADMAP (well, not yet really...
(See below)

Teach! -
 I have a difference against your mathematical definition! (ha ha)

I thought if  '1' is a proper divisor of a number, then the number itself is
also.
Upon your post I looked up Wikipedia: "divisor" (nice page) and copied from
it:
*
"For example, 7 is a divisor of 42 because 42/7 = 6. We also say 42 is
divisible by 7 or 42 is a multiple of 7 or 7 divides 42 and we usually write
7 | 42. For example, the positive divisors of 42 are 1, 2, 3, 6, 7, 14, 21,
42.
*
I don't think 42 is so different from 6. If you abandon "the number itself",
you MUST abandon the "1" as well and in that case 6, indeed nothing is a
perfect number.
I really had that suspicion that 'numbers' are not so perfect!
(metaphorically).

(I have an idea why it is important to leave out "the number proper": if '1'
and the 'number' are included, there would be NO PRIME NUMBER at all. Would
be a shame! Sorry for 37 indeed.
 Of course the definition of 'prime number' excludes 'the number itself and
'1' - which, however, is not binding to the 'definition' of a divisor.)

Pupil John
==

Le 19-août-06, à 21:13, <[EMAIL PROTECTED]> (John M.) a écrit :

> BTW I have a problem with the "perfect" 6:
> ITS DIVISORS are 1,2,3,6, the sum of which is 12, not 6 and it looks
> that
> there is NO other perfect number in this sense either.

I have define a number to be perfect when it is equal to the sum of its
proper divisor. Six is not a proper divisor of six.

Bruno

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





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Re: The anti-roadmap - an alternative 'Theology'

2006-08-22 Thread David Nyman

Bruno Marchal wrote:

> Because comp makes it possible to postulate a simple theory where
> everything is communicable in a third person way. By making the first
> person primitive, you loose the ability to explain it (or to get some
> best possible third person explanation).

I'm still not sure I've communicated this 'primitivity' correctly, but
IMO comp (in 'pure' AR+CT+YD form) achieves what you claim at the cost
of coherence about 'existence' (see below).

(BTW, is it simply the case that 'existence' in the sense described
below is not really your concern? When you said that grandma was 'very
very close indeed', what else is needed for Achilles to get abreast of
the tortoise, if I may thus egregiously mix my metaphors?)

> So yes, there is just a tiny difference between us. I just doubt you
> can axiomatize your first person indexical seriousness in a simple
> third person way. If comp is correct, you can't, I think, and
> eventually this gives a protection of the first person against
> normative theories.

But this suggests to me that comp, in the 'instantiation-free' AR+CT+YD
sense, *cannot* be correct, precisely because it makes 'existential'
claims for the 'axiomatisation of indexical existence in a 3rd-person
way'. The key issue here is surely the distinction between 'existence'
and 'truth' as Peter specifies in his post to me. Indexical seriousness
is believing that whatever exists does so 'in the sense that I exist'.
(The 'infinity' of this sense must be resolved within the infinity or
otherwise of whatever exists.) 'Truth' is an abstraction from whatever
exists, and there is no justification for hypothesising it to 'exist'
in any other sense whatsoever. Truths are 'dispositions to believe' -
highly organised metaphors, no more, just as 'I' am. What they are
'about' is other features of what exists, and this situation exists
self-referentially solely 'in the sense that I exist'. AR, CT, etc. are
functional instantiations of such metaphors within what exists. They
are just one part of what exists modelling another.

My view is that 'participation in what exists' exhausts what we can
'modestly' claim as 'axiomatic'. We agree, I think, that it is our
unique source of knowledge of anything whatsoever. Consequently, it
seems to me perverse to reject its brutely 'given' status in any
schematisation of 'what exists'. I think you seek to overcome this by
giving 'truth' primacy and then deriving 'what exists' from this. I
know you believe that this is a 'modest' assumption, but IMO its
modesty cannot compensate for its incoherence.

I would challenge you to demonstrate any natural language specifiable
meaning of truth that is not a mapping between putative features of
'what exists in the sense that I exist'. Mathematical truth is a
special version of this, the 'putative features' here being
metaphorised as highly abstracted/ highly structured 'mathematical
objects'. Ditto logic. The fact that a logical or mathematical analysis
can show what 3rd-person (i.e. logically) specifiable entities 'would
believe' is epistemologically insightful but existentially neither here
nor there, because the logic is the *model*, not the *referent*. And
it's the referent that 'possesses' the belief, not the model.

 I agree with Peter (1Z) when
> he criticize you by saying that a person is something complex, and I
> agree with Dennett when he says that something complex must be
> explained by something easier.

The 'sense in which I exist' is not dependent on my complexity. It's
rather the *bare participation* of 'whatever-I-am' in what exists, not
the specifics of this (as Peter points out, his formulation exists
precisely to leave questions of detail open). Consequently, what I've
been calling 'indexical' or '1st person' existence (and obviously these
are bad terms because they lead to such misunderstanding) is *not*
complex, and avoids Dennett's criticism, and also Peter's (because the
same confusion had unfortunately arisen between us).

> Yes and that is normal. I reduce the mystery of "here and now" to the
> much simpler mysteries of the type:  "why am I in Washington and not in
> Moscow", or "why am I in Moscow and not in Washington" after a WM
> self-duplication experiment. Surely with comp you could figure out that
> those questions, although first person meaningful, are third person
> meaningless. NO?

