Re: Neurobiologists Find that Weak Electrical Fields in the Brain Help Neurons Fire Together

2011-02-08 Thread Andrew Soltau

On 06/02/11 22:06, Russell Standish wrote:

Neurobiologists Find that Weak Electrical Fields in the Brain Help
Neurons Fire Together

http://media.caltech.edu/press_releases/13401

Reminds me of what Colin says he is doing...

Cheers

Fascinating. At every turn we seem to find additional complexity and 
holistic phenomena in the processes of life giving rise to biological 
computation. It reminds me of Bonnie Bassler's quorum function which 
enables bacteria in the body to act in concert as a single organism.


http://www.ted.com/index.php/talks/bonnie_bassler_on_how_bacteria_communicate.html

Andrew

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Re: The relative point of view

2011-02-08 Thread Bruno Marchal


On 07 Feb 2011, at 20:52, Andrew Soltau wrote:





How do you define the relative point of view?


Do you know Gödel's provability predicate? The points of view are  
defined by intensional variants of the current provability  
predicate of the machine with or without some oracle. There are 8  
basic points of view p (truth), Bp (provability/believability), Bp  
 p (knowability), Bp  Dp (observability), Bp  Dp  p  
(sensibility/feelability). Three of them inherits the G/G*  
splitting, making a total of 8. It is really 4 + 4*infinity,  
because the 'material points of view' (with Dp) admits themselves  
graded variants.



I know *about* Gödel's provability predicate!



Good.





(Is the 'intensional' referred to here the 'attach' you used in  
another email?)


Not really, although it is related.

Intensional refers to the fact that if you define a provable(x) by  
beweisbar(x) and x', where x' denote the proposition which has x as  
Gôdel number, you define a probability predicate, which is not  
definable by the machine, or in arithmetic, yet proves exactly the  
same proposition of arithmetic than the one provable. Provable(x) and  
beweisbar(x) are intensional variant of provability. They are  
extensionnally equivalent, but intensionnally different, a bit like  
different algorithm can have the same behavior.
More simple beweisbar(x)  ~beweisbar(~x)  is an intensional variant  
of beweisbar(x).


Intensional variant of bewesibar(x) have been introduced by Rosser in  
his elimination of Gödel's assumption of omega-completeness  in the  
proof of incompleteness of formal systems.







I am still no clearer about how you define the machine, with or  
without some oracle, and what defines the relative point of view.


Oracle have been introduced by Turing for the study of the degree of  
unsolvability. It is a package of usually infinite information,  
typically not computable. The halting oracle provides the halting  
information, that no computer can generate. The goal consisted in  
showing that some problem remains non solvable, and that some function  
remains uncomputable, even when powerful oracle are added, and this  
has been used to study the degrees of unsolvability of arithmetical  
and mathematical problems.


The UD generate all the oracles, like it dovetails on all the reals  
(trivial exercise; yet people are often wrong on this because they  
confuse the impossibility of enumerating the reals, with the  
impossibility of generating them). Think about the iterated self- 
duplication experiment.






Given that you are defining 8 basic points of view in the abstract,  
applied to  intensional variants of the current provability  
predicate of the machine with or without some oracle, it sounds a  
bit, well, abstract. Could you be a bit more specific?


I try to be more specific in sane04. May be we should start from that.  
Or search hypostasis or hypostases in the archive, or guardian  
angel, etc.

Read the book by Smullyan, and Boolos 1979 (simpler than Boolos 1993).

Read perhaps the Theaetetus by Plato.

In short you can say that I model belief or opinion by formal  
probability (Bp).  I define then knowledge, following Theaetetus by  
the true opinion (Bp  p), observation by the consistent opinion (Bp   
Dp), and sensibility by the true consistent opinion (Bp  Dp  p).  
Incompleteness motivates the initial model, even if it leads to a  
restriction on the ideally correct machine. The whole thing provides  
an arithmetical interpretation of Plotinus theory of the one, the  
intellect and the soul + his double (intelligible and sensible) matter  
theory. The arithmetical matter theory has been compared to the  
current inferred theory of matter, and it looks, up to now, that  
Nature is correct :)

(correct with respect to comp and its neoplatonist rendering, for sure).

Bruno

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



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Re: The propositions of comp?

