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

[1Z]

Stathis Papaioannou wrote:


> 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,


There is a basis for distinguishing between a programme and a process.


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

[Bruno Marchal]

John,

Le 23-août-06, à 22:24, <[EMAIL PROTECTED]> a écrit :

> As I 'believe': anything recognized by our 'senses' are our mental 
> interpretations of the unattainable 'reality' (if we condone its 
> validity). "My world" is a posteriori.


This is almost my favorite way to explain Plato in one sentence.
Now with "pythagorean-plato" (discussed in Plato, but even more by the 
neoplatonists), the question is open that the "ultimate reality" is the 
reality of the numbers law. Note that after Godel-Turing-Post-Church... 
, betting on our own consistency, we know, at least, why and how such 
an ultimate reality (numbers) is forever unattainable (contrary to the 
pregodelian, leibnizian old belief that "number" are easy to get 
through.
I mean "natural number" (real numbers or complex numbers are terrible 
simplification tools, unless you define the trigonometric function 
which reintroduce the natural numbers in the "real" or "complex" 
picture.

Best regards,

Bruno


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


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

[jamikes]

Bruno:
 
why do I have difficulties to go along 
with many of you?
E.g. when you wrote (and not you brought 
up the ominous "axiom"):
>"...Which axioms? Indeed, good 
question, that's makes my point. >Well, I was thinking about some physical 
theory the "someone" >would argue for.  Anyone a 
priori.<"
I dislike 'axioms', but do not trust my 
dislike, so I looked up Wikipedia's definition to have something to argue 
against . It said:

An axiom is a sentence or proposition that is taken for granted as 
true, and serves as a starting point for deducing other truths. In many usage 
axiom and postulate are 
used as synonyms.
In certain epistemological 
theories, an axiom is a self-evident 
truth upon which other knowledge must rest, and from which other knowledge is 
built up. An axiom in this sense can be known before one knows any of these 
other propostions. Not all epistemologists 
agree that any axioms, understood in that sense, exist.
In logic and mathematics, an 
axiom is not necessarily a self-evident truth, but rather a formal 
logical _expression_ used in a deduction to yield further results. To 
axiomatize a system of knowledge is to show that all of its claims can be 
derived from a small set of sentences that are independent of one another. This 
does not imply that they could have been known independently; and there are 
typically multiple ways to axiomatize a given system of knowledge (such as 
arithmetic). 
Mathematics distinguishes two types of axioms: logical 
axioms and non-logical 
axioms. 
It speaks for itself. "We" (not you and me) create axioms to make 'our' 
theories work. Then we consider the 'system' in question based on such axioms. I 
try to scrutinize them, to find alternates and scrutinize those also. 
The other one is an 'a priori (physical?) theory' - sounds in physics similar 
to 'your' numbers which you may consider 'a priori' existing. If I may ask: what 
'natural' senses may detect numbers? Unless. of course, you consider our mind a 
'natural sense' (what may be true).  As I 'believe': anything recognized by 
our 'senses' are our mental interpretations of the unattainable 'reality' (if we 
condone its validity). "My world" is a posteriori.
Cheerz
John M
 
- Original Message - 

From: "Bruno Marchal" 
<[EMAIL PROTECTED]>
To: <everything-list@googlegroups.com>
Sent: Wednesday, August 23, 2006 10:31 
AM
Subject: Re: Platonism vs Realism WAS: 
ROADMAP (well, not yet really...
Le 23-août-06, à 03:58, Brent Meeker a écrit 
:>>>> 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.I am glad you don't insist.>  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.OK, but for our 
reasoning it is enough consciousness is maintained a nanosecond (relatively 
to us).>>> I>> guess they have no problem 
with comatose people either.>> Comatose people are generally 
referred to as "unconscious".? ? ?I mean this *is* the question. In 
mind'sI (Dennett Hofstadter) we learn that a woman has been in comatose 
state during 50 years (if I remember correctly), and said she never stop to 
be conscious.They are more than one form of comatose state. To say they are 
"unconscious" is debatable at the least. And then there is the case of 
dreams. And for those who does not like dream, what about the following 
question: take a child and enclose him/her in a box completely isolated 
from the environement. Would that fact suppress his/her 
consciousness?Some parents will appreciate and feel less guilty with such 
ideas ...>>> 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.Yes. some "person" attached to 
(infinity) of special computations, indeed.>>>> 
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> c

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

[Brent Meeker]

Stathis Papaioannou wrote:
> Brent Meeker writes:
> 
> 
>>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.
> 
> 
> That's an assumption, 

No, it has empirical support. It is what is reported by people in extended 
sensory 
deprivation experiments.

>but even if true it would only say something about the 
> nature of human brains. It is easy enough to imagine a brain with 
> self-excitatory 
> neurons that provide the same kind of input as the environment does, 
> modulating
> their activity in response to feedback from other neurons. It would just be a 
> technical problem to ensure that it didn't go into an endless loop.

Without inherent (quantum) randomness?  I don't think so.  Close deterministic 
systems have a Poincare return time.

Brent Meeker


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

[Bruno Marchal]

Le 23-août-06, à 03:58, Brent Meeker a écrit :

>>
>> 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.

I am glad you don't insist.


>  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.


OK, but for our reasoning it is enough consciousness is maintained a 
nanosecond (relatively to us).


>
>> I
>> guess they have no problem with comatose people either.
>
> Comatose people are generally referred to as "unconscious".

? ? ?
I mean this *is* the question. In mind'sI (Dennett Hofstadter) we learn 
that a woman has been in comatose state during 50 years (if I remember 
correctly), and said she never stop to be conscious.
They are more than one form of comatose state. To say they are 
"unconscious" is debatable at the least. And then there is the case of 
dreams. And for those who does not like dream, what about the following 
question: take a child and enclose him/her in a box completely isolated 
from the environement. Would that fact suppress his/her consciousness?
Some parents will appreciate and feel less guilty with such ideas ...

>
>> 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.

Yes. some "person" attached to (infinity) of special computations, 
indeed.


>>
>> 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?

Sorry, I have used the word "decide" in the logician sense (like in 
undecidable). To decide = to proof, or to test, or to solve, in some 
math sense.
Which axioms? Indeed, good question, that's makes my point. Well, I was 
thinking about some physical theory the "someone" would argue for. 
Anyone a priori.

>
>> 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?

If by "physical" you mean what Peter Jones means, then indeed the 
"physical machine" is in contradiction. This means that her axioms are 
indeed contradictory. If moreover, the physical machine gives a 
"correct" proof, as as I say in the quotes, then we get a total 
contradiction, like a proof that PI is an integer, for example. That we 
are in contradiction.
As far as we are consistent, this just means that no X-machine can 
correctly proof that X-machine does not exist.


Bruno



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


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

[Stathis Papaioannou]

Brent Meeker writes:

> 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.

That's an assumption, but even if true it would only say something about the 
nature of human brains. It is easy enough to imagine a brain with 
self-excitatory 
neurons that provide the same kind of input as the environment does, modulating
their activity in response to feedback from other neurons. It would just be a 
technical problem to ensure that it didn't go into an endless loop.

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

[Bruno Marchal]

Le 21-août-06, à 22:20, Brent Meeker a écrit :

> 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.

I don't think it makes sense to ask if a program per se can be 
conscious.
Only a relative running program can have a  consciousness attributed to 
it. (and then by UDA that consciousness will be associated to an 
infinity of sufficiently similar running programs occuring in the UD 
(mathematical) execution.

Now Peter asks for a running program relatively to a real universe.
Then I say that the UDA shows that the "real universe" is a red herring.
All what is needed is a running program relatively to an infinity of 
(mathematical) universal number.

I recall that a number u is universal with respect to addition and 
multiplication (or any ontic theories in which you define the partial 
recursive functions) when Fu(x,y) = Fx(y) for all x and y. The Fi being 
defined in the ontic theory.

Bruno


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


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

[Stathis Papaioannou]

Peter Jones writes (quoting Bruno Marchal):

> > 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.

Clearly the brain *did* evolve to dream, although we don't really understand 
the 
evolutionary advantage of dreaming, or for that matter sleeping. But that is 
beside the point: the question is whether interaction with an external 
environment 
is necessary for consciousness, and I think dreaming is one situation which 
shows 
that it is not.

(To be fair, one could argue that dreaming does involve environmental input in 
that 
at the very least there is proprioceptive feedback from the rapid eye 
movements, 
and there is no dreaming during non-REM sleep. However, I think that is just a 
technical detail, as it is easy enough to imagine a brain dreaming without this 
input, 
or with the input provided by self-exciting neurons.)

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

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

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

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

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

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

[Brent Meeker]

Stathis Papaioannou wrote:
> Peter Jones writes:
> 
> 
>> And such a universe could be emulated as a running, deterministic process. 
>> But 
>> that won't get you into Plato's heaven, because it is a *running* process -- 
>> it
>> is still dynamic. A recording of the process could exist in Plato's heaven, 
>> but
>> it wouldn't have all the counterfactuals, so the computationalist is not
>> required to believe that it contains any real sentience -- the simulated 
>> beings
>> in it would have no more consciousness of their own than the characters in a
>> movie!
>> 
>> Likewise, the computationalist is not required to believe that an unexecuted
>> programme is sentient (even though it has, theoretically, the 
>> counterfactuals).
>> 
>> No-one would believe that a brain-scan, however detailed, is conscious, so  
>> not
>> computationalist, however ardent, is required to believe that a progamme
>> gathering udston a shelf is sentient, however good a piece of AI code it is.
> 
> 
> Leave aside for the moment the computer running in Platonia and consider a 
> real
> computer. You say that a computer program is defined in part by its ability to
> handle counterfactuals, distinguishing it from a mere recording, but it is 
> this
> distinction with which I have difficulties. The characters in a film are not
> conscious because the film only simulates external appearance, not because it
> lacks if-then statements. A film obviously does handle if-then statements, 
> because
> if the patterns on the film are different the projection on the screen would 
> also
> be different. 

That's not a proper example though.  It would imply to a rock - it would be 
different 
if it weren't a rock.  To be intelligent (much less conscious) the if-then must 
be 
inresponse to different environmental inputs.

>A computer program basically does the same thing: it consistently
> produces a certain output for a certain input. 

That's why you can't tell whether a program is intelligent by giving it a 
"certain 
input".  There must be a variety of inputs and the response will in general be 
different depending on their order (smart programs have memory).

>In the MWI of QM a computer program
> or human mind may have more luxuriant branchings than a recording, 

This seems to reify the branches as part of the program.  They are part of the 
*process of running* the program.  The branches arise from different inputs.

>but that is
> just a matter of degree, and in any case there is no reason to suppose that a
> program is any less valid or less conscious because of the presence or 
> absence of
> near-copies segregated in parallel universes. In the CI of QM it would be 
> possible
> to introduce true randomness into a computer program but the same could be 
> done
> for a recording, and again there is no reason to suppose that a program is any
> less valid or less conscious because it isn't random. Randomness and/or 
> parallel
> processes are not a prerequisite for a classical computer to function.

