Re: Numbers in Space

[Bruno Marchal]

On 20 Sep 2012, at 19:16, Craig Weinberg wrote:




On Thursday, September 20, 2012 12:26:07 PM UTC-4, Bruno Marchal  
wrote:


On 20 Sep 2012, at 17:02, Craig Weinberg wrote:

 Here's another reductio ad absurdum illustration of comp.

 If the version of comp we are discussing here is independent of
 physics, then shouldn't it be possible for us to program universal
 machines using only empty space?

You are quite quick here, but have a good insight, as comp makes space
non clonable, indeterministic in the details, and plausibly Turing
universal, as QM confirms. The 0-body problem (the quantum vacuum) is
already Turing universal (I think). For classical physics you need
three bodies at least).


What about an ideal vacuum? Just lengths multiplying and adding  
enumerated bundles of lengths. No quantum.


It would not be Turing universal.








 Length can be quantified, so why can't we just use millimeters or
 Planck lengths as the basis for our enumeration, addition, and
 multiplication and directly program from our mind to space?

Who we? In the universe nearby it costs a lot of energy/money/time to
handle matter already gigantic compared to the Planck length.

Or are you suggesting we are already simulated by the quantum vacuum.
Very plausible, but comp asks for justifying this in arithmetic.

I'm saying that whatever program we access when we choose what we  
think about should be able to run just as easily in space as it does  
through the brain.


Or just arithmetic. You don't need space. Only addition and  
multiplication of integers. Or justapplication and abstraction on  
lambda terms, etc.




I should be able to pick an area of my house and leave a bunch of  
memories there and then come back to them later just be occupying  
the same space.


Not at all. You are distributed in the whole UD*. You can go back to  
your memory only if the measure on computations makes such a  
persistence possible. This needs to be justified with the self- 
reference logics, and that is what is done with S4Grz1, Z1* and X1*.




That's if we define space as relative to my house and not the  
rotating planet, revolving sun, etc.


So it sounds like you are not opposed to this idea of computation  
with no resources whatsoever besides space,


No need for spaces. To invoke it is already too much physicalist for  
comp.




provided that it could be justified arithmetically (which I don't  
understand why it wouldn't be. how does comp know if it's running on  
matter or space?)


By UDA. Anything physical must be justified with the material  
hypostases. Up to now, this works, even by giving the shadows of the  
reason why destructive interference of the computations occurs below  
our substitution level.


Bruno








 Of course, it would be hard to know where it was because we would be
 constantly flying away from a space that was anchored to an absolute
 position independent of Earth, the solar system, Milky Way, etc, but
 that shouldn't matter anyhow since whatever method we use to
 directly program in empty space with our minds should also give us
 access to the results of the computations.

?

I mean if I could stand completely still then the planet would fly  
off from under my feet and I would be left standing exactly where I  
was with the Earth revolving past me at 107,000 km/hr. I would  
occupy the same space while the Earth, Sun, and galaxy sweep away  
from me.


If instead of me, it was memories I had stashed away in space, then  
my body would be soon separated from the absolute position that I  
had placed them. It shouldn't matter though, since by the same  
method of thinking numbers into space, I should be able to retrieve  
them too, regardless of the distance between my body and the numbers.





 What do you think? Just as wafers of silicon glass could in theory
 be functionally identical to a living brain, wouldn't it be equally
 prejudiced to say that empty space isn't good enough to host the
 computations of silicon?

Empty space, in any turing universal theory, is equivalent with
universal dovetailing. It is a trivial theory, as when we assume comp,
the space and belief in spaces have to be justified through number
dreams statistics.

So you are saying yes to the space doctor?


The advantage of comp is that we can use math and more easily reason
clearly. We can formulate key parts of the mind body problem
mathematically.

I don't question that, and I think that it may ultimately be the  
only way of engineering mind body solutions - but I still think that  
if we really want to know the truth about mind body, we can only  
find that in the un-numbered, un-named meta-juxtapostions of  
experienced sense.



And computationalists are cool as they don't think twice before giving
the restaurant menu to the puppet who asks politely. They don't judge
people from their religion, skin color, clothes, or if made of wood,
or metal or flesh, as long as they behave respectfully of course.