2011-02-08 Thread Bruno Marchal


On 07 Feb 2011, at 21:22, Andrew Soltau wrote:


On 07/02/11 19:42, Bruno Marchal wrote:
Many would agree that mind might be related to the execution of an  
algorithm on some physical machine, as I like to explore that idea,  
but this is at the starting point of the reasoning, and is not,  
then, related to the fact that physical machines appears as  
relatively stable products of some unknown number of algorithm too,  
and that this is already not just described in arithmetic, but  
emulated in arithmetical truth.


This is the starting point I am trying to agree between the two of us.

PROPOSITION 1
The mind is related to the execution of an algorithm -- for  
instance, on some physical machine.


Then, we propose, we go beyond the concept of the physical machine,  
and simply suppose that:


PROPOSITION 2
The mind is the execution of an algorithm, an algorithm which simply  
exists, without the requirement for any physical instantiation, or  
any physical universe / multiverse in actuality.
In other words, the algorithm simply exists, and simply runs, and  
the subjective experience of this algorithm:

Looks exactly like
Feels exactly like
Sounds exactly like
Smells and tastes exactly like
a real physical, relativistic, quantum mechanical reality.

The first proposition, that the mind is / is related to the  
execution of an algorithm, I have no problem with whatsoever. This  
is what I see emphasised in your steps 1-7, with examples of  
displacement of the observer in space, and then time, and then  
replacement, and then duplication in space and time.

This all makes perfect sense.
I think of this as tautological.


?

Comp is everything but tautological. It asks for an act of faith. It  
is a big jump. Even actual machine can prove that they cannot be sound  
and prove that they are machine. Also, I don't like using the notion  
of algorithm because it is a very complex notion which does not admit  
precise definition. I prefer to talk on more concrete programs,  
which can be see as numbers relative to a universal number. I fix the  
universal universal system to arithmetic (addition and  
multiplication), which I assume, and from that I prove the existence  
of universal numbers and many machines, and they discourses.

The consequence of comp are usually judge even more less obvious.





Equally, there is no problem, of course, that in the context of the  
execution of the algorithm, physical machines appears as relatively  
stable products of some unknown number of algorithm too.

But
The *obvious* implication is that the physical machines *are*  
relatively stable products of some unknown number of algorithm,  
specifically, the algorithm instantiated in the physical quantum  
mechanical universe.

And that
physical machines appears as relatively stable products of some  
unknown number of algorithm too, in the virtual reality each  
observer generates between the ears, as Deutsch describes.


Now
Going on from that starting point
We are philosophically interested in showing that this execution of  
the algorithm may be taking place in such a way as to give the  
appearance of the physical quantum mechanical universe, without  
there having to be an actual physical quantum mechanical universe.


I am delighted to entertain this possibility. However, I have not to  
date understood the basis on which you are claiming you have found  
support for it. I'm sure I'll get there!


You still miss the point. It is not a question of having any support  
of that idea. It is a question of understanding that it is a  
consequence of the comp assumption. It is a theorem, if you want. may  
be there is still a flaw, but people fails to find it, despite a  
reasonable number of people have tried. Some can sometimes show that  
the reasoning might be improved and more pedagogical, but I think it  
is just a theorem. You can obvioulsy still believe in a primitive  
physical universe by either abandoning comp, or by adding an invisible  
physical universe as an epiphenomenon (which is pretty ridiculous  
'course).
Anyway, I give the tools to extract the physics, so we can already  
compare. Eventually this can lead to a measuring of our degree of  
computationalism with respect to nature.


Bruno







It is hard for me to believe in any of this, but I just follow a  
theory toward its logical consequences.



I know exactly what you mean about this. For years, after I had I  
deduced the extraordinary implications of Everett's formulation, I  
acknowledged that very peculiar properties of the transtemporal  
experiential reality were implied, but I could not really take them  
as real and actual, let alone make them part of my personal  
epistemology. (Eventually, however, quite recently, these  
implications began to become real for me. This, I can report, is a  
wildly exciting, terrifying, and totally all consuming transition!)


I have titled the reply to your email as The propositions of comp?
In 

Re: CTM and ALG

2011-02-08 Thread Bruno Marchal


On 07 Feb 2011, at 21:50, Andrew Soltau wrote:



Many thanks you for your points 1) to 4) below. Now I am finding  
it much easier to see what you are saying.