I agree with that.

> 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.

Brent Meeker


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

[Stathis Papaioannou]

Peter Jones writes:

> And such a universe could be emulated
> as a running, deterministic process. But
> that won't get you into Plato's heaven,
> because it is a *running* process -- it is still
> dynamic. A recording of the process could
> exist in Plato's heaven, but it wouldn't have
> all the counterfactuals, so the computationalist
> is not required to believe that it contains
> any real sentience -- the simulated
> beings in it would have no more
> consciousness of their own than the characters in a movie!
> 
> Likewise, the computationalist is not
> required
> to believe that an unexecuted programme is sentient
> (even though it has, theoretically, the counterfactuals).
> 
> No-one would believe that a brain-scan, however detailed,
> is conscious, so  not computationalist, however ardent,
> is required to believe that a progamme gathering udston a shelf
> is sentient, however good a piece of AI code it is.

Leave aside for the moment the computer running in Platonia and consider a real 
computer. You say that a computer program is defined in part by its ability to 
handle counterfactuals, distinguishing it from a mere recording, but it is this 
distinction with which I have difficulties. The characters in a film are not 
conscious because the film only simulates external appearance, not because it 
lacks if-then statements. A film obviously does handle if-then statements, 
because if the patterns on the film are different the projection on the screen 
would also be different. A computer program basically does the same thing: it 
consistently produces a certain output for a certain input. In the MWI of QM a 
computer program or human mind may have more luxuriant branchings than a 
recording, but that is just a matter of degree, and in any case there is no 
reason to suppose that a program is any less valid or less conscious because of 
the presence or absence of near-copies segregated in parallel universes. In the 
CI of QM it would be possible to introduce true randomness into a computer 
program but the same could be done for a recording, and again there is no 
reason to suppose that a program is any less valid or less conscious because it 
isn't random. Randomness and/or parallel processes are not a prerequisite for a 
classical computer to function.

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.

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

[Brent Meeker]

Stathis Papaioannou wrote:
> 
> Right!
> 
> 
> 
> 
> 
>>From: [EMAIL PROTECTED]
>>To: everything-list@googlegroups.com
>>Subject: Re: Platonism vs Realism WAS: ROADMAP (well, not yet really...
>>Date: Sun, 20 Aug 2006 10:18:18 +0200
>>
>>
>>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.

Brent Meeker

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

[1Z]

Stathis Papaioannou wrote:
> Peter Jones writes:
>
> > Stathis Papaioannou wrote:
> > > Peter Jones writes:
> > >
> > > > > Is it possible that we are currently actors in a single, 
> > > > > deterministic, non-branching
> > > > > computer program, with the illusion of free will and if-then 
> > > > > contingency in general
> > > > > being due to the fact that we don't know the details of how the 
> > > > > program will play
> > > > > out?
> > > >
> > > > Lots of things are possible. The question is what to believe.
> > >
> > > True, but I thought you were saying that such a thing was incompatible 
> > > with consciousness,
> > > and I see no reason to believe that.
> >
> > There are a lot of prolems with what you are saying.
> >
> > I don't think it is possible to get dynamism out of stasis,
> > and I don't think it is possible to get qualia out of mathematical
> > structues
>
> But what about a physical computer which creates an entire virtual 
> environment, complete
> with sentient beings? Once started up it would be completely deterministic, 
> just as a recording
> would be. It could have if-then statements but these would not make any 
> difference, given initial
> conditions.

>  (A recording also has if-then statements, in that if the input were 
> different, the
> output would also be different.)


> This could as easily be a real model of a classical universe, with
> no interference from outside once initial conditions + laws of physics had 
> been set. The if-then
> statements are implicit in the laws of physics: if I throw a rock, it will 
> follow a parabolic trajectory
> and shatter the window.

Yes, that is my point. Computationalsim requires
processes that implement algorithms, algorithms require
counterfactuals, counterfactuals are underpinned by
physical causality.

But all you can have in Plato's heaven is a recording that
doesn't have counterfactual behaviour, or a programme (as opposed
to a process) that isn't implemented.

>  As an inhabitant of the univerese I think I have free will in deciding 
> whether
> or not to throw the rock, but in fact this is no more indeterminate than the 
> workings of a clockwork
> mechanism.

Assuming the universe is detrerministic. (Actually,
classical physics isn't computable...)

> My understanding is that standard computationalism allows for consciousness 
> to occur
> in such a universe, even if it isn't the universe we actually live in.

And such a universe could be emulated
as a running, deterministic process. But
that won't get you into Plato's heaven,
because it is a *running* process -- it is still
dynamic. A recording of the process could
exist in Plato's heaven, but it wouldn't have
all the counterfactuals, so the computationalist
is not required to believe that it contains
any real sentience -- the simulated
beings in it would have no more
consciousness of their own than the characters in a movie!

Likewise, the computationalist is not
required
to believe that an unexecuted programme is sentient
(even though it has, theoretically, the counterfactuals).

No-one would believe that a brain-scan, however detailed,
is conscious, so  not computationalist, however ardent,
is required to believe that a progamme gathering udston a shelf
is sentient, however good a piece of AI code it is.

>If not, then you have to abandon
> computationalism and embrace something like Penrose's theory in which 
> essentially non-computable
> quantum effects are responsible for consciousness; or maybe we've just all 
> been issued with a soul
> by God.

Standard computationalism refers to real, physical processes
running on material computers. You have 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.

(No *special* kind of physics is required).

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

[Stathis Papaioannou]

Peter Jones writes:

> Stathis Papaioannou wrote:
> > Peter Jones writes:
> >
> > > > Is it possible that we are currently actors in a single, deterministic, 
> > > > non-branching
> > > > computer program, with the illusion of free will and if-then 
> > > > contingency in general
> > > > being due to the fact that we don't know the details of how the program 
> > > > will play
> > > > out?
> > >
> > > Lots of things are possible. The question is what to believe.
> >
> > True, but I thought you were saying that such a thing was incompatible with 
> > consciousness,
> > and I see no reason to believe that.
> 
> There are a lot of prolems with what you are saying.
> 
> I don't think it is possible to get dynamism out of stasis,
> and I don't think it is possible to get qualia out of mathematical
> structues

But what about a physical computer which creates an entire virtual environment, 
complete 
with sentient beings? Once started up it would be completely deterministic, 
just as a recording 
would be. It could have if-then statements but these would not make any 
difference, given initial 
conditions. (A recording also has if-then statements, in that if the input were 
different, the 
output would also be different.) This could as easily be a real model of a 
classical universe, with 
no interference from outside once initial conditions + laws of physics had been 
set. The if-then 
statements are implicit in the laws of physics: if I throw a rock, it will 
follow a parabolic trajectory 
and shatter the window. As an inhabitant of the univerese I think I have free 
will in deciding whether 
or not to throw the rock, but in fact this is no more indeterminate than the 
workings of a clockwork 
mechanism. My understanding is that standard computationalism allows for 
consciousness to occur 
in such a universe, even if it isn't the universe we actually live in. If not, 
then you have to abandon 
computationalism and embrace something like Penrose's theory in which 
essentially non-computable 
quantum effects are responsible for consciousness; or maybe we've just all been 
issued with a soul 
by God.

Stathis Papaioannou


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

[Stathis Papaioannou]

Right!




> From: [EMAIL PROTECTED]
> To: everything-list@googlegroups.com
> Subject: Re: Platonism vs Realism WAS: ROADMAP (well, not yet really...
> Date: Sun, 20 Aug 2006 10:18:18 +0200
> 
> 
> 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
> 
> > 

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

[1Z]

Quentin Anciaux wrote:
> 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|

Which could be further simplified into

|HARCODED OUTPUT|

But not most people would call that "data", not "programme".

(in any case, this kind of one-shot progamme is not a good
model of mind. A mind is more like a fuzzy-logic real-time system).


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

[1Z]

Stathis Papaioannou wrote:
> Peter Jones writes:
>
> > > Is it possible that we are currently actors in a single, deterministic, 
> > > non-branching
> > > computer program, with the illusion of free will and if-then contingency 
> > > in general
> > > being due to the fact that we don't know the details of how the program 
> > > will play
> > > out?
> >
> > Lots of things are possible. The question is what to believe.
>
> True, but I thought you were saying that such a thing was incompatible with 
> consciousness,
> and I see no reason to believe that.

There are a lot of prolems with what you are saying.

I don't think it is possible to get dynamism out of stasis,
and I don't think it is possible to get qualia out of mathematical
structues

Oh, and "Non-branching programme" is close to being a cotnradiction in
terms.

>You could replace "computer program" with "machine"
> and have a description of the universe.

Really ? What would "machine" mean in that sentence ?
And according to which theory of physics ?

> Actually, you could leave out "non-branching" as well:
> the MWI is branching but deterministic, and still leaves room for first 
> person indeterminacy.

There are problems with MWI as a purely physical theory.

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

[Bruno Marchal]

Le 19-août-06, à 15:36, Günther wrote:

>> The existence of numbers is not like the existence of objects, and I 
>> don't
>> think that most mathematical Platonists would say that it is.

I agree with them. We have to distinguish many forms of "internal"  or 
epistemological existence, build from the simplest conceptual third 
person ontological commitments.
Comp necessitates the numbers for the "ontic" part, and the rest 
emerges as coherent overlapping set of of computations (quotientized 
through some undistinguishability first person equivalence relation).
To be short.

Bruno



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


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

[Quentin Anciaux]

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

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

[Stathis Papaioannou]

Peter Jones writes:

> > Is it possible that we are currently actors in a single, deterministic, 
> > non-branching
> > computer program, with the illusion of free will and if-then contingency in 
> > general
> > being due to the fact that we don't know the details of how the program 
> > will play
> > out?
> 
> Lots of things are possible. The question is what to believe.

True, but I thought you were saying that such a thing was incompatible with 
consciousness, 
and I see no reason to believe that. You could replace "computer program" with 
"machine" 
and have a description of the universe. Actually, you could leave out 
"non-branching" as well:
the MWI is branching but deterministic, and still leaves room for first person 
indeterminacy.

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

[Stathis Papaioannou]

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.
 
> >  and could it be a conscious program, given that
> > computationalism is true?
> 
> Obviously not, since people have inputs.

There are several possible responses to that. Firstly, it isn't necessarily 
true that only people 
can be conscious, even if people (and maybe some animals) are the only entities 
we have good 
reason to believe are conscious. 

Secondly, there is always the possibility that an inputless, deterministic 
machine might be able 
to receive input. We might open the case, connect a lead with alligator clips, 
and start communicating 
with it in morse code. To the program, it would be like a message from God. You 
would then have to 
decide at which point the program became conscious: when the case was opened, 
when the message 
was sent, or was it conscious all along? If you say it was not conscious until 
the message was actually 
sent you would have to say that an entity was only conscious while receiving 
input, and stopped 
being conscious while it was analysing the input already received.