I 

Re: Numbers in Space

[Bruno Marchal]

On 21 Sep 2012, at 03:39, Stephen P. King wrote:


On 9/20/2012 12:26 PM, Bruno Marchal wrote:


On 20 Sep 2012, at 17:02, Craig Weinberg wrote:


Here's another reductio ad absurdum illustration of comp.

If the version of comp we are discussing here is independent of  
physics, then shouldn't it be possible for us to program universal  
machines using only empty space?


You are quite quick here, but have a good insight, as comp makes  
space non clonable, indeterministic in the details, and plausibly  
Turing universal, as QM confirms. The 0-body problem (the quantum  
vacuum) is already Turing universal (I think). For classical  
physics you need three bodies at least).




Dear Bruno,

   I agree 100% with you. That the quantum vacuum is TU, is obvious  
to me. I think that Svozil has something written on this.. maybe or  
't Hoft.






Length can be quantified, so why can't we just use millimeters or  
Planck lengths as the basis for our enumeration, addition, and  
multiplication and directly program from our mind to space?


Who we? In the universe nearby it costs a lot of energy/money/time  
to handle matter already gigantic compared to the Planck length.


   Only because we are trying to do things the classical way...


?
Explain this to those who build the LHC.






Or are you suggesting we are already simulated by the quantum  
vacuum. Very plausible, but comp asks for justifying this in  
arithmetic.


   I am not sure if that is possible because it seems to me that  
that requires the specification of an uncountable infinity.


I don't see the problem. You might confuse Turing emulable and  
Turing recoverable. In the last case we take into account the first  
person indeterminacy, and comp already explains that it is uncountable.











Of course, it would be hard to know where it was because we would  
be constantly flying away from a space that was anchored to an  
absolute position independent of Earth, the solar system, Milky  
Way, etc, but that shouldn't matter anyhow since whatever method  
we use to directly program in empty space with our minds should  
also give us access to the results of the computations.


?




What do you think? Just as wafers of silicon glass could in theory  
be functionally identical to a living brain, wouldn't it be  
equally prejudiced to say that empty space isn't good enough to  
host the computations of silicon?


Empty space, in any turing universal theory, is equivalent with  
universal dovetailing. It is a trivial theory, as when we assume  
comp, the space and belief in spaces have to be justified through  
number dreams statistics.


   But the numbers build an arithmetic body


The numbers arithmetically dream of a non arithmetic body.


and then populate a space with multiple copies of it... so that they  
can implement the UD.


No, they are implemented by the UD, which exists like prime numbers  
exists. Primitively.






Their dreaming is this! http://en.wikipedia.org/wiki/Dreamlands



The advantage of comp is that we can use math and more easily  
reason clearly. We can formulate key parts of the mind body problem  
mathematically.


   I disagree. We can only formalize the mind, never the body, if we  
wish to never be inconsistent.


We can't formalize neither the (1p) mind nor the body.







And computationalists are cool as they don't think twice before  
giving the restaurant menu to the puppet who asks politely. They  
don't judge people from their religion, skin color, clothes, or if  
made of wood, or metal or flesh, as long as they behave  
respectfully of course.


   Maybe it is because they are really not people at all! They are  
algorithms hiding in a puppet.


In that case comp is false.


Bruno





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



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Re: Re: Numbers in Space

[Roger Clough]

Hi Jason Resch 

In the Platonic world space and time don't exist.


Roger Clough, rclo...@verizon.net
9/21/2012 
Forever is a long time, especially near the end. -Woody Allen


- Receiving the following content - 
From: Jason Resch 
Receiver: everything-list 
Time: 2012-09-21, 01:19:04
Subject: Re: Numbers in Space





On Thu, Sep 20, 2012 at 8:10 PM, Stephen P. King stephe...@charter.net wrote:

On 9/20/2012 11:48 AM, Jason Resch wrote:




On Thu, Sep 20, 2012 at 10:02 AM, Craig Weinberg whatsons...@gmail.com wrote:

Here's another reductio ad absurdum illustration of comp.

If the version of comp we are discussing here is independent of physics, then 
shouldn't it be possible for us to program universal machines using only empty 
space? Length can be quantified, so why can't we just use millimeters or Planck 
lengths as the basis for our enumeration, addition, and multiplication and 
directly program from our mind to space? 