Yes, but I don't think these conclusions are dependent on comp. They
are simply an aspect of point-of-view, or the localising effect of
'information horizons'. Identity is global, point-of-view is local. My
criticism was not this, but rather against the invocation of 'global
indexicality' as an artefact of 3rd person models. Metaphorically, 3rd
person is 'over there', indexical necessity 'over here'. You can't make
something appear 'over here', whatever you do 'over there', because
what's 'over there' is just your *story* about what's going on 'over
here'. So my point is that the story about 'indexicality' has to b

Re: Platonism vs Realism WAS: ROADMAP (well, not yet really...

2006-08-22 Thread 1Z


Bruno Marchal wrote:
> Le 22-août-06, à 15:26, Stathis Papaioannou a écrit :
>
> > OK, I suppose you could say "I'm intelligent" but not "I + my
> > environment are intelligent".
> > That still allows that an inputless program might contain intelligent
> > beings, and you are left
> > with the problem of how to decide whether a physical system is
> > implementing such a program
> > given that you can't talk to it.
>
>
> People who believes that inputs (being either absolute-material or
> relative-platonical) are needed for consciousness should not believe
> that we can be conscious in a dream, given the evidence that the brain
> is almost completely cut out from the environment during rem sleep.

The brain didn't evolve to dream.

> I
> guess they have no problem with comatose people either.
> Of course they cannot be even just troubled by the UD, which is a
> program without inputs and without outputs.
>
> Now, without digging in the movie-graph, I would still be interested if
> someone accepting "standard comp" (Peter's expression) could explain
> how a digital machine could correctly decide that her environment is
> "real-physical".

A *person* can decide their enviroment is *uncomputable*.

If classical physics had been true, the environment would
have been uncomputable.

> If such machine and reasoning exist, it will be done
> in Platonia, and, worst, assuming comp, it will be done as correctly as
> the real machine argument. This would lead to the fact that in
> Platonia, there are (many) immaterial machines proving *correctly* that
> they are immaterial. Contradiction.

If the mind is a computation, its errors are computations
as well. Platonia wil contain every mathematical possibility --
every combination of mind and environment.
Competent minds correctly judging their environments are computable,
competent minds correctly judging their environments are uncomputable,
incompetent minds incorrectly judging their environments are
uncomputable,  incompetent minds incorrectly judging their environments
are computable.


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Re: The anti-roadmap - an alternative 'Theology'

2006-08-22 Thread 1Z


Tom Caylor wrote:
> But then I think this search
> for invariance eventually brings us full circle to a self-referential
> paradox.  Math is whatever we observe (to be true / to exist)
> independent of the observer.

The fact that an observer can observe something doesn't make it
dependent
on the observer.


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Re: The anti-roadmap - an alternative 'Theology'

2006-08-22 Thread Tom Caylor

1Z wrote:
> Tom Caylor wrote:
>
> > I'd say a candidate for making AR false is the behavior of the prime
> > numbers, as has been discussed regarding your Riemann zeta function
> > TOE.  As I suggested on that thread, it could be that the behavior of
> > the Riemann zeta function follows a collapse that is dependent on the
> > observer.
>
>  That's the strangest thign I've read ina long
> time.
>

Truth is stranger than fiction.  Something strange may be just what is
needed to break out of going around in circles.

> BTW, do you find AR umabiguous? Is it about truth or existence, in your
> view ?

The way I see it, we define math in the first place as being "whatever
is independent of the observer" (i.e. invariance).  (This is why
observer-dependent math seems absurd.)  But then I think this search
for invariance eventually brings us full circle to a self-referential
paradox.  Math is whatever we observe (to be true / to exist)
independent of the observer.  Is AR about truth or existence?  Is "the
earth is flat" about truth or existence?  I believe only in a
"relative/local/apparent AR", but that really isn't AR.


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Re: The anti-roadmap - an alternative 'Theology'

2006-08-22 Thread 1Z


Bruno Marchal wrote:

> I can agree. No physicist posit matter in a fundamental theory.

All physical theories are theories of matter (mass/energy).


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Re: The anti-roadmap - an alternative 'Theology'

2006-08-22 Thread David Nyman

1Z wrote:

>  That's the strangest thign I've read ina long
> time.

!!! That's odd, because this's the stringest thagn I've road ina ling
tome.

David

> Tom Caylor wrote:
>
> > I'd say a candidate for making AR false is the behavior of the prime
> > numbers, as has been discussed regarding your Riemann zeta function
> > TOE.  As I suggested on that thread, it could be that the behavior of
> > the Riemann zeta function follows a collapse that is dependent on the
> > observer.
>
>  That's the strangest thign I've read ina long
> time.
>
> BTW, do you find AR umabiguous? Is it about truth or existence, in your
> view ?


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Re: Rép: ROADMAP (well, not yet really...

2006-08-22 Thread jamikes



Bruno:
 
I read you. I wanted to make a 'link' to 
"heaven". Feynman had a humorous mind (as most intelligent people).  He 
also referred to the medieval silliness of realizing angels (in any 
discussion).
 
Now back to numbers:
I always considered the "world" of (pure) math 
[numbers?] a separate one on its own. This is why I differentiated between 
"Math" (cap. introduced by Robert Rosen) from "math",  the applied 
quantizing in the (reductionist) sciences. 
The ("other?") world is what makes sense 
(sensible non-number meanings). 
 