Finally, it is possible to have the same kind of interaction that a machine 
with environmental inputs  
has by connecting two previously inputless machines to each other. They can 
then have a two way 
conversation, each surprised by the other's responses, but the system as a 
whole remains inputless 
and deterministic. The ultimate example of this is, as Brent Meeker suggested, 
a self-contained virtual 
reality. The universe as a whole could be seen as just this, unless you believe 
that God speaks to us 
from outside.

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

[Bruno Marchal]

Le 18-août-06, à 22:59, complexitystudies a écrit :

>>
>
> As 1Z has so nicely put, existence implies causal interaction.
> Numbers cannot causally interact, therefore they do not exist,
> save as thoughts in our brains.

Don(t say this to a logician. there are as many notion of "causality" 
than there are modal logics.
(But I guess you assume a physical world and define "causal" by some 
"interaction").
I don't need that. I need only math "causality", like if p divide 8 
then p divides 24.



>
> Of course I do not believe that 37 could be a non prime number,
> simply because what it means to be "prime" has been exactly
> defined in arithmetic.

You reassure me.



> I just say that these are thought constructs
> with no independent existence (independent of human brains, not of a
> concrete human brain).
>
> You might say, that 37 was prime even in the Jurassic, but I say:
> nobody had invented arithmetic yet, so it's about as true as the
> fact that James Bond was played by Sean Connery was in the Jurassic.
>
> I define a system:
>
> 1 + 1 = 2
> 2 + 1 = 1
> 1 + 2 = 1
>
> That's all. Okay, it doesn't describe much and probably isn't very
> useful, but other than that it is not inferior to peano arithmetic.
> Does my system now exist mind-independtly for all eternity?


Yes, and even Robinson Arithmetic can prove that. It exists because 
among all fortran programs there exist an infinity of programs which 
compute your table. (it is a Wi or a Fi)
Of course "existing" does not mean interesting. Some numbers could be 
(relatively) boring, but that is hardly provably so in general.



>
>
>> I have not yet seen a book on human brain which does not presuppose 
>> the
>> understanding of the natural numbers.
>
> Of course, because it is a useful way to describe reality. But in our
> brains, not numbers operate, but chemicals.


I agree. The question here is what are eventually the chemicals. Comp 
answers: it is necessarily an average of point of views on an infinity 
of possible computational continuations. Put in that way, it even looks 
like some formulation of QM. The details are tricky of course (both 
with comp and with the QM only).





>
>
>  I let you
>> discover that, and feel free to ask questions if you have a problem
>> with UDA.
>
> Thank you, I will.
>
>
>>
>> It is really the point of the UDA. It shows that computationalism (the
>> idea that I am a digitalizable machine) is incompatible with "weak
>> materialism" (the idea that there is a primary stuff or matter or
>> aristotelian substances).
> Ok, I'll watch for this in UDA.
>>
>
>> But until now, comp leads only to weirdness, not contradiction. And
>> then that weirdness seems to explain the quantum weirdness ...
>> Intuitively and qualitatively (already by UDA), and then technically
>> through the interview of some universal turing machine.
>
> But wouldn't this universal turing machine need to be composed of
> matter, and then the whole caboodle starts from the beginning?


No. The additive+multiplicative structure of the non negative integers 
(what logician called the natural numbers) is already a video-game rich 
enough to generate coherent and sharable set of computational first 
person plural histories. That *is* the point. Don't take this for 
granted at all. UDA explain why. The lobian interview explain how.
The question is not does Humty-Dumpty "exist"? The question is "does 
not comp entails too much probable Humpty-Dumpty in my neighborhood" 
and "how to test that".
The question is "does comp entails *more*, or *less* white rabbits than 
QM already predicts apparently with some accuracy".

Bruno


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

[1Z]

Stathis Papaioannou wrote:
> Günther writes:
>
> > Well, let's see: in Alice in Wonderland, Humpty Dumpty fell off a
> > wall. This is true, isn't it? It is certainly true independent
> > of our minds. Indeed, it is true in such a way that even when
> > all humans have died, this universe will have a contained a life-form
> > which produced an author who wrote a book in which Humpty Dumpty
> > fell off a wall. But neither Humpty Dumpty nor the fact that he
> > fell off a wall were ever true in this universe - only that this
> > story was written, and that many people read about it and could
> > converse about it.
> >
> > So if you believe that numbers have an independent existence, then you
> > would definitely also have to believe that Humpty Dumpty exists.
> > Both are products of the mind. Either both exist, or both don't
> > (other than as brain patterns).
> >
> > As much as I would like Humpty Dumpty to exist, I'm afraid that
> > it is not so.
>
> The existence of numbers is not like the existence of objects, and I don't
> think that most mathematical Platonists would say that it is.

Most Platonists ar not Mathematical Monists. M-Monists *do*
have to  think it is the same.


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

[1Z]

Stathis Papaioannou wrote:

> Is it possible that we are currently actors in a single, deterministic, 
> non-branching
> computer program, with the illusion of free will and if-then contingency in 
> general
> being due to the fact that we don't know the details of how the program will 
> play
> out?

Lots of things are possible. The question is what to believe.


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

[1Z]

Stathis Papaioannou wrote:
> Peter Jones writes (quoting SP):
>
> > > I've never really understood why computationalists insist that a system
> > > must be able to handle counterfactuals in order for consciousness to 
> > > occur,
> >
> > I've explained that several times: computer programmes contain
> > if-then statements.
> >
> > > other than that otherwise any physical system could be seen as 
> > > implementing
> > > any computation, which does not seem to me a good reason. In any case,
> > > Maudlin shows that the requirement for handling counterfactuals leads to
> > > a situation where of two systems with identical physical activity, one is
> > > conscious and the other not.
> >
> > If two systems differ counterfactually, they are not physically
> > identical.
>
> 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.

>  and could it be a conscious program, given that
> computationalism is true?

Obviously not, since people have inputs.

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

[1Z]

Bruno Marchal wrote:
> Le 18-août-06, à 17:02, 1Z a écrit :
>
> > It is for Pythagorenas and Platonists to explain what they mean by
> > "exist".
> >
> > However, if you are going to claim that we are actually *in* Platonia,
> > (mathematical monism) there must be some equivalence between the
> > existence we
> > have and the existence numbers have.
>
>
>
> Of course! But that is what I am currently explaining. If you have
> follow the UDA, then, even if you could not yet be completely convinced
> by each steps, you should at least be able to figure out in which sense
> "you", here and now, in the "shape" of an OM, to borrow the list
> vocabulary, exist as a relative number.


I cna't be persuaded of that without first being
persuaded that numbers exist.

> Third personally you exist in
> aleph-zero relative number form (like snapshots of a running program).
> First personally you exist in the same shape (although you cannot know
> that) but you are "multiplied" by a continuum: the computational
> histories generated by the UD, in the mathematical sense, going through
> those third person states.
> 
> Bruno
> 
> 
> 
> http://iridia.ulb.ac.be/~marchal/


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

[1Z]

Bruno Marchal wrote:
> Le 18-août-06, à 17:38, 1Z a écrit :
>
> > That is an explanation of mind-independence, not of  existence.
> > The anti-Platonist (e.g. the formalist) can claim that
> > the truth of mathematical statments is mind-independent,
> > but their existence isn't.
>
>
> "Their" existence ? Mathematical statements needs "chatty" machines.

Mathematics proceded for centuries without any machines at all.

> Mathematical truth, a priori doesn't (although "free structures" can
> feature some chatty aspects many times).
>
> Let us make the following convention. When I will say "I believe there
> exist a perfect number", it is a shorter expression for, I believe the
> proposition "There is a perfect number" is true (satisfied in (N,+,*))
> independently of me, or of any theory of cognition. (A good thing,
> giving that a theory of cognition is build *from* digital machine, that
> is from number theoretical relations).

If AR makes no existential commitments, it cannot lead
to the existential conclusion that there is no such thing
as matter.

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


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

[Bruno Marchal]

Le 18-août-06, à 17:38, 1Z a écrit :

> That is an explanation of mind-independence, not of  existence.
> The anti-Platonist (e.g. the formalist) can claim that
> the truth of mathematical statments is mind-independent,
> but their existence isn't.


"Their" existence ? Mathematical statements needs "chatty" machines. 
Mathematical truth, a priori doesn't (although "free structures" can 
feature some chatty aspects many times).

Let us make the following convention. When I will say "I believe there 
exist a perfect number", it is a shorter expression for, I believe the 
proposition "There is a perfect number" is true (satisfied in (N,+,*)) 
independently of me, or of any theory of cognition. (A good thing, 
giving that a theory of cognition is build *from* digital machine, that 
is from number theoretical relations).

Bruno


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


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

[Bruno Marchal]

Le 18-août-06, à 17:02, 1Z a écrit :

> It is for Pythagorenas and Platonists to explain what they mean by
> "exist".
>
> However, if you are going to claim that we are actually *in* Platonia,
> (mathematical monism) there must be some equivalence between the
> existence we
> have and the existence numbers have.



Of course! But that is what I am currently explaining. If you have 
follow the UDA, then, even if you could not yet be completely convinced 
by each steps, you should at least be able to figure out in which sense 
"you", here and now, in the "shape" of an OM, to borrow the list 
vocabulary, exist as a relative number. Third personally you exist in 
aleph-zero relative number form (like snapshots of a running program). 
First personally you exist in the same shape (although you cannot know 
that) but you are "multiplied" by a continuum: the computational 
histories generated by the UD, in the mathematical sense, going through 
those third person states.

Bruno



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


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

[Bruno Marchal]

Le 19-août-06, à 08:48, Brent Meeker wrote quoting Stathis Papaioannou

>>
>> What more could we possibly ask of a theorem other than that it be 
>> true relative to some
>> axioms? That a theorem should describe some aspect of the real world, 
>> or that it should
>> be discovered by some mathematician, is contingent on the nature of 
>> the real world, but that
>> it is true is not.
>
> That it is a true description of the real world, or that it is a true 
> theorem
> relative to the axioms.  It is a mistake to conflate the two, which I 
> suspect is
> done by people claiming mathematical theorems are true.


No. It is done by people claiming true mathematical propositions are 
theorem.

Robinson Arithmetic (Q or RA) and Peano Arithmetic (PA), which in our 
context are better seen as a (mathematical) *machines*, are SOUND with 
respect to the so-called (by logicians) standard model of arithmetic, 
which is the mathematical structure (N,+,*) given by the non negative 
integers N together with addition and multiplication (learned in high 
school).
Now RA and all its consistent extensions (and thus PA, "ZF", ...) are 
INCOMPLETE with respect to that mathematical structure (N,+,*), in the 
sense that for any of those theories there exist always infinitely many 
true propositions, "true" meaning really: satisfied by (N,+,*) which 
are unprovable by those theories.
There is no complete TOE for the "standard" additive and multiplicative 
behavior of the natural numbers.
But there is nothing wrong asserting that a theorem of PA is true 
(always with that meaning of being statisfied in (N,+,*)), because 
nobody (serious) doubt the axioms of PA, or doubt truth couldn't be 
preserved by the modus ponens inference rule or by the quantifier rules 
(and thus nobody doubts in the theorems proved by PA).