By 'first person indeterminacy' in 1 below, I am reading this as  
the indeterminacy regarding the actual location and thus physical  
context / instantiation of this observer. I would include this as  
an automatic concomitant of the mind being a computation ( dynamic  
structure of information) i.e. ALG.
By 2 below I understand you to be saying that just as the observer  
can be, and in fact in some circumstances must be, existent  
simultaneously at two different locations in space at the same  
time, the observer is similarly existent simultaneously at two  
different locations in time 'at the same time'. I would also  
include this as an automatic concomitant with ALG.
Point 3 seems to be a direct implication of point 2, the mind is  
non-local. The observer as mind (as structure of information /  
algorithm) exists ubiquitously in all physical environments



If above you accept arithmetical, you make treachery to invoke the  
physical here.
All right, call it all quantum mechanical environments, meaning  
simply the mathematical form of quantum mechanics, instantiated as  
physical or arithmetical environments.


It is the same error. You cannot use quantum mechanics at all. I mean  
in this context.

I think you still miss something in the seven step.




It is a bit like some one defend the theory of evolution up to the  
apes, and then say and God appears an creates man.
Nice one! LOL! [god thinks this evolution rubbish isn't getting  
anywhere. Let's have some real people to watch / talk to / wind up /  
be god to ...]
Once you accept that at some level you are Turing emulable, you  
somehow disperse yourself in infinities of variants, and the  
physical is some sum on all those variants.

Yes, no problem here. Exactly what I hold as 'universe superposition'.


Really? So you should understand why you cannot use QM (even just the  
mathematical QM). If QM is correct, then QM has to be entirely  
justified in term of machine's dream, that is arithmetical relations  
and internal measure. That is what the Bp  Dp does, with p  
arithmetical and sigma_1 (DU-accessible).





So a physical body is, despite the appearance, a bad locus for  
instantiating a mind.
Why 'bad'? The physical body is one of many possible instantiations,  
*no more no less* in my view.


The problem is that we don't know what is a body. And the first clues  
from comp is that a body is a projection of the mind, emulated by  
infinitely many arithmetical relations. The picture is hard to figure  
out, that is one reason why I eventually use formal tools.





The mind, even individual is more associated to a continuum of  
possible bodies/projection.
I would not say 'more'. It is not only associate with a continuum of  
possible bodies/projection, it is instantiated, given aritmetic and  
algorithmic form, in continuum of possible bodies/projection. All  
exist. All are aspects of the arithmetic totality.
It is instantiated, simultaneously, in all environments, simulated  
or physical (simulated physical if you like), in which this mind is  
formulated.
The effective environment of this mind is the simultanetiy of all  
such possible bodies/projection.
This does not mean that the whole thing is not instantiated in the  
physical.


When you will get closer to the tilt, you will understand that we just  
cannot take for granted any obvious interpretation of the word  
physical.





It is true that it need not be instantiated in a physical reality,  
but, in my opinion, we still have not made any particular progress  
towards that point!


I think that tiny progresses have been done, but are ignored because  
physicists have a problem with computer science and mathematical  
logic, and logicians are not interested in physics or realities. And  
very few scientist care about persons and consciousness. So in front  
of hard works ...




In fine it depends on the math, the comp physical logic still lacks  
(a bit laike quantum logic) a good tensor product.

My strategy is top down, I work from hypothesis toward constrains.
That is all very well and good, but we know the physical explanation  
works. Quantum mechanics *does* explain the observed results of  
experiments.


Not completely. It explains by using comp, but comp reminds them, or  
should remind them, that the first person qualia related to the  
observation cannot be attached to the physical body of the  
experimenter. Everett QM still use the identity thesis, and this is  
refuted by comp. QM explains one halve of the picture.





If we are going to supersede it, we need a powerful logic which not  
only does the same thing, fully and completely, without requiring an  
underlying physical reality. I stay tuned.


The necessity of abandoning comp or of solving the comp body problem  
has been proved. 

Re: Multisolipsism

2011-02-08 Thread Bruno Marchal


On 08 Feb 2011, at 08:52, Andrew Soltau wrote:


On 07/02/11 21:28, Bruno Marchal wrote:

Hi Andrew,


On 07 Feb 2011, at 19:22, Andrew Soltau wrote:


Hi Bruno



The first seven steps of UDA makes the following points:

1) that comp entails the existence of first person indeterminacy  
in a deterministic context. Step 1-3. This is an original result  
that I published in 1988 (although I made a dozen of conference  
on this in the seventies). Many academics have criticize this,  
but their argument have been debunked. Chalmers did criticize it  
at the ASSC4.