Of course, it would be hard to know where it was because we would be constantly 
flying away from a space that was anchored to an absolute position independent 
of Earth, the solar system, Milky Way, etc, but that shouldn't matter anyhow 
since whatever method we use to directly program in empty space with our minds 
should also give us access to the results of the computations.



Right this is already the case. ?hat we can use our minds to access the results.
?

What do you think? Just as wafers of silicon glass could in theory be 
functionally identical to a living brain, wouldn't it be equally prejudiced to 
say that empty space isn't good enough to host the computations of silicon?


We don't even need empty space, we can use thought alone to figure out the 
future evolution of computers that already exist in Platonia and then get the 
result of any computation. ?he problem is we are slow at doing this, so we 
build machines that can tell us what these platonic machines do with greater 
speed and accuracy than we ever could.


It's not doing the computations that is hard, the computations are already 
there. ?he problem is learning their results.


Jason


?? It takes the consumption of resources to learn the results. This is what I 
have been yelling at Bruno about the entire time since I first read his 
beautiful papers. Understanding is never free.




For us (in this universe) to learn the results of a platonic computation may 
take resources, but if you happen to be that very platonic computation in 
question, then you don't need to do anything extra to get the result. ?ou are 
the result.


Jason
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Re: Re: Numbers in Space

[Roger Clough]

Hi Stephen P. King 

If by exist I mean physically exi,sts
and by lives I mean nonphysically exists,
Then

Computers exist.
Computer programs live.



Roger Clough, rclo...@verizon.net
9/21/2012 
Forever is a long time, especially near the end. -Woody Allen


- Receiving the following content - 
From: Stephen P. King 
Receiver: everything-list 
Time: 2012-09-20, 20:50:22
Subject: Re: Numbers in Space


On 9/20/2012 11:02 AM, Craig Weinberg wrote:
 Here's another reductio ad absurdum illustration of comp.

 If the version of comp we are discussing here is independent of 
 physics, then shouldn't it be possible for us to program universal 
 machines using only empty space? Length can be quantified, so why 
 can't we just use millimeters or Planck lengths as the basis for our 
 enumeration, addition, and multiplication and directly program from 
 our mind to space?

 Of course, it would be hard to know where it was because we would be 
 constantly flying away from a space that was anchored to an absolute 
 position independent of Earth, the solar system, Milky Way, etc, but 
 that shouldn't matter anyhow since whatever method we use to directly 
 program in empty space with our minds should also give us access to 
 the results of the computations.

 What do you think? Just as wafers of silicon glass could in theory be 
 functionally identical to a living brain, wouldn't it be equally 
 prejudiced to say that empty space isn't good enough to host the 
 computations of silicon?


 Craig

Hey Craig,

 What do you think physical computers actually are? universal 
machines using only empty space. But Nature hates a vacuum...

-- 
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Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html


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Re: Re: Numbers in Space

[Roger Clough]

Hi Stephen P. King  

Platonia doesn't exist, it lives. 


Roger Clough, rclo...@verizon.net 
9/21/2012  
Forever is a long time, especially near the end. -Woody Allen 


- Receiving the following content -  
From: Stephen P. King  
Receiver: everything-list  
Time: 2012-09-20, 21:28:02 
Subject: Re: Numbers in Space 


On 9/20/2012 12:14 PM, Craig Weinberg wrote: 



On Thursday, September 20, 2012 11:48:15 AM UTC-4, Jason wrote:  



On Thu, Sep 20, 2012 at 10:02 AM, Craig Weinberg  wrote: 

Here's another reductio ad absurdum illustration of comp. 

If the version of comp we are discussing here is independent of physics, then 
shouldn't it be possible for us to program universal machines using only empty 
space? Length can be quantified, so why can't we just use millimeters or Planck 
lengths as the basis for our enumeration, addition, and multiplication and 
directly program from our mind to space?  

Of course, it would be hard to know where it was because we would be constantly 
flying away from a space that was anchored to an absolute position independent 
of Earth, the solar system, Milky Way, etc, but that shouldn't matter anyhow 
since whatever method we use to directly program in empty space with our minds 
should also give us access to the results of the computations. 



Right this is already the case.  That we can use our minds to access the 
results. 