Bruno

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


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

[Stathis Papaioannou]

Brent Meeker writes (quoting SP):

> >>But the fact that a theorem is true relative to some axioms doesn't make it 
> >>true 
> >>or existent.  Some mathematicians I know regard it as a game.  Is true that 
> >>a 
> >>bishop can only move diagonally?  It is relative to chess.  Does chess 
> >>exist? 
> >>It does in our heads.  But without us it wouldn't.
> > 
> > 
> > What more could we possibly ask of a theorem other than that it be true 
> > relative to some 
> > axioms? That a theorem should describe some aspect of the real world, or 
> > that it should 
> > be discovered by some mathematician, is contingent on the nature of the 
> > real world, but that 
> > it is true is not.
> 
> That it is a true description of the real world, or that it is a true theorem 
> relative to the axioms.  It is a mistake to conflate the two, which I suspect 
> is 
> done by people claiming mathematical theorems are true.

OK then, I agree. The two should not be conflated.

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

[Brent Meeker]

Stathis Papaioannou wrote:
> Brent Meeker writes:
> 
> 
>>>Even if you say that, there is still a sense in which arithmetic is 
>>>independent of the 
>>>real world. The same can be said of Euclidian geometry: it follows from 
>>>Euclid's axioms 
>>>*despite* the fact that real space is not Euclidian. The fact that real 
>>>space is not 
>>>Euclidian means that Euclidian geometry does not describe the real world, 
>>>not that 
>>>it is false or non-existent.
>>>
>>>Stathis Papaioannou
>>
>>But the fact that a theorem is true relative to some axioms doesn't make it 
>>true 
>>or existent.  Some mathematicians I know regard it as a game.  Is true that a 
>>bishop can only move diagonally?  It is relative to chess.  Does chess exist? 
>>It does in our heads.  But without us it wouldn't.
> 
> 
> What more could we possibly ask of a theorem other than that it be true 
> relative to some 
> axioms? That a theorem should describe some aspect of the real world, or that 
> it should 
> be discovered by some mathematician, is contingent on the nature of the real 
> world, but that 
> it is true is not.

That it is a true description of the real world, or that it is a true theorem 
relative to the axioms?  It is a mistake to conflate the two, which I suspect 
is 
done by people claiming mathematical theorems are true.

Brent Meeker

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

[Brent Meeker]

Stathis Papaioannou wrote:
> Brent Meeker writes:
> 
> 
>>>Even if you say that, there is still a sense in which arithmetic is 
>>>independent of the 
>>>real world. The same can be said of Euclidian geometry: it follows from 
>>>Euclid's axioms 
>>>*despite* the fact that real space is not Euclidian. The fact that real 
>>>space is not 
>>>Euclidian means that Euclidian geometry does not describe the real world, 
>>>not that 
>>>it is false or non-existent.
>>>
>>>Stathis Papaioannou
>>
>>But the fact that a theorem is true relative to some axioms doesn't make it 
>>true 
>>or existent.  Some mathematicians I know regard it as a game.  Is true that a 
>>bishop can only move diagonally?  It is relative to chess.  Does chess exist? 
>>It does in our heads.  But without us it wouldn't.
> 
> 
> What more could we possibly ask of a theorem other than that it be true 
> relative to some 
> axioms? That a theorem should describe some aspect of the real world, or that 
> it should 
> be discovered by some mathematician, is contingent on the nature of the real 
> world, but that 
> it is true is not.

That it is a true description of the real world, or that it is a true theorem 
relative to the axioms.  It is a mistake to conflate the two, which I suspect 
is 
done by people claiming mathematical theorems are true.

Brent Meeker

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

[Stathis Papaioannou]

Günther writes:

> Well, let's see: in Alice in Wonderland, Humpty Dumpty fell off a
> wall. This is true, isn't it? It is certainly true independent
> of our minds. Indeed, it is true in such a way that even when
> all humans have died, this universe will have a contained a life-form
> which produced an author who wrote a book in which Humpty Dumpty
> fell off a wall. But neither Humpty Dumpty nor the fact that he
> fell off a wall were ever true in this universe - only that this
> story was written, and that many people read about it and could
> converse about it.
> 
> So if you believe that numbers have an independent existence, then you
> would definitely also have to believe that Humpty Dumpty exists.
> Both are products of the mind. Either both exist, or both don't
> (other than as brain patterns).
> 
> As much as I would like Humpty Dumpty to exist, I'm afraid that
> it is not so.

The existence of numbers is not like the existence of objects, and I don't 
think that most mathematical Platonists would say that it is. It is indeed 
true independent of our minds that, if someone were to write a story 
in which Humpty Dumpty falls off the wall, then Humpty Dumpty would fall 
off the wall in that story. That is different to saying that Humpty Dumpty 
actually did fall off the wall in the real world, such as it is. It is also 
true 
that given the axioms of Euclidian geometry, the angles in a triangle add 
up to 180 degrees, and this is so independently of whether the angles of 
a triangle in the real world add up to 180 degrees, or whether Euclid ever 
lived.

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

[Stathis Papaioannou]

Brent Meeker writes:
 
> 1Z wrote:
> > 
> > Stathis Papaioannou wrote:
> ...
> >>I've never really understood why computationalists insist that a system
> >>must be able to handle counterfactuals in order for consciousness to occur,
> > 
> > 
> > I've explained that several times: computer programmes contain
> > if-then statements.
> > 
> > 
> >>other than that otherwise any physical system could be seen as implementing
> >>any computation, which does not seem to me a good reason. In any case,
> >>Maudlin shows that the requirement for handling counterfactuals leads to
> >>a situation where of two systems with identical physical activity, one is
> >>conscious and the other not.
> > 
> > 
> > If two systems differ counterfactually, they are not physically
> > identical.
> 
> I don't think I understand this either.  Computer programs contain if-then 
> statements which branch the process depending on the data input to the 
> program. 
>   But there is no real distinction between data an program.  So if you insist 
> that  computed intelligence or consciousness depends on counterfactuals in 
> the 
> program that seems to me to be the same as insisting that the computation is 
> implemented in some way that divides it from input data, i.e. it is in an 
> environment.
> 
> I'm sympathetic to this view.  I think intelligence is relative to an 
> environment.  But I'm not sure what computationalists think of this; I 
> believe 
> they suppose the environment can be simulated too and so then the whole thing 
> is 
> a closed system and there are no conuterfactual branchings.
> 
> Brent Meeker

Is it possible that we are currently actors in a single, deterministic, 
non-branching 
computer program, with the illusion of free will and if-then contingency in 
general 
being due to the fact that we don't know the details of how the program will 
play 
out?

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

[Stathis Papaioannou]

Brent Meeker writes:

> > Even if you say that, there is still a sense in which arithmetic is 
> > independent of the 
> > real world. The same can be said of Euclidian geometry: it follows from 
> > Euclid's axioms 
> > *despite* the fact that real space is not Euclidian. The fact that real 
> > space is not 
> > Euclidian means that Euclidian geometry does not describe the real world, 
> > not that 
> > it is false or non-existent.
> > 
> > Stathis Papaioannou
> 
> But the fact that a theorem is true relative to some axioms doesn't make it 
> true 
> or existent.  Some mathematicians I know regard it as a game.  Is true that a 
> bishop can only move diagonally?  It is relative to chess.  Does chess exist? 
> It does in our heads.  But without us it wouldn't.

What more could we possibly ask of a theorem other than that it be true 
relative to some 
axioms? That a theorem should describe some aspect of the real world, or that 
it should 
be discovered by some mathematician, is contingent on the nature of the real 
world, but that 
it is true is not.

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

[Stathis Papaioannou]

Peter Jones writes (quoting SP):

> > I've never really understood why computationalists insist that a system
> > must be able to handle counterfactuals in order for consciousness to occur,
> 
> I've explained that several times: computer programmes contain
> if-then statements.
> 
> > other than that otherwise any physical system could be seen as implementing
> > any computation, which does not seem to me a good reason. In any case,
> > Maudlin shows that the requirement for handling counterfactuals leads to
> > a situation where of two systems with identical physical activity, one is
> > conscious and the other not.
> 
> If two systems differ counterfactually, they are not physically
> identical.

What about an inputless computer program, running deterministically like a 
recording. 
Would that count as a program at all, and could it be a conscious program, 
given that 
computationalism is true?

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

[Colin Geoffrey Hales]

>
>
>
> 1Z wrote:
>
>> Not even remotely. I fact, what I have said can be written as two valid
>> syllogisms.
>>
>> Existence is availability for causal interaction
>> Numbers are not available for causal interaction
>> Numbers do not exist
>>
>> Platonism is the claim that numbers exist
>> Numbers do not exist
>> Platonism is false
>
> Wonderful!
>

What about real-world 'existent' causal interaction that _causally_
behaves 'as-if' a platonic 'quantity' exists to interact with? Same for
the non-existant platonic object RED. Same for the non-existant platonic
object ORGASM.

What is the existence status of the causality thus instantiated? What
aspect of the platonic object map to the subsequent causally existent of
the interaction?

If it 'like something' to be an 'existent' causal interaction,
ever(and it most certainly can be in brain material)
then what would it be 'like' to be a virtual interaction with a
platonic object?

They may not exist, but they may be 'examinable'.

Indeed... I'd say it could 'be like' QUANTITYness, REDness and
ORGASMness... to some extent, anyway.

If you insist that everything is shoved into 'realism' or 'platonism',
just because we have the words...you miss entirely a wonderful
intermediate class of existence.

Colin Hales
(where's my 'Law of Science' post gone?)


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

[Brent Meeker]

complexitystudies wrote:
> 
>>I think it has been said several times :
>>
>>The existence of a number/arithmetical proposition is the fact that its 
>>existence/truth does not depend on the fact that you exist/that it exists 
>>conscious beings capable of thinking of it.
>>
>>So the truth value of a proposition is independant of me.
> 
> 
> Well, let's see: in Alice in Wonderland, Humpty Dumpty fell off a
> wall. This is true, isn't it? It is certainly true independent
> of our minds. Indeed, it is true in such a way that even when
> all humans have died, this universe will have a contained a life-form
> which produced an author who wrote a book in which Humpty Dumpty
> fell off a wall. But neither Humpty Dumpty nor the fact that he
> fell off a wall were ever true in this universe - only that this
> story was written, and that many people read about it and could
> converse about it.
> 
> So if you believe that numbers have an independent existence, then you
> would definitely also have to believe that Humpty Dumpty exists.
> Both are products of the mind. Either both exist, or both don't
> (other than as brain patterns).
> 
> As much as I would like Humpty Dumpty to exist, I'm afraid that
> it is not so.
> 
> Regards,
> Günther

I agree.  But truth need not imply existence.  That's the idea of "free logic" 
(i.e. free of existential suppositions).  So one can say "Shelock Holmes lived 
on Baker Street." is true and "Sherlock Holmes drove a car." is false.  But 
then 
some statments, such as "Sherlock Holmes had a mole on his left side." are 
neither true nor false.