I still cannot see a bridge 
between the (theoretical) churning of numbers (by whatever symbolics) and the 
ideational (other?) world, to assign sensible meaning (content?) as equivalent 
to number-monsters, or mental events in the 'sensible' world as referring to 
'number-manipulations'.  
(I call mental events also those that are 
reflected as 'events of material world')
The only 'comp' that does that is a - not 
binary, not decimal, but 26-ary device (in English, meaning letters as symbols) 
the churning of which DOES represent 'meaning' (called words in semantics). The 
rules of such math are translatable into 'sensible' meaning from their 26ary 
comp (not by illiterates). 
The binary (present embryonic-level comp) 
reaches such result by the system of transforming the 26ary into binary and 
applying additional binary rules into the 26ary meaning. 
This is not new, my 1928 Underwood typewriter 
did the trick (without binary). 
The program was in the typists' brain and 
fingers. 
 
So where is the "key" to translate 
number-monsters into "thought-monsters"? 
 
Regards
 
John
 
 

  - Original Message - 
  From: 
  Bruno Marchal 
  
  To: everything-list@googlegroups.com 
  
  Sent: Tuesday, August 22, 2006 6:10 
  AM
  Subject: Re: Rép: ROADMAP (well, not yet 
  really...
  Le 22-août-06, à 05:32, <[EMAIL PROTECTED]> a écrit 
:
  
- Original 
  Message -From: 
Bruno 
Marchal To: 
everything-list@googlegroups.com 
Sent: 
  Monday, August 21, 2006 6:39 AMSubject: 
  Re: Rép: ROADMAP (well, not yet 
  really...
  skipI already told you that I 
  interpretThere exists a prime number "in plato 
  heaven",by"There exist a prime number" is true 
  independently of me, you, the universe ...comp does not need a 
  magical platonic realm in your sense. I don't introduce it for the notion 
  of matter and it would be a fatal damage for comp if we were needing such 
  a magic stuff for numbers.Comp needs just arithmetical realism AR. It 
  is just the idea that the truth value of arithmetical proposition, 
  including existential propositions, does not depend on me or of any 
  cognition apparatus (indeed "cognition apparatus" are defined, with comp, 
  by relation between numbers, like in Artificial Intelligence, or in comp 
  cognitive science. BrunoThere exist infinite 
  prime numbers in Plato's heaven and 1000 of them can dance on the 
  point of a pin.I am sure you have something better thn 
  that!John Feynman 
  discovered quantum computation by asking himself how many bits can be handled 
  for a period of time on the point of a pin.Engineers would appreciate to 
  know how many primes numbers we could encode on a pin. This is not a silly 
  question, although out of topic in our fundamental quest, I 
  guess.Brunohttp://iridia.ulb.ac.be/~marchal/  
  

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Re: The anti-roadmap - an alternative 'Theology'

2006-08-22 Thread Bruno Marchal


Le 21-août-06, à 04:14, David Nyman a écrit :

>
> Bruno
>
> (BTW please delete any previous version of this posted in error.)
>
> I'm absolutely sincere in what I've said about approaching comp in 'as
> if' mode.



All right. I thought so. Let us try to see if and where we differ.





> But at the same time I've hoped from the beginning that we
> could make explicit the choices that motivate our different ontic
> starting assumptions. Are there perhaps irreconcilable issues of style
> or preference, or are there fundamental logical, philosophical, or even
> semantic errors entailed in one or other position? Well, let me
> continue in the effort by trying to clarify my position on some of your
> recent points.
>
>> So, either you put in AR something which is not there (like peter D
>> Jones who want me doing "Aristotle error" on the numbers (like if I 
>> was
>> reifying some concreteness about them), or you should have a powerful
>> argument against AR, but then you should elaborate.
>> To be honest I have not yet seen where you postulates comp wrong in
>> your long anti-roadmap post.
>> Recall that I take comp as YD + CT + AR (Yes Doctor + Church Thesis +
>> Arithmetical Realism).
>
> OK.  I've already agreed to accept AR in 'as if' mode. So that implies
> I'm staying on the comp road in the same 'as if' spirit to see where it
> leads. It's very interesting! Also I genuinely think that AR is not
> 'false' from any of the *logical* perspectives from which you
> defend it.


OK.




> My problem - outside 'as if' mode (and this goes back to the
> 'primacy' issue) - is with adopting *any* essentially 'non-indexical'
> (or in Colin's usage 'non-situated') postulate as 'ontic ground zero'.
> My view - and I'm still not clear whether you think it unjustified, or
> that you simply *prefer* to start elsewhere - is that we go wrong the
> moment we fail to treat reflexive indexical necessity with maximal -
> *extreme* - seriousness. My most basic claim is that to make *any*
> non-indexical assumption primary - even one as apparently 'modest' as
> AR - is to try to 'sneak past' this, and thereby to fail *the* crucial
> test of ontic realism.


Because comp makes it possible to postulate a simple theory where 
everything is communicable in a third person way. By making the first 
person primitive, you loose the ability to explain it (or to get some 
best possible third person explanation). I agree with Peter (1Z) when 
he criticize you by saying that a person is something complex, and I 
agree with Dennett when he says that something complex must be 
explained by something easier. Now comp shows the ultimate fundamental 
role of the first person, and that is why I appreciate your seriousness 
here, and in principle you still could try to formalize it in a third 
person way, but your last attempt led to some explosion of more 
complicated concepts.
The same remark works when you are making "indexical" primitive, 
although "indexical" can be translated in purely third person way (that 
is exactly what Post, Turing, Godel ... Kleene have proved). The case 
of platonist or classical machine gives rise to the indexical but 
purely arithmetical "provability predicate" B, and this one is 
quasi-primitive in the sense that all others notions of persons (the 
hypostases) are variant of B.
So yes, there is just a tiny difference between us. I just doubt you 
can axiomatize your first person indexical seriousness in a simple 
third person way. If comp is correct, you can't, I think, and 
eventually this gives a protection of the first person against 
normative theories.
To sum up, the notion of first person is too complex to be be 
primitive, especially when you see that comp explains why the first 
person is correct when thinking it is primitive (but false by trying to 
put this in a third person discourse.
And the, unlike Peter, I consider that the notion of "matter" is also 
complex, and assuming it also thhrows away any hope foir explanation, 
and then comp forbid that move anyway by the UDA.