Why do you say this is the case? We aren't storing memories in space. When we 
lose our memory capacity it isn't because the universe is running out of space. 
We access experience through what we are, not through nothingness. 
  



What do you think? Just as wafers of silicon glass could in theory be 
functionally identical to a living brain, wouldn't it be equally prejudiced to 
say that empty space isn't good enough to host the computations of silicon? 


We don't even need empty space, we can use thought alone to figure out the 
future evolution of computers that already exist in Platonia and then get the 
result of any computation.  The problem is we are slow at doing this,  

Why is being 'slow' a problem? What's the rush? What time is it in Platonia? 
Why aren't we in Platonia now? 

Hi Craig, 

We are! We just don't feel it... 



so we build machines that can tell us what these platonic machines do with 
greater speed and accuracy than we ever could. 

Why would speed and accuracy matter, objectively? What is speed? 


What is the speed of light? Same question! 






It's not doing the computations that is hard, the computations are already 
there.  The problem is learning their results. 

The problem is doing anything in the first place. Computations don't do 
anything at all. The reason that we do things is that we are not computations. 
We use computations. We can program things, but we can't thing programs without 
something to thing them with. This is a fatal flaw. If Platonia exists, it 
makes no sense for anything other than Platonia to exist. It would be redundant 
to go through the formality of executing any function is already executed 
non-locally. Why 'do' anything? 


Bruno can 't answer that question. He is afraid that it will corrupt 
Olympia. 



--  
Onward! 

Stephen 

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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Re: Numbers in Space

[Stephen P. King]

On 9/21/2012 1:19 AM, Jason Resch wrote:



On Thu, Sep 20, 2012 at 8:10 PM, Stephen P. King 
stephe...@charter.net mailto:stephe...@charter.net wrote:


On 9/20/2012 11:48 AM, Jason Resch wrote:



On Thu, Sep 20, 2012 at 10:02 AM, Craig Weinberg
whatsons...@gmail.com mailto:whatsons...@gmail.com wrote:

Here's another reductio ad absurdum illustration of comp.

If the version of comp we are discussing here is independent
of physics, then shouldn't it be possible for us to program
universal machines using only empty space? Length can be
quantified, so why can't we just use millimeters or Planck
lengths as the basis for our enumeration, addition, and
multiplication and directly program from our mind to space?

Of course, it would be hard to know where it was because we
would be constantly flying away from a space that was
anchored to an absolute position independent of Earth, the
solar system, Milky Way, etc, but that shouldn't matter
anyhow since whatever method we use to directly program in
empty space with our minds should also give us access to the
results of the computations.


Right this is already the case.  That we can use our minds to
access the results.


What do you think? Just as wafers of silicon glass could in
theory be functionally identical to a living brain, wouldn't
it be equally prejudiced to say that empty space isn't good
enough to host the computations of silicon?


We don't even need empty space, we can use thought alone to
figure out the future evolution of computers that already exist
in Platonia and then get the result of any computation.  The
problem is we are slow at doing this, so we build machines that
can tell us what these platonic machines do with greater speed
and accuracy than we ever could.

It's not doing the computations that is hard, the computations
are already there.  The problem is learning their results.

Jason


It takes the consumption of resources to learn the results.
This is what I have been yelling at Bruno about the entire time
since I first read his beautiful papers. Understanding is never free.


For us (in this universe) to learn the results of a platonic 
computation may take resources, but if you happen to be that very 
platonic computation in question, then you don't need to do anything 
extra to get the result.  You are the result.


Jason

Jason,

That is not the point! I think we all agree on what you remark 
upon! It is how everything gets partitioned up so that we have the kind 
of world we observe. We observe a classical world where things don't 
work with infinite resources or infinite speed or infinite connectivity. 
We are asking for the fact that we observe an illusion to be explained!


--
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Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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Re: Numbers in Space

[Stephen P. King]

On 9/21/2012 4:10 AM, Bruno Marchal wrote:


On 21 Sep 2012, at 03:28, Stephen P. King wrote:


On 9/20/2012 12:14 PM, Craig Weinberg wrote:



On Thursday, September 20, 2012 11:48:15 AM UTC-4, Jason wrote:


It's not doing the computations that is hard, the computations
are already there.  The problem is learning their results.