Brent Meeker

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

[Brent Meeker]

complexitystudies wrote:
...
> 
> 
> Not exactly. Animals and babies can distinguish up to 2-3 objects
> (innate arithmetic, subitizing). The experiments with which this has
> been ascertained are both fascinating and entertaining (google is your
> friend ;-)
> This ability has an evolutionary advantage: it is necessary for higher
> organisms to distinguish more or less abundant food sources or numbers
> of predators. But this meaning this "countability", arises out of the
> physical world, and is not independent of it.

The experiment I recall from the '50s was with crows.  If men went into a blind 
in the middle of a corn field where crows were feeding the crows would fly up 
into the surrounding trees.  Then the men would leave one or two at a time.  If 
the number were five or fewer the crows would know when the last one had left 
and immediately come back to feed.  With six they were sometimes wrong.  With 
seven or more they would wait and then return cautiously a few at a time.

Of course they probably weren't counting, mapping cardinality to sequence, but 
they had the concept of number.

Brent Meeker

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

[complexitystudies]

Bruno Marchal wrote:
> 
> Le 17-août-06, à 00:14, complexitystudies a écrit :
> I recall it is just the belief that the
> propositions of elementary arithmetic are independent of you. Do you 
> sincerley belief that 37 could be a non prime number? Or that the 
> square root of 2 can equal to a ratio of two integers?
> Or that if you run a program fortran it could neither stop nor not 
> stop?  (When all the default assumption are on, to evacuate contingent 
> stopping of a machine implemented in some deep story)?

As 1Z has so nicely put, existence implies causal interaction.
Numbers cannot causally interact, therefore they do not exist,
save as thoughts in our brains.

Of course I do not believe that 37 could be a non prime number,
simply because what it means to be "prime" has been exactly
defined in arithmetic. I just say that these are thought constructs
with no independent existence (independent of human brains, not of a
concrete human brain).

You might say, that 37 was prime even in the Jurassic, but I say:
nobody had invented arithmetic yet, so it's about as true as the
fact that James Bond was played by Sean Connery was in the Jurassic.

I define a system:

1 + 1 = 2
2 + 1 = 1
1 + 2 = 1

That's all. Okay, it doesn't describe much and probably isn't very
useful, but other than that it is not inferior to peano arithmetic.
Does my system now exist mind-independtly for all eternity?


> I have not yet seen a book on human brain which does not presuppose the 
> understanding of the natural numbers. 

Of course, because it is a useful way to describe reality. But in our
brains, not numbers operate, but chemicals.

> Numbers are not symbol. Symbols can be used to talk about numbers, but 
> they should not be confused with numbers.

You are right there of course. Symbols are only referents. What counts
is meaning. What I meant to say is that the meanings we assign to number
symbols exist only in our minds. Indeed, meaning _is_ only created by
interactions between an agent and an environment. With both of these,
no meaning. Indeed, in an mind-and-matter independent (=non existing
)universe, arithmetic would be about as meaningless as it gets.



> The notion of "same number" seems to have occur much before we 
> discovered counting. Farmers have most probably learn to compare the 
> size of the herds of sheep without counting, just by associating each 
> sheep from one herd to the another. But this as nothing to do with the 
> fact that sheeps were "countable" before humans learn to count it.
> Humans and brains learn to count countable things because they are 
> countable.

Not exactly. Animals and babies can distinguish up to 2-3 objects
(innate arithmetic, subitizing). The experiments with which this has
been ascertained are both fascinating and entertaining (google is your
friend ;-)
This ability has an evolutionary advantage: it is necessary for higher
organisms to distinguish more or less abundant food sources or numbers
of predators. But this meaning this "countability", arises out of the
physical world, and is not independent of it.


> I think you are confusing the subject or object of math, and the human 
> mathematical theories, which are just lantern putting a tiny light on 
> the subject.

Indeed I am not. I am just saying that there is no independent subject
of math outside of human brains. Mathematics is the study of rules we
make up (axioms) and what follows of them (theorems).
If we pick our axioms wisely, we can even model some aspects of the
real, physical world with it.

> If numbers and their math was really invented, why should 
> mathematicians hide some results, like Pythagoras with the 
> irrationality of the square root of two, ... As David Deutsch says: 
> math kicks back.

That is very easy: the Pythagoreans assumed axioms, and thought they
knew what would follow from them. Then, to their dismay, they found
out that also somewhat else followed from the axioms than they had
ideally envisioned, something that displeased their aesthetic sense.
Only human factors involved here,
no independent existence of math. It just shows how limited our thought
is, and that we do not even anticipate theorems that follow from our
axioms when they are rather simple.

> 
>> Also, concepts like infinity are most definitely not universal
>> concepts "out there", but products of our mind.
> 

> I doubt any mind could ever produce infinity.

But indeed, _only_ minds produce them, because, as you say, infinity
is a concept, and concepts exist only in minds.

In reality, there is no such thing as infinity. Even if space
would expand infinitely, this "infinity" would not exist as a thing
(except in the trivial *lol* sense as the universe exists), but would
be a concept for us humans to talk about it.
Concepts need not be precisely understood as to be concepts.
For example, consciousness is definitely not understood, but talked
about a lot.

How does the human mind create the concept of infinity:
Lakoff

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

[Quentin Anciaux]

Hi,

Le Vendredi 18 Août 2006 22:17, complexitystudies a écrit :
> > I think it has been said several times :
> >
> > The existence of a number/arithmetical proposition is the fact that its
> > existence/truth does not depend on the fact that you exist/that it exists
> > conscious beings capable of thinking of it.
> >
> > So the truth value of a proposition is independant of me.
>
> Well, let's see: in Alice in Wonderland, Humpty Dumpty fell off a
> wall. This is true, isn't it? It is certainly true independent
> of our minds. Indeed, it is true in such a way that even when
> all humans have died, this universe will have a contained a life-form
> which produced an author who wrote a book in which Humpty Dumpty
> fell off a wall. But neither Humpty Dumpty nor the fact that he
> fell off a wall were ever true in this universe - only that this
> story was written, and that many people read about it and could
> converse about it.
>
> So if you believe that numbers have an independent existence, then you
> would definitely also have to believe that Humpty Dumpty exists.
> Both are products of the mind. Either both exist, or both don't
> (other than as brain patterns).

Well, if computationalism is true, then there exists observer moment of an "I" 
(not talking about me here ;) who is Humpty Dumpty, so there is an universe 
where Humpty Dumpty exists in the same sense I exist. The fact that in our 
universe Humpty Dumpty only exist in a story does not tell anything about a 
real Humpty Dumpty living in (at least) one (but in fact an infinity) of the 
computed universe by for example the UD (Universal Dovetailer). You must at 
least accept multiple world, ie a multiverse. This multiverse should also be 
fairly large (the UD trace is very very large ;).

Now I think UD could be false if it is impossible to have a real turing 
machine (no memory bound, no time bound), because if it is possible then the 
majority of OM will be computed by the UD, so the probability of your current 
OM being computed on a "physical" computer is zero. UD could also be false if 
we are not turing emulable... ie consciousness is not a computation 
process... but physicalism doesn't tell what it is then.

Regards,
Quentin

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

[1Z]

Brent Meeker wrote:
> 1Z wrote:
> >
> > Brent Meeker wrote:
> >
> >>1Z wrote:
> ...
> >>>If two systems differ counterfactually, they are not physically
> >>>identical.
> >>
> >>I don't think I understand this either.
> >
> >
> > Either that, or counterfactuallity is  asupernatural phenomenon.
> >
> >
> >>Computer programs contain if-then
> >>statements which branch the process depending on the data input to the 
> >>program.
> >>  But there is no real distinction between data an program.
> >
> >
> > There is a difference between data and process --i.e. running
> > programme.
>
> I don't disagree, but I don't see what that has to do with programs having
> if-thens.  Given the program and the data, the process is only going down one
> branch.

But that's not what makes it computation. What makes
it computation is behaving differently for different data.

> So when you talk about counterfactuals it must be because you are
> considering other possible data as input.

> > Standard computationalism says mentation (as an activity)
> > is computation (as  a process). It is a rare computationalist
> > who think that a spool of tape gathering dust in a cupboardi
> > is mentating. (Not much of a Yes Doctor).
> >
> >
> >>  So if you insist
> >>that  computed intelligence or consciousness depends on counterfactuals in 
> >>the
> >>program that seems to me to be the same as insisting that the computation is
> >>implemented in some way that divides it from input data, i.e. it is in an
> >>environment.
> >
> >
> > Well, it is divided -- by the programme/process distinction.
>
> That's the (program+data)/process distinction.  But ISTM that without a
> program/data distinction, counterfactuals are a distinction without a 
> difference.

I am saying there is a programme/data distinction, which rests on
the programme/process distinction.

> Brent Meeker


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

[complexitystudies]

1Z wrote:

> Not even remotely. I fact, what I have said can be written as two valid
> syllogisms.
> 
> Existence is availability for causal interaction
> Numbers are not available for causal interaction
> Numbers do not exist
> 
> Platonism is the claim that numbers exist
> Numbers do not exist
> Platonism is false

Wonderful!

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

[complexitystudies]

> I think it has been said several times :
> 
> The existence of a number/arithmetical proposition is the fact that its 
> existence/truth does not depend on the fact that you exist/that it exists 
> conscious beings capable of thinking of it.
> 
> So the truth value of a proposition is independant of me.

Well, let's see: in Alice in Wonderland, Humpty Dumpty fell off a
wall. This is true, isn't it? It is certainly true independent
of our minds. Indeed, it is true in such a way that even when
all humans have died, this universe will have a contained a life-form
which produced an author who wrote a book in which Humpty Dumpty
fell off a wall. But neither Humpty Dumpty nor the fact that he
fell off a wall were ever true in this universe - only that this
story was written, and that many people read about it and could
converse about it.

So if you believe that numbers have an independent existence, then you
would definitely also have to believe that Humpty Dumpty exists.
Both are products of the mind. Either both exist, or both don't
(other than as brain patterns).

As much as I would like Humpty Dumpty to exist, I'm afraid that
it is not so.

Regards,
Günther

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

[Brent Meeker]

1Z wrote:
> 
> Brent Meeker wrote:
> 
>>1Z wrote:
...
>>>If two systems differ counterfactually, they are not physically
>>>identical.
>>
>>I don't think I understand this either.
> 
> 
> Either that, or counterfactuallity is  asupernatural phenomenon.
> 
> 
>>Computer programs contain if-then
>>statements which branch the process depending on the data input to the 
>>program.
>>  But there is no real distinction between data an program.
> 
> 
> There is a difference between data and process --i.e. running
> programme.

I don't disagree, but I don't see what that has to do with programs having 
if-thens.  Given the program and the data, the process is only going down one 
branch.  So when you talk about counterfactuals it must be because you are 
considering other possible data as input.