2) that any measure of uncertainty of the comp first person  
indeterminacy is independent of the reconstitution delays (step  
four).


3) that comp entails first person non locality (step this has  
been more developed in my thesis, long and short version are in  
my web page). This has been retrieved from sane04 (for reason of  
place), but is developed in the original 1994 thesis (and in the  
1998 short version, recently published).


4) That first person experience does not distinguish real from  
virtual implementation (this is not original, it is in Galouye,  
and it is a comp version of the old dream argument in the greek  
chinese and indian antic literature). Step six. In particular  
indeterminacy and non locality does not depend on the real or  
virtual nature of the computation.

All good so far.

Step seven itself shows the reversal between physics and  
arithmetic (or any first order theory of any universal system in  
post Church Turing sense) in case the physical universe exists  
primitively and is sufficiently big.

Because?


Because if you universe is as big as running a UD, and containing  
UD*, if by luck you were here and now in a physical universe, at  
the next instant you are in the UD* with any reasonable measure of  
first person uncertainty.  Even multiplied by 2^aleph_0.
If, and only if, you *assume* existence without needing a physical  
universe! But this is what you are trying to demonstrate.



Not at all. The role of the big universe consists in getting the  
reversal before showing we don't need the physical running.
The big universe elimination is step 8. Only after step 8 we can  
understand the big universe is not needed, nor any universe, to  
explain why machine believes in a physical universe, indeed most  
probably in a quantum universe.






In what sense does step seven demonstrate the reversal between  
physics and arithmetic a priori, as opposed to a working assumption?


Answer precisely my question in my last post. I recall it:

Could you explain to me how you predict what you will see (qualia)  
when you abandon an apple free in the air, in a big universe with a  
running UD in it? How do you predict your experience?
If you agree with step 1-6, you don't have much choice, and you will  
understand the reversal.






So UDA1-7 is the one of the main result of the thesis. A theory  
which want to explain and unify quanta and qualia, and respect  
comp, has to derive quanta and qualia without postulating them.

Yes


So you agree we cannot postulate the quanta? We cannot postulate  
the physical ? That's the point.
NO. I agree that A theory which want to explain and unify quanta  
and qualia, and respect comp, has to derive quanta and qualia  
without postulating them., which is, of course, the tricky bit!


But that is wrong. Without comp, I could keep materialism and keep  
quantum mechanics as explaining the quanta. But with comp, and the  
understanding of the qualia problem, we can understand that we have no  
other choice than to explain both the quanta and the qualia from  
arithmetic. It might not work, and comp can be false (and thus CTM  
also).


Take it easy.

Bruno


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



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Re: Maudlin How many times does COMP have to be false before its false?

2011-02-08 Thread Bruno Marchal


On 07 Feb 2011, at 23:58, 1Z wrote:




On Feb 7, 6:29 pm, Bruno Marchal marc...@ulb.ac.be wrote:

Peter,

Everything is fine. You should understand the reasoning by using only
the formal definition of arithmetical realism,


You reasoning *cannot* be both valid and ontologically
neutral because it has ontological conclusions.


Wrong. It is enough it has ontological premise.





.which is that a

machine is arithmetical realist if she believes in the axiom of
elementary arithmetic *with* (the realist part) the principle of the
third excluded middle (allowing non constructive reasoning, as  
usual).


What machine? Show me one!


See my papers. Read a book on logic and computability. Boolos and  
Jeffrey, or Mendelson, or the Dover book by Martin Davis are excellent.
It is a traditional exercise to define those machine in arithmetic.  
Recently Brent Meeker sent an excellent reference by Calude  
illustrating how PA can prove the existence of universal machine (or  
number). I will search it.
And I encourage you to interpret all this, including my thesis in  
purely formal term. AUDA shows, notably, that this is possible.