>
> We could call this position maximal personal, or indexical,
> seriousness, but what's in a name? It frustrates me almost beyond
> endurance that this isn't simply 'obvious' (though error, especially
> one's own, is subtle).

As a first person discourse, comp tells that you are correct. As a 
third person discourse you are on the verge of inconsistency.


> But it seems as though we're somehow 'tricked'
> out of seeing it because all 'personal' interaction (including that
> with the 'self') is relational, and 3rd-person is the characteristic
> mode of relational interaction. So all natural language just assumes
> it.
>
> Consequently when you say:
>
>> What you say is exactly what the lobian *first person* will feel.  I 
>> hope you will
>> see this eventually.
>
> I think I do 'see' it. I understand that the lobian first person
> *emerging* from your non-indexical AR postulate could indeed be
> decribed as 'possessing' such 

Re: Platonism vs Realism WAS: ROADMAP (well, not yet really...

2006-08-22 Thread Bruno Marchal


Le 22-août-06, à 15:26, Stathis Papaioannou a écrit :

> OK, I suppose you could say "I'm intelligent" but not "I + my 
> environment are intelligent".
> That still allows that an inputless program might contain intelligent 
> beings, and you are left
> with the problem of how to decide whether a physical system is 
> implementing such a program
> given that you can't talk to it.


People who believes that inputs (being either absolute-material or 
relative-platonical) are needed for consciousness should not believe 
that we can be conscious in a dream, given the evidence that the brain 
is almost completely cut out from the environment during rem sleep. I 
guess they have no problem with comatose people either.
Of course they cannot be even just troubled by the UD, which is a 
program without inputs and without outputs.

Now, without digging in the movie-graph, I would still be interested if 
someone accepting "standard comp" (Peter's expression) could explain 
how a digital machine could correctly decide that her environment is 
"real-physical". If such machine and reasoning exist, it will be done 
in Platonia, and, worst, assuming comp, it will be done as correctly as 
the real machine argument. This would lead to the fact that in 
Platonia, there are (many) immaterial machines proving *correctly* that 
they are immaterial. Contradiction.

Remark: the key idea which is used here is that not only programs 
belong to Platonia, but their relative computations also. It is 
important to keep the distinction between (static) programs and their 
"dynamical" computations. I will write Fi, as the function computed by 
the ith programs in some universal enumeration of partial recursive 
functions (like an infinite list of fortran programs, say). I will 
write Fi(x) for the value of that function with input x, if that value 
exists. I will write sFi(x) the "s-trace" of that program (with input 
x), where the trace stops after the sth steps in the relative run of 
Fi(x). The trace is computer scientist name for a description of the 
computational steps---it can be shown that such computational steps can 
always be defined for the Fi and Wi.
I will define a (3-PERSON) computation of Fi(x) as being the sequence 
1Fi(x), 2Fi(x), 3Fi(x), etc ...
This is well defined relatively to some universal number or code. In 
this sense, computations belong to Platonia. The reason why I feel 
myself here and now can then be reduced to the relative 1-person comp 
indeterminacy a-la Washington/Moscow. Note that the adjective 
"relative" is capital here. Without it, the indexical conception of 
time (and space) would not work.

Bruno

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


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Re: Are First Person prime?

2006-08-22 Thread Bruno Marchal


Le 22-août-06, à 14:36, 1Z a écrit :

>
>
> Quentin Anciaux wrote:
>> Hi,
>>
>> concerning process and programs, all boils down to the timeless/time 
>> argument.
>>
>> I'm astonished that you accept time as is, I mean if time there is it 
>> has been
>> created at the same time as our universe in the bigbang. Time begin 
>> when the
>> universe begin, so you accept that time can occur in a timeless system
>> because if you don't then it means time existed before it was 
>> created... that
>> make me write nonsensical sentences ;)
>
> We don't know what the BB emerged out of. It might have had
> more than enough ontological resources to generate time. It did not
> have time as we know it , but for all we know
> time as we know it is a mere privation or degenerate case of
> some funky hyper-time.
>
> But we do know what the resources of Platonia are.



What do you mean by "resources of Platonia" ?





>
> It is a very wide, but very flat country; it contains every possible
> static eternal
> structure, but only static, eternal structures.



No physical block universe then. But that confirms what Quentin Anciaux 
said, it all boils down to the question of a primitive time or not.
Obviously, comp makes time (and space and all physicalities) form of  
"stable illusion" from inside. (But I dislike the word "illusion"). 
Many physicist, like Sanders for example, and many philosophers defend 
the indexical version of time (which is also defended by Deutsch).

Peter, be patient for a comment to your long post of today, I am trying 
to finish a comment on another long post by David.



Bruno


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


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RE: Platonism vs Realism WAS: ROADMAP (well, not yet really...