> Standard computationalism says mentation (as an activity)
> is computation (as  a process). It is a rare computationalist
> who think that a spool of tape gathering dust in a cupboardi
> is mentating. (Not much of a Yes Doctor).
> 
> 
>>  So if you insist
>>that  computed intelligence or consciousness depends on counterfactuals in the
>>program that seems to me to be the same as insisting that the computation is
>>implemented in some way that divides it from input data, i.e. it is in an
>>environment.
> 
> 
> Well, it is divided -- by the programme/process distinction.

That's the (program+data)/process distinction.  But ISTM that without a 
program/data distinction, counterfactuals are a distinction without a 
difference.

Brent Meeker

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

[1Z]

Brent Meeker wrote:
> 1Z wrote:
> >
> > Stathis Papaioannou wrote:
> ...
> >>I've never really understood why computationalists insist that a system
> >>must be able to handle counterfactuals in order for consciousness to occur,
> >
> >
> > I've explained that several times: computer programmes contain
> > if-then statements.
> >
> >
> >>other than that otherwise any physical system could be seen as implementing
> >>any computation, which does not seem to me a good reason. In any case,
> >>Maudlin shows that the requirement for handling counterfactuals leads to
> >>a situation where of two systems with identical physical activity, one is
> >>conscious and the other not.
> >
> >
> > If two systems differ counterfactually, they are not physically
> > identical.
>
> I don't think I understand this either.

Either that, or counterfactuallity is  asupernatural phenomenon.

> Computer programs contain if-then
> statements which branch the process depending on the data input to the 
> program.
>   But there is no real distinction between data an program.

There is a difference between data and process --i.e. running
programme.

Standard computationalism says mentation (as an activity)
is computation (as  a process). It is a rare computationalist
who think that a spool of tape gathering dust in a cupboardi
is mentating. (Not much of a Yes Doctor).

>   So if you insist
> that  computed intelligence or consciousness depends on counterfactuals in the
> program that seems to me to be the same as insisting that the computation is
> implemented in some way that divides it from input data, i.e. it is in an
> environment.

Well, it is divided -- by the programme/process distinction.

> I'm sympathetic to this view.  I think intelligence is relative to an
> environment.  But I'm not sure what computationalists think of this; I believe
> they suppose the environment can be simulated too and so then the whole thing 
> is
> a closed system and there are no conuterfactual branchings.
> 
> Brent Meeker


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

[1Z]

Brent Meeker wrote:

> But the fact that a theorem is true relative to some axioms doesn't make it 
> true
> or existent.

It doesn't make it *false* relative to those axioms. It has
to be estbalished that a mathematical statement needs to or
can aspire to further kinds of truth,


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

[Brent Meeker]

1Z wrote:
> 
> Stathis Papaioannou wrote:
...
>>I've never really understood why computationalists insist that a system
>>must be able to handle counterfactuals in order for consciousness to occur,
> 
> 
> I've explained that several times: computer programmes contain
> if-then statements.
> 
> 
>>other than that otherwise any physical system could be seen as implementing
>>any computation, which does not seem to me a good reason. In any case,
>>Maudlin shows that the requirement for handling counterfactuals leads to
>>a situation where of two systems with identical physical activity, one is
>>conscious and the other not.
> 
> 
> If two systems differ counterfactually, they are not physically
> identical.

I don't think I understand this either.  Computer programs contain if-then 
statements which branch the process depending on the data input to the program. 
  But there is no real distinction between data an program.  So if you insist 
that  computed intelligence or consciousness depends on counterfactuals in the 
program that seems to me to be the same as insisting that the computation is 
implemented in some way that divides it from input data, i.e. it is in an 
environment.

I'm sympathetic to this view.  I think intelligence is relative to an 
environment.  But I'm not sure what computationalists think of this; I believe 
they suppose the environment can be simulated too and so then the whole thing 
is 
a closed system and there are no conuterfactual branchings.

Brent Meeker

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

[Brent Meeker]

Stathis Papaioannou wrote:
> Brent Meeker writes (quoting Peter Jones and SP):
> 
> 
Arithemtical Platonism is the belief that mathematical
structures *exist* independently of you,
not just that they are true independently of you.
>>>
>>>
>>>What's the difference?
>>>
>>>Stathis Papaioannou
>>
>>You could regard the theorems of arithmetic as just being relative to Peano's 
>>axioms: "1+1=2 assuming Peano"  Somewhat as Bruno presents his theorems as 
>>relative to the "axiom" of COMP.
>>
>>Brent Meeker
> 
> 
> Even if you say that, there is still a sense in which arithmetic is 
> independent of the 
> real world. The same can be said of Euclidian geometry: it follows from 
> Euclid's axioms 
> *despite* the fact that real space is not Euclidian. The fact that real space 
> is not 
> Euclidian means that Euclidian geometry does not describe the real world, not 
> that 
> it is false or non-existent.
> 
> Stathis Papaioannou

But the fact that a theorem is true relative to some axioms doesn't make it 
true 
or existent.  Some mathematicians I know regard it as a game.  Is true that a 
bishop can only move diagonally?  It is relative to chess.  Does chess exist? 
It does in our heads.  But without us it wouldn't.

Brent Meeker

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

[1Z]

Quentin Anciaux wrote:
> Le Vendredi 18 Août 2006 14:21, 1Z a écrit :
> > Quentin Anciaux wrote:
> > > Hi,
> > >
> > > Le vendredi 18 août 2006 11:52, 1Z a écrit :
> > > > Stathis Papaioannou wrote:
> > > > > Peter Jones writes (quoting Bruno Marchal):
> > > > > > > Frankly I don't think so. Set platonism can be considered as a
> > > > > > > bold assumption, but number platonism, as I said you need a
> > > > > > > sophisticated form of finitism to doubt it. I recall it is just
> > > > > > > the belief that the propositions of elementary arithmetic are
> > > > > > > independent of you.
> > > > > >
> > > > > > Arithemtical Platonism is the belief that mathematical
> > > > > > structures *exist* independently of you,
> > > > > > not just that they are true independently of you.
> > > > >
> > > > > What's the difference?
> > > >
> > > > Things that exist are available for causal interaction. Numbers aren't.
> > >
> > > You were defining arithmetical platonism and now you define existing.
> > > Your two comments are contradictory.
> >
> > Not even remotely. I fact, what I have said can be written as two valid
> > syllogisms.
>
> Yes you were... You were denying the definition of Bruno (arithmetical
> realism) by giving yours


Firstly, that isn't *self* contradiciton.

Secondly, Bruno's approach is ambiguous. (If he clearly states
that AR is only about truth and not about existence, he can't claim
that
matter doesn't exist if COMP is true, because "matter doesn't exist"
is an existential statement and COMP (absent Platonism) isn't.
If he clearly states AR ia about existence, he can no longer
claim that COMP is his only premiss).

> ... then Bruno and Stathis ask for the difference
> between yours and their definition.

Defintion of what ? Existence ? Yes, I do have
a different definition.

> .. Which you respond with a contradiction
> to say platonism is false...

Platonism *is* false using my definitions. They must
be using  a different defintion. That still doesn't
mean I am contradicting *myself*. I may be comtradicting other peopel:
well,
people are allowed to contradict each other.

> then either you were effectively contradicting
> yourself or you did not answer Stathis and Bruno question (it's one or the
> other).



> > Existence is availability for causal interaction
> > Numbers are not available for causal interaction
> > Numbers do not exist
>
> That's your definition of existence... this is your claim. Now a definition
> game will not resolve this problem obviously.

Then the problem cannot be solved at all, since there is no
other way of solving abstract problems. (All mathematical
problems are solved using definitions!)

Why, BTW, do you assume there is no way
of arriving at the correct definition ? Isn't that
what dictionaries are for.

> > Platonism is the claim that numbers exist
> > Numbers do not exist
> > Platonism is false
>
> Platonism does not claim number exist by your definition of existence hence
> your conclusion is ill based.

It isn't false if my definition of existence is the only defintion.
The ball is in the Platonists' court: they need to come
up with another definition of existence.

However, they presumably don't have one, or they would not be
asking me what "existence" means.


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

[1Z]

Quentin Anciaux wrote:
> Le Vendredi 18 Août 2006 17:02, 1Z a écrit :
> > Stathis Papaioannou wrote:
> > > Peter Jones writes:
> > > > > What's the difference?
> > > >
> > > > Things that exist are available for causal interaction. Numbers aren't.
> > >
> > > What could it possibly mean for numbers to "exist" in the sense you claim
> > > they do not? Could I be mugged by a burly number 6 in a dark alley? I
> > > don't think that even number-worshipping Pythagoras would have
> > > entertained such a notion.
> >
> > It is for Pythagorenas and Platonists to explain what they mean by
> > "exist".
>
> I think it has been said several times :
>
> The existence of a number/arithmetical proposition is the fact that its
> existence/truth does not depend on the fact that you exist/that it exists
> conscious beings capable of thinking of it.

That is an explanation of mind-independence, not of  existence.
The anti-Platonist (e.g. the formalist) can claim that
the truth of mathematical statments is mind-independent,
but their existence isn't.


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

[Quentin Anciaux]

Le Vendredi 18 Août 2006 17:02, 1Z a écrit :
> Stathis Papaioannou wrote:
> > Peter Jones writes:
> > > > What's the difference?
> > >
> > > Things that exist are available for causal interaction. Numbers aren't.
> >
> > What could it possibly mean for numbers to "exist" in the sense you claim
> > they do not? Could I be mugged by a burly number 6 in a dark alley? I
> > don't think that even number-worshipping Pythagoras would have
> > entertained such a notion.
>
> It is for Pythagorenas and Platonists to explain what they mean by
> "exist".

I think it has been said several times :

The existence of a number/arithmetical proposition is the fact that its 
existence/truth does not depend on the fact that you exist/that it exists 
conscious beings capable of thinking of it.

So the truth value of a proposition is independant of me.

Quentin

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

[1Z]

Stathis Papaioannou wrote:
> Peter Jones writes:
>
> > Stathis Papaioannou wrote:
> > > Peter Jones writes:
> > >
> > > > A claim about truth as opposed to existence cannot
> > > > support the conclusion that matter does not actually exist.
> > >
> > > It can if you can show that the mental does not supervene
> > > on the physical.
> >
> > I don't see how that is connected,
>
> If you can conceptualise of a virtual reality generated by a computation
> or a mind, and that computation or mind does not require physical
> hardware on which to run, then it is possible (Bruno argues, necessary)
> that our reality is a virtual reality without any underlying "real" world.


A "virtual reality" that is being "generated" is an existing (in some
sense)
virtual reality that is being really (in some sense)
generated.

A computation that does not require
physical hardware is either non-existent simpliciter
(in which case we are simply not such a computation, since nothing
existing is identical to anythig non-existing) or it exists
Platonically
(non-physically, in some sense),

A valid argument cannot, in genral, come to a conlusion
that is not already implcit in its premises.

Either existence is implict in the "virtual reality" premiss, or it
isn't. If it is, a Platonic quesiton is being begged. If it isn't,
the existential conclusion is invalid.