You might also read the book by Judson Webb, which has been recently  
republished and which shows the positive impact of Gödel on both  
formalism and mechanism. Actually Webb argues that formalism and  
mechanism are basically the same philosophy, or the same type of  
philosophy. And I do follow him on that. A machine is before all a  
form. A digital machine is a form which can be described locally  
(relatively to a universal number) by a number. Webb call the kind of  
AR used here: finitism.







And with AUDA you get a conversation with a machine, and a quasi
correct explanation why she is not a machine? How could a formalist
not love that 

Gödel is not just the discovery of the provability limitations of
formalisms and machines,


Godel has no impact on game playing formalism.


?

(Well the more usual critic in our context is that Gödel has *only*  
impact on game playing formalism).


I was just saying that Gödel's second incompleteness theorem is a  
theorem in Peano arithmetic, about Peano arithmetic. Or by Peano  
Arithmetic, about Peano arithmetic.



Bruno


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



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Re: Neurobiologists Find that Weak Electrical Fields in the Brain Help Neurons Fire Together

2011-02-08 Thread Bruno Marchal


On 08 Feb 2011, at 09:03, Andrew Soltau wrote:


On 06/02/11 22:06, Russell Standish wrote:

Neurobiologists Find that Weak Electrical Fields in the Brain Help
Neurons Fire Together

http://media.caltech.edu/press_releases/13401

Reminds me of what Colin says he is doing...

Cheers

Fascinating. At every turn we seem to find additional complexity and  
holistic phenomena in the processes of life giving rise to  
biological computation. It reminds me of Bonnie Bassler's quorum  
function which enables bacteria in the body to act in concert as a  
single organism.


http://www.ted.com/index.php/talks/bonnie_bassler_on_how_bacteria_communicate.html



Ah ah ! I 3 Bonnie. I 3 bacteria. It is always a pleasure to listen  
to her.


Bacteria are 100% Turing universal.

Give me one thousand molecular biologists, and I will build the most   
powerful parallel computers. The difficulty: mixing a big number of  
phages and bacteria. Ethical difficulties too.


Are bacteria Löbian? I doubt this, but who knows, really. I mean, in  
great numbers.


I think that the eucaryote cells is a bacteria (+ virus, for the  
nucleus) construction, like the choroplast is a descendent of the  
cyanobacteria.


We are bacteria colonies, bacteria swarm.

All my interest in mechanism stemmed from my interest for bacteria and  
cells, notably at the molecular level. I discovered the computer  
science IF ... THEN in the Lactose Operon (Jacob and Monod, and then  
in Gödel's paper).


I consider Kleene second recursion theorem (AxEeAz phi_e(z) = phi_x(e,  
z)) as being the most fundamental theorem in abstract biology. I  
apply it in the long version of the thesis to program finite and  
infinite 'planaria' (my favorite worm). The program, when cutted in  
part, is such that each part generate the whole program, like the bio  
Planarias who are the champion of animal regeneration. I used an  
operator form of the theorem due to John Case.


I think recursion theory contains an abstract biology, an abstract  
psychology and an abstract theology, including the theory of matter.


--

And recursion theory is easily embedded in the theory of diophantine  
polynomial. You don't even need more than a polynomial of degree 4, by  
the work of Matiyazevitch and Jones.


This is hardly believable. You can verify the truth on any sigma_1  
true sentence by less than 100 additions and multiplication. Of course  
to emulate the collision between the Milky Way and Andromeda with a  
low degree universal diophantine polynomial, you will have to encode a  
lot of information in individual numbers. But no matter the complexity  
of the task, you can verify it in less than 100 hundred operation  
(addition and multiplication).

You might as well code for the quantum vacuum.

The simple counting algorithm 0, 1, 2, 3, ... is not turing universal,  
but that was close! Just one 100 operations for testing arbitrary  
lengthy computations.


Diophantine polynomials are Turing universal. That would have pleased  
Hypatia who was teaching Plotinus and Diophantus in Alexandria, some  
time ago. I am pretty sure.


Of degree four!
The question of the existence of a universal diophantine polynomial of  
degree three remains open. We know that there are no universal  
diophantine polynomial of degree two. (diophantine means that the  
variables variate on the integers).
On the reals, you don't get the Turing universality with the  
polynomials,. You need the sine or the cosine, to reintroduce the  
natural numbers, or the complex numbers.