2006-08-22 Thread Stathis Papaioannou

Brent meeker writes (quoting Peter Jones, Quentin Anciaux and SP):

> >>Hi,
> >>
> >>Le Dimanche 20 Août 2006 05:17, Stathis Papaioannou a écrit :
> >>
> >>>Peter Jones writes (quoting SP):
> >>>
> >What about an inputless computer program, running deterministically
> >like a recording. Would that count as a program at all,
> 
> It would be a trivial case.
> >>>
> >>>Trivial does not mean false.
> >>
> >>It seems to me that the set of inputless programs contains the set of 
> >>programs 
> >>which have inputs. Because a program which have inputs could be written as 
> >>the following inputless program :
> >>
> >>|HARDCODED INPUT||CODE|
> >>
> >>The resulting program is input less but the "substructure" denominated CODE 
> >>here is not inputless, it takes the hardcoded input.
> >>
> >>So in any case I don't see why inputless program should be "trivial case".
> >>
> >>Regards,
> >>Quentin
> 
> I thought the question was not about computation, but whether a program was 
> intelligent or conscious.  I think that intelligence means being able to 
> respond to a 
> variety of differenet inputs.  So above |CODE| might be intelligent but not 
> the 
> overall inputless program.

OK, I suppose you could say "I'm intelligent" but not "I + my environment are 
intelligent". 
That still allows that an inputless program might contain intelligent beings, 
and you are left 
with the problem of how to decide whether a physical system is implementing 
such a program 
given that you can't talk to it.

Stathis Papaioannou
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Re: computationalism and supervenience

2006-08-22 Thread 1Z


Russell Standish wrote:
> On Tue, Aug 22, 2006 at 01:32:14PM +1000, Stathis Papaioannou wrote:
> >
> > Bruno Marchal writes:
> >
> > > > The other sticking point is, given computationalism
> > > > is right, what does it take to implement a computation? There have
> > > > been arguments
> > > > that a computation is implemented by any physical system (Putnam,
> > > > Searle, Moravec)
> > > > and by no physical system (Maudlin, Bruno Marchal).
> > >
> > >
> > >
> > > OK. To be sure Maudlin would only partially agree. Maudlin shows (like
> > > me) that we have:
> > >
> > > NOT COMP or NOT PHYSICAL SUPERVENIENCE
> >
> > That sentence summarises the problem pretty well. We have to agree that 
> > there is this dichotomy before proceeding further, and I don't think most 
> > computationalists do.
> >
>
> To be sure, this is not how I interpret Maudlin or the movie-graph
> argument. I interpret it as NOT COMP or NOT PHYS SUP or NOT SINGLE_UNIVERSE.
>
> In a multiple universe (eg Everett style MWI), all counterfactuals are
> instantiated as well, so physical supervenience (over all branches) is
> compatible to COMP, and not equivalent to a recording.

That is an interesting point. However, a computation would have to be
associated
with all related branches in order to bring all the counterfactuals (or
rather
conditionals) into a single computation.

 (IOW treating branches individually would fall back into the problems
of the Movie approach)

If a computation is associated with all branches, consciousness will
also be
according to computationalism. That will bring on a White Rabbit
problem with a vengeance.

However, it is not that computation cannot be associated with
counterfactuals
in single-universe theories -- in the form of unrealised possibilities,
dispositions and so on. If consciousness supervenes on
computation , then it supervenes on such counterfactuals too;
this amounts to the response to Maudlin's argument in
wich the physicalist abandons the claim that consciousness supervenes
on activity.

Of ocurse, unactualised possibilities in a sinlge universe are never
going to lead to
any White Rabbit!.

> Cheers
>
> --
> *PS: A number of people ask me about the attachment to my email, which
> is of type "application/pgp-signature". Don't worry, it is not a
> virus. It is an electronic signature, that may be used to verify this
> email came from me if you have PGP or GPG installed. Otherwise, you
> may safely ignore this attachment.
>
> 
> A/Prof Russell Standish  Phone 8308 3119 (mobile)
> Mathematics  0425 253119 (")
> UNSW SYDNEY 2052   [EMAIL PROTECTED]
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> 


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RE: Are First Person prime?

2006-08-22 Thread Stathis Papaioannou

Brent meeker writes (quoting SP):

> > Every physical system contains if-then statements. If the grooves on the 
> > record were different, 
> > then the sound coming out of the speakers would also be different.
> 
> That's not a statement contained in the physical system; it's a statement 
> about other 
>similar physical systems that you consider possible. You could as well 
> say, (print 
> "Hello world.") contains an if-then because if the characters in the string 
> were 
> different the output would be different.

I don't see how you could make the distinction well-defined. Consider the 
following two programs:

(a)
input: x
if x=1 print "hello"
if x=0 print "goodbye"
data: 1

and

(b)
print "hello"

As written, program (a) will print "hello" just as consistently as program (b). 
It looks like program (a) has a conditional in that if the 4th line were "data: 
0" it would print "goodbye". However, program (b) would also print "goodbye" if 
that string were substituted for "hello". Both programs do the same thing, and 
both would do something else if the programmer intervened and changed them. In 
(a) the code is separated into "program" and "data" but as you pointed out 
recently there is no real difference between these. Subroutines within a larger 
program could be intelligent entities interacting with a virtual environment 
with no input from outside the program in the same way as intelligent entities 
within the real universe interact with the environment with no input from 
outside the universe.

It's worth standing back at this point and looking at what a computer + program 
+ data really is: a collection of plastic, metal, and semiconductors assembled 
in a specified way which has no choice but to follow the laws of physics. The 
if-then statements amount to a particular physical configuration such that 
stimulus x will make the computer behave one way while stimulus y will make it 
behave in a different way. This is not fundamentally different to saying that, 
for example, a car is configured so that it will turn left or right depending 
on which way the steering wheel is turned. In both situations, dumb matter 
blindly follows the laws of physics. The difference is in the details, 
complexity and intended purpose of each device; it is not that the computer 
interacts with its environment and handles counterfactuals while the car does 
not.