> > and I don't want to claim that the mental
> > does not supervene on the physical.
>
> I didn't think you would.
>
> > > This is far from a generally accepted fact,
> > > but I am not yet aware of convincing arguments
> > > against the sort of challenge posed to the supervenience
> > > theory by eg. Tim Maudlin - unless you reject computationalism.
> >
> > Materialism/physicalism is better supported than computationalism.
>
> Maybe, but mind would be something very mysterious if it isn't computation,

Most things aren't computation. Most things also aren't mysterious.

> and mysteriouness goes against the grain for physicalists.



> > Maudlin's arguments rest on the  idea that physicalists must ignore
> > counterfactuals.
> > That assumption can  easilly be abandoned.
>
> I've never really understood why computationalists insist that a system
> must be able to handle counterfactuals in order for consciousness to occur,

I've explained that several times: computer programmes contain
if-then statements.

> other than that otherwise any physical system could be seen as implementing
> any computation, which does not seem to me a good reason. In any case,
> Maudlin shows that the requirement for handling counterfactuals leads to
> a situation where of two systems with identical physical activity, one is
> conscious and the other not.

If two systems differ counterfactually, they are not physically
identical.

> If anyone should find such an idea unpalatable
> it should be the physicalists.

So I am told, but I remain unconvinced.

> Stathis Papaioannou
>
> _
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Re: Platonism vs Realism WAS: ROADMAP (well, not yet really...

[1Z]

Stathis Papaioannou wrote:
> Peter Jones writes:

> > > What's the difference?
> >
> >
> > Things that exist are available for causal interaction. Numbers aren't.
>
> What could it possibly mean for numbers to "exist" in the sense you claim
> they do not? Could I be mugged by a burly number 6 in a dark alley? I don't
> think that even number-worshipping Pythagoras would have entertained
> such a notion.

It is for Pythagorenas and Platonists to explain what they mean by
"exist".

However, if you are going to claim that we are actually *in* Platonia,
(mathematical monism) there must be some equivalence between the
existence we
have and the existence numbers have.


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

[Quentin Anciaux]

Le Vendredi 18 Août 2006 14:21, 1Z a écrit :
> Quentin Anciaux wrote:
> > Hi,
> >
> > Le vendredi 18 août 2006 11:52, 1Z a écrit :
> > > Stathis Papaioannou wrote:
> > > > Peter Jones writes (quoting Bruno Marchal):
> > > > > > Frankly I don't think so. Set platonism can be considered as a
> > > > > > bold assumption, but number platonism, as I said you need a
> > > > > > sophisticated form of finitism to doubt it. I recall it is just
> > > > > > the belief that the propositions of elementary arithmetic are
> > > > > > independent of you.
> > > > >
> > > > > Arithemtical Platonism is the belief that mathematical
> > > > > structures *exist* independently of you,
> > > > > not just that they are true independently of you.
> > > >
> > > > What's the difference?
> > >
> > > Things that exist are available for causal interaction. Numbers aren't.
> >
> > You were defining arithmetical platonism and now you define existing.
> > Your two comments are contradictory.
>
> Not even remotely. I fact, what I have said can be written as two valid
> syllogisms.

Yes you were... You were denying the definition of Bruno (arithmetical 
realism) by giving yours... then Bruno and Stathis ask for the difference 
between yours and their definition... Which you respond with a contradiction 
to say platonism is false... then either you were effectively contradicting 
yourself or you did not answer Stathis and Bruno question (it's one or the 
other).

> Existence is availability for causal interaction
> Numbers are not available for causal interaction
> Numbers do not exist

That's your definition of existence... this is your claim. Now a definition 
game will not resolve this problem obviously.

> Platonism is the claim that numbers exist
> Numbers do not exist
> Platonism is false

Platonism does not claim number exist by your definition of existence hence 
your conclusion is ill based.

Quentin

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

[Stathis Papaioannou]

Peter Jones writes:

> Stathis Papaioannou wrote:
> > Peter Jones writes:
> >
> > > A claim about truth as opposed to existence cannot
> > > support the conclusion that matter does not actually exist.
> >
> > It can if you can show that the mental does not supervene
> > on the physical.
> 
> I don't see how that is connected,

If you can conceptualise of a virtual reality generated by a computation
or a mind, and that computation or mind does not require physical 
hardware on which to run, then it is possible (Bruno argues, necessary) 
that our reality is a virtual reality without any underlying "real" world.

> and I don't want to claim that the mental
> does not supervene on the physical.

I didn't think you would.
 
> > This is far from a generally accepted fact,
> > but I am not yet aware of convincing arguments
> > against the sort of challenge posed to the supervenience
> > theory by eg. Tim Maudlin - unless you reject computationalism.
> 
> Materialism/physicalism is better supported than computationalism.

Maybe, but mind would be something very mysterious if it isn't computation, 
and mysteriouness goes against the grain for physicalists.

> Maudlin's arguments rest on the  idea that physicalists must ignore
> counterfactuals.
> That assumption can  easilly be abandoned.

I've never really understood why computationalists insist that a system 
must be able to handle counterfactuals in order for consciousness to occur, 
other than that otherwise any physical system could be seen as implementing 
any computation, which does not seem to me a good reason. In any case, 
Maudlin shows that the requirement for handling counterfactuals leads to 
a situation where of two systems with identical physical activity, one is 
conscious and the other not. If anyone should find such an idea unpalatable 
it should be the physicalists.

Stathis Papaioannou

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

[Stathis Papaioannou]

Peter Jones writes:

> Stathis Papaioannou wrote:
> > Peter Jones writes (quoting Bruno Marchal):
> >
> > > > Frankly I don't think so. Set platonism can be considered as a bold
> > > > assumption, but number platonism, as I said you need a sophisticated
> > > > form of finitism to doubt it. I recall it is just the belief that the
> > > > propositions of elementary arithmetic are independent of you.
> > >
> > > Arithemtical Platonism is the belief that mathematical
> > > structures *exist* independently of you,
> > > not just that they are true independently of you.
> >
> > What's the difference?
> 
> 
> Things that exist are available for causal interaction. Numbers aren't.

What could it possibly mean for numbers to "exist" in the sense you claim 
they do not? Could I be mugged by a burly number 6 in a dark alley? I don't 
think that even number-worshipping Pythagoras would have entertained 
such a notion. 

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

[1Z]

Quentin Anciaux wrote:
> Hi,
>
> Le vendredi 18 août 2006 11:52, 1Z a écrit :
> > Stathis Papaioannou wrote:
> > > Peter Jones writes (quoting Bruno Marchal):
> > > > > Frankly I don't think so. Set platonism can be considered as a bold
> > > > > assumption, but number platonism, as I said you need a sophisticated
> > > > > form of finitism to doubt it. I recall it is just the belief that the
> > > > > propositions of elementary arithmetic are independent of you.
> > > >
> > > > Arithemtical Platonism is the belief that mathematical
> > > > structures *exist* independently of you,
> > > > not just that they are true independently of you.
> > >
> > > What's the difference?
> >
> > Things that exist are available for causal interaction. Numbers aren't.

> You were defining arithmetical platonism and now you define existing. Your
> two comments are contradictory.

Not even remotely. I fact, what I have said can be written as two valid
syllogisms.

Existence is availability for causal interaction
Numbers are not available for causal interaction
Numbers do not exist

Platonism is the claim that numbers exist
Numbers do not exist
Platonism is false


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

[1Z]

Stathis Papaioannou wrote:
> Peter Jones writes:
>
> > A claim about truth as opposed to existence cannot
> > support the conclusion that matter does not actually exist.
>
> It can if you can show that the mental does not supervene
> on the physical.

I don't see how that is connected,
and I don't want to claim that the mental
does not supervene on the physical.

> This is far from a generally accepted fact,
> but there but I am not yet aware of convincing arguments
> against the sort of challenge posed to the supervenience
> theory by eg. Tim Maudlin - unless you reject computationalism.

Materialism/physicalism is better supported than computationalism.

Maudlin's arguments rest on the  idea that physicalists must ignore
counterfactuals.
That assumption can  easilly be abandoned.

> Stathis Papaioannou
>
> _
> Be one of the first to try Windows Live Mail.
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RE: Platonism vs Realism WAS: ROADMAP (well, not yet really...

[Stathis Papaioannou]

Brent Meeker writes (quoting Peter Jones and SP):

> >>Arithemtical Platonism is the belief that mathematical
> >>structures *exist* independently of you,
> >>not just that they are true independently of you.
> > 
> > 
> > What's the difference?
> > 
> > Stathis Papaioannou
> 
> You could regard the theorems of arithmetic as just being relative to Peano's 
> axioms: "1+1=2 assuming Peano"  Somewhat as Bruno presents his theorems as 
> relative to the "axiom" of COMP.
> 
> Brent Meeker

Even if you say that, there is still a sense in which arithmetic is independent 
of the 
real world. The same can be said of Euclidian geometry: it follows from 
Euclid's axioms 
*despite* the fact that real space is not Euclidian. The fact that real space 
is not 
Euclidian means that Euclidian geometry does not describe the real world, not 
that 
it is false or non-existent.

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

[Quentin Anciaux]

Hi,

Le vendredi 18 août 2006 11:52, 1Z a écrit :
> Stathis Papaioannou wrote:
> > Peter Jones writes (quoting Bruno Marchal):
> > > > Frankly I don't think so. Set platonism can be considered as a bold
> > > > assumption, but number platonism, as I said you need a sophisticated
> > > > form of finitism to doubt it. I recall it is just the belief that the
> > > > propositions of elementary arithmetic are independent of you.
> > >
> > > Arithemtical Platonism is the belief that mathematical
> > > structures *exist* independently of you,
> > > not just that they are true independently of you.
> >
> > What's the difference?
>
> Things that exist are available for causal interaction. Numbers aren't.
You were defining arithmetical platonism and now you define existing. Your 
two comments are contradictory. Because following your description of 
existing, mathematical structure are not available for causal interaction 
(like numbers... )

If you think you're not contradicting yourself, could you explain more in 
detail what you mean.

Regards,
Quentin Anciaux

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

[1Z]

Stathis Papaioannou wrote:
> Peter Jones writes (quoting Bruno Marchal):
>
> > > Frankly I don't think so. Set platonism can be considered as a bold
> > > assumption, but number platonism, as I said you need a sophisticated
> > > form of finitism to doubt it. I recall it is just the belief that the
> > > propositions of elementary arithmetic are independent of you.
> >
> > Arithemtical Platonism is the belief that mathematical
> > structures *exist* independently of you,
> > not just that they are true independently of you.
>
> What's the difference?


Things that exist are available for causal interaction. Numbers aren't.


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

[Brent Meeker]

Stathis Papaioannou wrote:
> Peter Jones writes (quoting Bruno Marchal):
> 
> 
>>>Frankly I don't think so. Set platonism can be considered as a bold
>>>assumption, but number platonism, as I said you need a sophisticated
>>>form of finitism to doubt it. I recall it is just the belief that the
>>>propositions of elementary arithmetic are independent of you.
>>
>>Arithemtical Platonism is the belief that mathematical
>>structures *exist* independently of you,
>>not just that they are true independently of you.
> 
> 
> What's the difference?
> 
> Stathis Papaioannou

You could regard the theorems of arithmetic as just being relative to Peano's 
axioms: "1+1=2 assuming Peano"  Somewhat as Bruno presents his theorems as 
relative to the "axiom" of COMP.