The problem is doing anything in the first place. Computations don't 
do anything at all. The reason that we do things is that we are not 
computations. We use computations. We can program things, but we 
can't thing programs without something to thing them with. This is a 
fatal flaw. If Platonia exists, it makes no sense for anything other 
than Platonia to exist. It would be redundant to go through the 
formality of executing any function is already executed non-locally. 
Why 'do' anything?


Bruno can 't answer that question. He is afraid that it will 
corrupt Olympia.


Not at all, the answer is easy here. In the big picture, that is 
arithmetic, nothing is done. The computations are already done in 
it. doing things is a relative internal notion coming from the first 
person perspectives.


Also, Platonia does not really exist, nor God, as existence is what 
belongs to Platonia. Comp follows Plotinus on this, both God and 
Matter does not belong to the category exist (ontologically). They are 
epistemological beings.


Bruno


Dear Bruno,

OK, but you are ignoring my question: How does the existence become 
decomposed such that there are epistemological beings? So far your 
explanation is focused on the representation in terms of arithmetics and 
I accept your reasonings: In the big picture, that is arithmetic, 
nothing is done. There is no action, no change, all that exists just 
is. But then what do we make of time? We can dismiss it as an illusion? 
But that would be just an evasion of the obvious question: Why does the 
illusion occur?
I am interested in explanation that at least try to answer this 
question: How does the illusion persist? What might cause it? Why do 
special purpose computations occur such that we can identify physical 
systems with them? My proposal is to weaken the concept of Computational 
Universality a tiny bit and thus allow room for the possibility of an 
answer to the questions that I have.
Consider this: What happens is there does *not* exist any physical 
system that can implement a particular computation X? Is it possible for 
us, humans, or any other sentient physical being to know anything 
about X, such that we might have some model of X that is faithfully 
representative?



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Stephen

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Re: Numbers in Space

[Stephen P. King]

On 9/21/2012 4:18 AM, Bruno Marchal wrote:


On 20 Sep 2012, at 19:16, Craig Weinberg wrote:




On Thursday, September 20, 2012 12:26:07 PM UTC-4, Bruno Marchal wrote:


On 20 Sep 2012, at 17:02, Craig Weinberg wrote:

 Here's another reductio ad absurdum illustration of comp.

 If the version of comp we are discussing here is independent of
 physics, then shouldn't it be possible for us to program universal
 machines using only empty space?

You are quite quick here, but have a good insight, as comp makes
space
non clonable, indeterministic in the details, and plausibly Turing
universal, as QM confirms. The 0-body problem (the quantum
vacuum) is
already Turing universal (I think). For classical physics you need
three bodies at least).


What about an ideal vacuum? Just lengths multiplying and adding 
enumerated bundles of lengths. No quantum.


It would not be Turing universal.


Dear Bruno,

How so? What is the proof? Craig is allowing for N, + and *. So why 
not?










 Length can be quantified, so why can't we just use millimeters or
 Planck lengths as the basis for our enumeration, addition, and
 multiplication and directly program from our mind to space?

Who we? In the universe nearby it costs a lot of
energy/money/time to
handle matter already gigantic compared to the Planck length.


Or are you suggesting we are already simulated by the quantum
vacuum.
Very plausible, but comp asks for justifying this in arithmetic.


I'm saying that whatever program we access when we choose what we 
think about should be able to run just as easily in space as it does 
through the brain.


Or just arithmetic. You don't need space. Only addition and 
multiplication of integers. Or justapplication and abstraction on 
lambda terms, etc.


What do Integers represent? Are they just primitive objects with 
inherent properties?






I should be able to pick an area of my house and leave a bunch of 
memories there and then come back to them later just be occupying the 
same space.


Not at all. You are distributed in the whole UD*. You can go back to 
your memory only if the measure on computations makes such a 
persistence possible. This needs to be justified with the 
self-reference logics, and that is what is done with S4Grz1, Z1* and X1*.


You lost us ... Eyes glaze over No explanation is being offered 
as to how the measure comes to be. I am asking you about the measure. 
Why do you avoid my questions? I will not stop until you answer me 
coherently!






That's if we define space as relative to my house and not the 
rotating planet, revolving sun, etc.