Stathis Papaioannou
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Re: Are First Person prime?

2006-08-22 Thread 1Z


Quentin Anciaux wrote:
> Hi,
>
> concerning process and programs, all boils down to the timeless/time argument.
>
> I'm astonished that you accept time as is, I mean if time there is it has been
> created at the same time as our universe in the bigbang. Time begin when the
> universe begin, so you accept that time can occur in a timeless system
> because if you don't then it means time existed before it was created... that
> make me write nonsensical sentences ;)

We don't know what the BB emerged out of. It might have had
more than enough ontological resources to generate time. It did not
have time as we know it , but for all we know
time as we know it is a mere privation or degenerate case of
some funky hyper-time.

But we do know what the resources of Platonia are.

It is a very wide, but very flat country; it contains every possible
static eternal
structure, but only static, eternal structures.


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Re: Are First Person prime?

2006-08-22 Thread Quentin Anciaux

Hi,

concerning process and programs, all boils down to the timeless/time argument.

I'm astonished that you accept time as is, I mean if time there is it has been 
created at the same time as our universe in the bigbang. Time begin when the 
universe begin, so you accept that time can occur in a timeless system 
because if you don't then it means time existed before it was created... that 
make me write nonsensical sentences ;)

Regards,
Quentin


Le mardi 22 août 2006 13:45, 1Z a écrit :
> Bruno Marchal wrote:
> > Le 21-août-06, à 16:01, 1Z a écrit :
> > > Exactly. And if non-phsyical systems (Plato' Heaven) don't
> > > implement counterfactuals, then they can't run programmes,
> > > and if Plato's heaven can't run programmes, it can't be running us as
> > > programmes.
> >
> > I would say that only non-physical system implement counterfactuals.
>
> A counterfactual is somethingthat could have happened, but didn't.
> A static, immaterial systems can only handle counterfactuals by
> turning them into factuals -- everything that can happen does
> happen. It can fully capture the *conditional* structure of a
> programme,
> (unlike a "recording") at the expense of not being a process.
>
> A programme is not the same thing as a process.
>
> Computationalism refers to real, physical processes running on material
> computers. Proponents of the argument need to show that the causality
> and dynamism are inessential (that there is no relevant difference
> between process and programme) before you can have consciousness
> implemented Platonically.
>
> To exist Platonically is to exist eternally and necessarily. There is
> no time or changein Plato's heave. Therefore, to "gain entry", a
> computational mind will have to be translated from a running process
> into something static and acausal.
>
> One route is to replace the process with a programme. After all, the
> programme does specify all the possible counterfactual behaviour, and
> it is basically a string of 1's and 0's, and therefore a suitabale
> occupant of Plato's heaven. But a specification of counterfactual
> behaviour is not actual counterfactual behaviour. The information is
> the same, but they are not the same thing.
>
> No-one would believe that a brain-scan, however detailed, is conscious,
> so not computationalist, however ardent, is required to believe that a
> progamme on a disk, gathering dust on a shelf, is sentient, however
> good a piece of AI code it may be!
>
> Another route is "record" the actual behaviour, under some
> circumstances of a process, into a stream of data (ultimately, a string
> of numbers, and therefore soemthing already in Plato's heaven). This
> route loses the conditonal structure, the counterfactuals that are
> vital to computer programmes and therefore to computationalism.
>
> Computer programmes contain conditional (if-then) statements. A given
> run of the programme will in general not explore every branch. yet the
> unexplored branches are part of the programme. A branch of an if-then
> statement that is not executed on a particular run of a programme will
> constitute a counterfactual, a situation that could have happened but
> didn't. Without counterfactuals you cannot tell which programme
> (algorithm) a process is implementing because two algorithms could have
> the same execution path but different unexecuted branches.
>
> Since a "recording" is not computation as such, the computationalist
> need not attribute mentality to it -- it need not have a mind of its
> own, any more than the characters in a movie.
>
> (Another way of looking at this is via the Turing Test; a mere
> recording would never pass a TT since it has no
> condiitonal/counterfactual behaviour and therfore cannot answer
> unexpected questions).
>
> > That counterfactuality is the essence of (immaterial) comp. Although
> > here Russell has a point: the quantum multiverse seems to handle
> > counterfactual.
>
> Multiverse theories seek to turn the 3rd-person "X could have happened
> but didn't"
> into the 1st-person "X could have been observed by me, but wasn't".
>
> >  Now if comp is correct, I cannot distinguish a
> > "genuine" quantum multiverse from any of its emulation in Platonia,
>
> A quantum multiverse is sitll only a tiny corner of Platonia.
>
> Physical many-world theories have resources to keep counterfactuals
> unobserved that immaterial MW-theories lack (including the simple
> of one that many mathematical possibilities do not
> exist physically).
>
> For instance, even if their are two informationally identical me's
> in different branches of a phsycial universe, it is not
> inevitable that any sharing or corss-over of
> consicousness would occur, because in  a phsyical
> universe, cosnciousness would have something other
> than informational structures to supervene on.
>
> Thus me might
> well be able to tell that we are in a quantum multiverse rather than
> Platonia, on the basis that we just do not observe enough weirdness.
>

Re: Are First Person prime?