Brent Meeker

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

[Stathis Papaioannou]

Peter Jones writes:

> A claim about truth as opposed to existence cannot
> support the conclusion that matter does not actually exist.

It can if you can show that the mental does not supervene 
on the physical. This is far from a generally accepted fact, 
but there but I am not yet aware of convincing arguments 
against the sort of challenge posed to the supervenience 
theory by eg. Tim Maudlin - unless you reject computationalism.

Stathis Papaioannou

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

[Stathis Papaioannou]

Peter Jones writes (quoting Bruno Marchal):

> > Frankly I don't think so. Set platonism can be considered as a bold
> > assumption, but number platonism, as I said you need a sophisticated
> > form of finitism to doubt it. I recall it is just the belief that the
> > propositions of elementary arithmetic are independent of you.
> 
> Arithemtical Platonism is the belief that mathematical
> structures *exist* independently of you,
> not just that they are true independently of you.

What's the difference?

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

[1Z]

Bruno Marchal wrote:
> Le 17-août-06, à 16:41, 1Z a écrit :
>
> > Arithemtical Platonism is the belief that mathematical
> > structures *exist* independently of you,
> > not just that they are true independently of you.
>
> What is the difference between ""the proposition "it exists a prime
> number" is true independently of me", and the proposition "it exists a
> prime number (independently of me)"?

The contextual meaning of "exists".

What is the difference between

"Sherlock Holmes lives at 221B Baker Street"

and

"Sherlock Holmes lives" ?

> I can see a nuance, and that is why I prefer to use the expression "
> Arithmetical Realism (AR)" (and then I always define what I mean by
> that) instead of "platonism" (which I prefer to reserve when Plato is
> actually mentionned, like with the Theatetical definition of
> knowledge).

A claim about truth as opposed to existence cannot
support the conclusion that matter does not actually exist.


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

[Bruno Marchal]

Le 17-août-06, à 16:41, 1Z a écrit :

> Arithemtical Platonism is the belief that mathematical
> structures *exist* independently of you,
> not just that they are true independently of you.

What is the difference between ""the proposition "it exists a prime 
number" is true independently of me", and the proposition "it exists a 
prime number (independently of me)"?

I can see a nuance, and that is why I prefer to use the expression " 
Arithmetical Realism (AR)" (and then I always define what I mean by 
that) instead of "platonism" (which I prefer to reserve when Plato is 
actually mentionned, like with the Theatetical definition of 
knowledge).
Of course some people use some other term, and I just try not to bore 
people with terminological remark. You can take AR negatively as the 
statement : "arithmetical truth" is not a human construction or 
convention. It is not even a lobian machine invention, because I need 
numbers to define what is a digital machine. Perhaps you should focus 
on the reasoning to see how the expression are used, instead on 
focusing on terminological issues, if I may suggest.

Bruno


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


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

[1Z]

Bruno Marchal wrote:
> Le 17-août-06, à 00:14, complexitystudies a écrit :
>
> >
> >> Again we are discussing the arithmetical realism (which I just
> >> assume).
> >
> > A bold assumption, if I may say so.
>
>
> Frankly I don't think so. Set platonism can be considered as a bold
> assumption, but number platonism, as I said you need a sophisticated
> form of finitism to doubt it. I recall it is just the belief that the
> propositions of elementary arithmetic are independent of you.

Arithemtical Platonism is the belief that mathematical
structures *exist* independently of you,
not just that they are true independently of you.


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

[Bruno Marchal]

Le 17-août-06, à 00:14, complexitystudies a écrit :

>
>> Again we are discussing the arithmetical realism (which I just 
>> assume).
>
> A bold assumption, if I may say so.


Frankly I don't think so. Set platonism can be considered as a bold 
assumption, but number platonism, as I said you need a sophisticated 
form of finitism to doubt it. I recall it is just the belief that the 
propositions of elementary arithmetic are independent of you. Do you 
sincerley belief that 37 could be a non prime number? Or that the 
square root of 2 can equal to a ratio of two integers?
Or that if you run a program fortran it could neither stop nor not 
stop?  (When all the default assumption are on, to evacuate contingent 
stopping of a machine implemented in some deep story)?




> But my exploration into cognitive neuroscience has exposed to me
> how mathematical thinking comes about, and that it is indeed not
> separable from our human brains.


I have not yet seen a book on human brain which does not presuppose the 
understanding of the natural numbers. Note just for using the index, 
but in the neuronal explanation themselves, implicitly or explicitly.
Eventually with comp the brain itself appears as a construct of the 
mind. The mathematical mind of the "Lobian" machines. Those are the 
self-referentially correct universal (sufficiently chatty) machines.




> Numbers are symbols we create in our minds to communicate with
> fellow individuals about things of importance to us.


Numbers are not symbol. Symbols can be used to talk about numbers, but 
they should not be confused with numbers.



> To paraphrase Descartes very liberally:
> We group, therefore we can count.
>
> Our act of arbitrary grouping (made a bit less arbitrary by
> evolution, which makes us group things which are good to
> our survival, like gazelles and spears or berries) let's us
> count and communicate the number.


The notion of "same number" seems to have occur much before we 
discovered counting. Farmers have most probably learn to compare the 
size of the herds of sheep without counting, just by associating each 
sheep from one herd to the another. But this as nothing to do with the 
fact that sheeps were "countable" before humans learn to count it.
Humans and brains learn to count countable things because they are 
countable.
I think you are confusing the subject or object of math, and the human 
mathematical theories, which are just lantern putting a tiny light on 
the subject.

If numbers and their math was really invented, why should 
mathematicians hide some results, like Pythagoras with the 
irrationality of the square root of two, ... As David Deutsch says: 
math kicks back.



> For the universe "one apple" may not exist, because in effect
> there are only quarks interacting. And at this level indeterminacy
> strikes mercilessly, making it all but meaningless to count quarks.


You will not find a book explaining that "meaninglessness" without 
taking for granted the idea of counting at the start.



>
> Also, concepts like infinity are most definitely not universal
> concepts "out there", but products of our mind.


I doubt any mind could ever produce infinity.



> Of course, symbolisms are arbitrary, but physical instantiation makes
> all the difference.


(note that my goal consists in explaining "physical instantiation" 
without using "physical things" at all. My point is that if we 
postulate comp, then we have to do this).



>
>> Note that if you understand the whole UDA,
>
> Unfortunately, not yet, but I'm reading!


Ah, ok. UDA mainly shows that the mind-body problem is two times more 
difficult than most materialist are thinking. Indeed, with comp, matter 
can no more be explained by postulating a physical world. I let you 
discover that, and feel free to ask questions if you have a problem 
with UDA.



>
>> you should realize that the
>> price of assuming a physical universe (and wanting it to be related
>> with our experiences *and* our experiments) is to postulate that you
>> (and us, if you are not solipsistic) are not turing emulable. No
>> problem.
>
> Why is that so? Could you clarify this issue?



It is really the point of the UDA. It shows that computationalism (the 
idea that I am a digitalizable machine) is incompatible with "weak 
materialism" (the idea that there is a primary stuff or matter or 
aristotelian substances).




> Absolutely. But I think we have to start with our assumptions and
> try to scrutinize them very carefully. After all, we want to devote
> our minds to problems arising out of them during our lives, and
> thus the initial choice should not be made rashly, but only after
> careful review of our current body of knowledge.



OK, but don't forget that here the idea is also to get some 
contradiction from hypotheses, so as to abandon them.
But until now, comp leads only to weirdness, not contradiction. And 
then that weirdness seems to explain the quantum weirdness ... 
Intuitively and 

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

[Tom Caylor]

complexitystudies wrote:
> Hi Bruno,
>
> > Again we are discussing the arithmetical realism (which I just assume).
>
> A bold assumption, if I may say so.
>
> > To be clear on that hypothesis, I do indeed find plausible that the
> > number six is perfect, even in the case the "branes would not have
> > collide, no big bang, no physical universe".
> > Six is perfect just because its divisors are 1, 2, and 3; and that
> > 1+2+3 = 6. Not because I know that. I blieve the contrary: it is the
> > independent truth of "6 = sum of its proper divisors" than eventually
> > I, and you, can learn it.
>
> I understand your argumentation well, because maybe one or two years
> ago I said nearly the same sentences to colleagues.
> But my exploration into cognitive neuroscience has exposed to me
> how mathematical thinking comes about, and that it is indeed not
> separable from our human brains.
>
>
> > If you want, numbers are what makes any counting possible.
>
> Numbers are symbols we create in our minds to communicate with
> fellow individuals about things of importance to us.
>
> To paraphrase Descartes very liberally:
> We group, therefore we can count.
>
> Our act of arbitrary grouping (made a bit less arbitrary by
> evolution, which makes us group things which are good to
> our survival, like gazelles and spears or berries) let's us
> count and communicate the number.
>
> For the universe "one apple" may not exist, because in effect
> there are only quarks interacting. And at this level indeterminacy
> strikes mercilessly, making it all but meaningless to count quarks.
>
> Also, concepts like infinity are most definitely not universal
> concepts "out there", but products of our mind.
>

This sounds very much like my view of math.

>
> > It is not because some country put salt on pancakes that pancakes do
> > not exist there. Roman where writing 8 -3 for us 8 - 2. It is like
> > saying 3*7 = 25 on planet TETRA. They mean 3*7 = 21, they just put it
> > differently.
>
> Of course, symbolisms are arbitrary, but physical instantiation makes
> all the difference.
>
>
> > No problem. I see you assume a physical universe. I don't. We havejust
> > different theories.
>
> So, which experiment decides which is true? I think "platonism" derives
> it's power from misconceptions of the human mind.
> The unthinking stone would never construe such a thing as platonism.
> It would just exist - in a very real world ;-)
>
> >Note that if you understand the whole UDA,
>
> Unfortunately, not yet, but I'm reading!
>

The UDA is not precise enough for me, maybe because I'm a
mathematician?
I'm waiting for the interview, via the roadmap.

>
> > you should realize that the
> >price of assuming a physical universe (and wanting it to be related
> >with our experiences *and* our experiments) is to postulate that you
> >(and us, if you are not solipsistic) are not turing emulable. No
> >problem.
>
> Why is that so? Could you clarify this issue?
>
>
> >(I like to separate issues concerning the choice of theory, and issues
> >concerning propositions made *in* a theory, or accepting that theory).
>
> Absolutely. But I think we have to start with our assumptions and
> try to scrutinize them very carefully. After all, we want to devote
> our minds to problems arising out of them during our lives, and
> thus the initial choice should not be made rashly, but only after
> careful review of our current body of knowledge.
> 
> Best Regards,
> Günther


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