Bruno

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



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Re: The relative point of view

2011-02-08 Thread Brent Meeker

On 2/8/2011 8:47 AM, Bruno Marchal wrote:


On 07 Feb 2011, at 20:52, Andrew Soltau wrote:





How do you define the relative point of view?


Do you know Gödel's provability predicate? The points of view are 
defined by intensional variants of the current provability predicate 
of the machine with or without some oracle. There are 8 basic points 
of view p (truth), Bp (provability/believability), Bp  p 
(knowability), Bp  Dp (observability), Bp  Dp  p 
(sensibility/feelability). Three of them inherits the G/G* 
splitting, making a total of 8. It is really 4 + 4*infinity, because 
the 'material points of view' (with Dp) admits themselves graded 
variants.



I know *about* Gödel's provability predicate!



Good.





(Is the 'intensional' referred to here the 'attach' you used in 
another email?)


Not really, although it is related.

Intensional refers to the fact that if you define a provable(x) by 
beweisbar(x) and x', where x' denote the proposition which has x as 
Gôdel number, you define a probability predicate, 


You mean provability predicate don't you?

which is not definable by the machine, or in arithmetic, yet proves 
exactly the same proposition of arithmetic than the one provable. 
Provable(x) and beweisbar(x) are intensional variant of provability. 
They are extensionnally equivalent, but intensionnally different, a 
bit like different algorithm can have the same behavior.
More simple beweisbar(x)  ~beweisbar(~x)  is an intensional variant 
of beweisbar(x).


Intensional variant of bewesibar(x) have been introduced by Rosser in 
his elimination of Gödel's assumption of omega-completeness  in the 
proof of incompleteness of formal systems.







I am still no clearer about how you define the machine, with or 
without some oracle, and what defines the relative point of view.


Oracle have been introduced by Turing for the study of the degree of 
unsolvability. It is a package of usually infinite information, 
typically not computable. The halting oracle provides the halting 
information, that no computer can generate. The goal consisted in 
showing that some problem remains non solvable, and that some function 
remains uncomputable, even when powerful oracle are added, and this 
has been used to study the degrees of unsolvability of arithmetical 
and mathematical problems.


The UD generate all the oracles, like it dovetails on all the reals 
(trivial exercise; yet people are often wrong on this because they 
confuse the impossibility of enumerating the reals, with the 
impossibility of generating them). Think about the iterated 
self-duplication experiment.






Given that you are defining 8 basic points of view in the abstract, 
applied to  intensional variants of the current provability 
predicate of the machine with or without some oracle, it sounds a 
bit, well, abstract. Could you be a bit more specific?


I try to be more specific in sane04. May be we should start from that. 
Or search hypostasis or hypostases in the archive, or guardian 
angel, etc.

Read the book by Smullyan, and Boolos 1979 (simpler than Boolos 1993).

Read perhaps the Theaetetus by Plato.

In short you can say that I model belief or opinion by formal 
probability (Bp). 


You mean formal provability?  Mind your ps and vs.  :-)

I define then knowledge, following Theaetetus by the true opinion (Bp 
 p), 


You've never said what your answer is to Gettier's example.

Brent

observation by the consistent opinion (Bp  Dp), and sensibility by 
the true consistent opinion (Bp  Dp  p). Incompleteness motivates 
the initial model, even if it leads to a restriction on the ideally 
correct machine. The whole thing provides an arithmetical 
interpretation of Plotinus theory of the one, the intellect and the 
soul + his double (intelligible and sensible) matter theory. The 
arithmetical matter theory has been compared to the current inferred 
theory of matter, and it looks, up to now, that Nature is correct :)

(correct with respect to comp and its neoplatonist rendering, for sure).

Bruno

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





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Re: Multisolipsism

2011-02-08 Thread Brent Meeker

On 2/8/2011 9:52 AM, Bruno Marchal wrote:

Answer precisely my question in my last post. I recall it:

Could you explain to me how you predict what you will see (qualia) 
when you abandon an apple free in the air, in a big universe with a 
running UD in it? How do you predict your experience?
If you agree with step 1-6, you don't have much choice, and you will 
understand the reversal. 


??  Obviously I would predict seeing the apple fall.  This is a 
consequence of my inference from past experience and even my 
evolutoinary ancestry.  Even babies expect unsupported objects to fall.  
Do you claim you can predict that apples should be seen to fall from 
comp+arithimetic alone?


Brent

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