2006-08-22 Thread 1Z


Bruno Marchal wrote:
> Le 21-août-06, à 16:01, 1Z a écrit :
>
> > Exactly. And if non-phsyical systems (Plato' Heaven) don't
> > implement counterfactuals, then they can't run programmes,
> > and if Plato's heaven can't run programmes, it can't be running us as
> > programmes.
>
> I would say that only non-physical system implement counterfactuals.

A counterfactual is somethingthat could have happened, but didn't.
A static, immaterial systems can only handle counterfactuals by
turning them into factuals -- everything that can happen does
happen. It can fully capture the *conditional* structure of a
programme,
(unlike a "recording") at the expense of not being a process.

A programme is not the same thing as a process.

Computationalism refers to real, physical processes running on material
computers. Proponents of the argument need to show that the causality
and dynamism are inessential (that there is no relevant difference
between process and programme) before you can have consciousness
implemented Platonically.

To exist Platonically is to exist eternally and necessarily. There is
no time or changein Plato's heave. Therefore, to "gain entry", a
computational mind will have to be translated from a running process
into something static and acausal.

One route is to replace the process with a programme. After all, the
programme does specify all the possible counterfactual behaviour, and
it is basically a string of 1's and 0's, and therefore a suitabale
occupant of Plato's heaven. But a specification of counterfactual
behaviour is not actual counterfactual behaviour. The information is
the same, but they are not the same thing.

No-one would believe that a brain-scan, however detailed, is conscious,
so not computationalist, however ardent, is required to believe that a
progamme on a disk, gathering dust on a shelf, is sentient, however
good a piece of AI code it may be!

Another route is "record" the actual behaviour, under some
circumstances of a process, into a stream of data (ultimately, a string
of numbers, and therefore soemthing already in Plato's heaven). This
route loses the conditonal structure, the counterfactuals that are
vital to computer programmes and therefore to computationalism.

Computer programmes contain conditional (if-then) statements. A given
run of the programme will in general not explore every branch. yet the
unexplored branches are part of the programme. A branch of an if-then
statement that is not executed on a particular run of a programme will
constitute a counterfactual, a situation that could have happened but
didn't. Without counterfactuals you cannot tell which programme
(algorithm) a process is implementing because two algorithms could have
the same execution path but different unexecuted branches.

Since a "recording" is not computation as such, the computationalist
need not attribute mentality to it -- it need not have a mind of its
own, any more than the characters in a movie.

(Another way of looking at this is via the Turing Test; a mere
recording would never pass a TT since it has no
condiitonal/counterfactual behaviour and therfore cannot answer
unexpected questions).



> That counterfactuality is the essence of (immaterial) comp. Although
> here Russell has a point: the quantum multiverse seems to handle
> counterfactual.

Multiverse theories seek to turn the 3rd-person "X could have happened
but didn't"
into the 1st-person "X could have been observed by me, but wasn't".

>  Now if comp is correct, I cannot distinguish a
> "genuine" quantum multiverse from any of its emulation in Platonia,

A quantum multiverse is sitll only a tiny corner of Platonia.

Physical many-world theories have resources to keep counterfactuals
unobserved that immaterial MW-theories lack (including the simple
of one that many mathematical possibilities do not
exist physically).

For instance, even if their are two informationally identical me's
in different branches of a phsycial universe, it is not
inevitable that any sharing or corss-over of
consicousness would occur, because in  a phsyical
universe, cosnciousness would have something other
than informational structures to supervene on.

Thus me might
well be able to tell that we are in a quantum multiverse rather than
Platonia, on the basis that we just do not observe enough weirdness.

Too broad: If I am just a mathematical structure, I should have a much
wider range of experience than I do. There is a mathemtical structure
corresponding to myself with all my experiences up to time T. There is
a vast array of mathematical structures corresponding to other versions
of me with having a huge range of experiences -- ordinary ones, like
continuing to type, extraordinary ones like seeing my computer sudenly
turn into bowl of petunias. All these versions of me share the memories
of the "me" who is writing this, so they all identify themselves as me.
Remember, that for mathematical monism it is only necessary that a
possible experience has a

Re: The anti-roadmap - an alternative 'Theology'

2006-08-22 Thread 1Z


Tom Caylor wrote:

> I'd say a candidate for making AR false is the behavior of the prime
> numbers, as has been discussed regarding your Riemann zeta function
> TOE.  As I suggested on that thread, it could be that the behavior of
> the Riemann zeta function follows a collapse that is dependent on the
> observer.

 That's the strangest thign I've read ina long
time.

BTW, do you find AR umabiguous? Is it about truth or existence, in your
view ?


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Re: Rép: ROADMAP (well, not yet really...

2006-08-22 Thread Bruno Marchal

Le 22-août-06, à 05:32, <[EMAIL PROTECTED]> a écrit :

 
- Original Message -
From: Bruno Marchal 
To: everything-list@googlegroups.com 
Sent: Monday, August 21, 2006 6:39 AM
Subject: Re: Rép: ROADMAP (well, not yet really...


skip

I already told you that I interpret

There exists a prime number "in plato heaven",

by


"There exist a prime number" is true independently of me, you, the universe ...

comp does not need a magical platonic realm in your sense. I don't introduce it for the notion of matter and it would be a fatal damage for comp if we were needing such a magic stuff for numbers.
Comp needs just arithmetical realism AR. It is just the idea that the truth value of arithmetical proposition, including existential propositions, does not depend on me or of any cognition apparatus (indeed "cognition apparatus" are defined, with comp, by relation between numbers, like in Artificial Intelligence, or in comp cognitive science. 

Bruno


There exist infinite prime numbers in Plato's heaven and 1000 of them can dance on the point of a pin.
I am sure you have something better thn that!
John 


Feynman discovered quantum computation by asking himself how many bits can be handled for a period of time on the point of a pin.
Engineers would appreciate to know how many primes numbers we could encode on a pin. This is not a silly question, although out of topic in our fundamental quest, I guess.

Bruno



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


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Re: ROADMAP (well, not yet really...

2006-08-22 Thread Bruno Marchal


Le 19-août-06, à 21:13, <[EMAIL PROTECTED]> (John M.) a écrit :

> BTW I have a problem with the "perfect" 6:
> ITS DIVISORS are 1,2,3,6, the sum of which is 12, not 6 and it looks 
> that
> there is NO other perfect number in this sense either.

I have define a number to be perfect when it is equal to the sum of its 
proper divisor. Six is not a proper divisor of six.

Bruno

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


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Re: Are First Person prime?

2006-08-22 Thread Bruno Marchal


Le 21-août-06, à 16:01, 1Z a écrit :

> Exactly. And if non-phsyical systems (Plato' Heaven) don't
> implement counterfactuals, then they can't run programmes,
> and if Plato's heaven can't run programmes, it can't be running us as
> programmes.

I would say that only non-physical system implement counterfactuals. 
That counterfactuality is the essence of (immaterial) comp. Although 
here Russell has a point: the quantum multiverse seems to handle 
counterfactual. Now if comp is correct, I cannot distinguish a 
"genuine" quantum multiverse from any of its emulation in Platonia, and 
the physical laws must take that into account.

Bruno


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


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Re: Are First Person prime?

2006-08-22 Thread Bruno Marchal


Le 19-août-06, à 16:35, 1Z a écrit :

> No, I am suggesting that 0-width slices don't contain
> enough information to predict future states in physics.

What about a quantum state?

Bruno

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


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Re: computationalism and supervenience

2006-08-22 Thread Bruno Marchal


Le 21-août-06, à 20:28, Russell Standish a écrit :

>
> On Tue, Aug 22, 2006 at 01:32:14PM +1000, Stathis Papaioannou wrote:
>>
>> Bruno Marchal writes:
>>
 The other sticking point is, given computationalism
 is right, what does it take to implement a computation? There have
 been arguments
 that a computation is implemented by any physical system (Putnam,
 Searle, Moravec)
 and by no physical system (Maudlin, Bruno Marchal).
>>>
>>>
>>>
>>> OK. To be sure Maudlin would only partially agree. Maudlin shows 
>>> (like
>>> me) that we have:
>>>
>>> NOT COMP or NOT PHYSICAL SUPERVENIENCE
>>
>> That sentence summarises the problem pretty well. We have to agree 
>> that there is this dichotomy before proceeding further, and I don't 
>> think most computationalists do.
>>
>
> To be sure, this is not how I interpret Maudlin or the movie-graph
> argument. I interpret it as NOT COMP or NOT PHYS SUP or NOT 
> SINGLE_UNIVERSE.
>
> In a multiple universe (eg Everett style MWI), all counterfactuals are
> instantiated as well, so physical supervenience (over all branches) is
> compatible to COMP, and not equivalent to a recording.




This is a very interesting remark, although I am not convinced. I have 
also believed for a while that a material universe could be saved by 
the way the quantum multiverse actualizes the counterfactuals.
But if that were true, consciousness would not supervene on a 
*classical* machine running deterministically an emulation of a 
universal quantum turing itself running my brain, making comp false. 
Your move could belong to what I will perhaps eventually call "the 
magical use of matter for explaining (away) consciousness". That move 
is subtler with respect to the movie-graph, than with respect to the 
seven first step of UDA.
But I think you are correct, and it could be a pedagogical clever idea 
to show first clearly that the movie graph entails (not-comp OR 
not-phys-sup OR many-world), and then to show the perhaps less easy 
point that the concrete primitively material many-world is a red 
herring in this setting.
We should come back on this in a "the 8th step" (movie graph) thread.

Bruno


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


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RE: computationalism and supervenience

2006-08-22 Thread Stathis Papaioannou

Tom Caylor writes:

> As I remember it, my interpretation/expansion of the "Yes Doctor"
> assumption is that 1) there is a (finite of course) level of (digital)
> substitution (called the "correct level of substitution") that is
> sufficient to represent "all that I am", and "all that I could be if I
> hadn't undergone a substitution", and 2) we (including the doctor)
> cannot know what the correct level of substitution is, therefore we
> have to gamble that the doctor will get it right when we say "Yes
> Doctor".
> 
> Suppose that the level of substitution actually *performed* by the
> Doctor is S_p.  Denote the *correct* level of substitution S_c.  S_p
> can be expressed by a finite number, since the substitution itself can
> be expressed by a finite number (whatever is written on the tape/CD or
> other storage/transmitting device).  We know what S_p is and it is a
> *fixed* finite number. But since S_c (*correct* level) is totally
> unknowable, all we "know" about it is our assumption that it is finite.
>  The next *obvious* step in the logical process is that the probability
> that S_p >= S_c is infinitesimal.  I.e. the probability that the doctor
> got it right is zilch.  This is because most numbers are bigger than
> any fixed finite number S_p.
> 
> So it seems that our step of faith in saying Yes Doctor in not well
> founded.  It's definitely a bad bet.
> 
> It seems that we need a stronger statement than S_c is finite.

Surely an upper limit can be ascribed to S_c, probably way lower than the 
Beckenstein bound for a brain-sized object.

Stathis Papaioannou
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