So it sounds like you are not opposed to this idea of computation 
with no resources whatsoever besides space,


No need for spaces. To invoke it is already too much physicalist for comp.


So all spaces are physical? What about a Hilbert space? Is it not 
a mathematical object?






provided that it could be justified arithmetically (which I don't 
understand why it wouldn't be. how does comp know if it's running on 
matter or space?)


By UDA. Anything physical must be justified with the material 
hypostases. Up to now, this works, even by giving the shadows of the 
reason why destructive interference of the computations occurs below 
our substitution level.




What determines the substitution level?


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Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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Re: Numbers in Space

[Stephen P. King]

On 9/21/2012 4:34 AM, Bruno Marchal wrote:

  But the numbers build an arithmetic body


The numbers arithmetically dream of a non arithmetic body.


and then populate a space with multiple copies of it... so that they 
can implement the UD.


No, they are implemented by the UD, which exists like prime numbers 
exists. Primitively.


So the dreams exists like prime numbers exists. Primitively.  and 
the dreams are of a non arithmetic body, thus a non arithmetic body 
exists primitively. How is this different from anything that I have 
tried to tell you of my ideas? We agree!! This is dual aspect 
monism! I used to call it process dualism, but realized that that 
working caused too much confusion.



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Re: Numbers in Space

[Stephen P. King]

On 9/21/2012 4:34 AM, Bruno Marchal wrote:


And computationalists are cool as they don't think twice before 
giving the restaurant menu to the puppet who asks politely. They 
don't judge people from their religion, skin color, clothes, or if 
made of wood, or metal or flesh, as long as they behave respectfully 
of course.


   Maybe it is because they are really not people at all! They are 
algorithms hiding in a puppet.


In that case comp is false.



No, it is not false. Only the strong version of step 8 is false.



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Re: Numbers in Space

[Jason Resch]

On Sep 21, 2012, at 6:55 AM, Stephen P. King stephe...@charter.net  
wrote:



On 9/21/2012 1:19 AM, Jason Resch wrote:



On Thu, Sep 20, 2012 at 8:10 PM, Stephen P. King stephe...@charter.net 
 wrote:

On 9/20/2012 11:48 AM, Jason Resch wrote:



On Thu, Sep 20, 2012 at 10:02 AM, Craig Weinberg whatsons...@gmail.com 
 wrote:

Here's another reductio ad absurdum illustration of comp.

If the version of comp we are discussing here is independent of  
physics, then shouldn't it be possible for us to program universal  
machines using only empty space? Length can be quantified, so why  
can't we just use millimeters or Planck lengths as the basis for  
our enumeration, addition, and multiplication and directly program  
from our mind to space?


Of course, it would be hard to know where it was because we would  
be constantly flying away from a space that was anchored to an  
absolute position independent of Earth, the solar system, Milky  
Way, etc, but that shouldn't matter anyhow since whatever method  
we use to directly program in empty space with our minds should  
also give us access to the results of the computations.


Right this is already the case.  That we can use our minds to  
access the results.



What do you think? Just as wafers of silicon glass could in theory  
be functionally identical to a living brain, wouldn't it be  
equally prejudiced to say that empty space isn't good enough to  
host the computations of silicon?


We don't even need empty space, we can use thought alone to figure  
out the future evolution of computers that already exist in  
Platonia and then get the result of any computation.  The problem  
is we are slow at doing this, so we build machines that can tell  
us what these platonic machines do with greater speed and accuracy  
than we ever could.


It's not doing the computations that is hard, the computations are  
already there.  The problem is learning their results.


Jason

It takes the consumption of resources to learn the results.  
This is what I have been yelling at Bruno about the entire time  
since I first read his beautiful papers. Understanding is never free.



For us (in this universe) to learn the results of a platonic  
computation may take resources, but if you happen to be that very  
platonic computation in question, then you don't need to do  
anything extra to get the result.  You are the result.


Jason

Jason,

That is not the point! I think we all agree on what you remark  
upon! It is how everything gets partitioned up so that we have the  
kind of world we observe. We observe a classical world where things  
don't work with infinite resources or infinite speed or infinite  
connectivity. We are asking for the fact that we observe an illusion  
to be explained!


Does 38 have any factors?

Does program xyz stop in fewer than 10^100 steps?

Both of these are mathematical questions with only one possible  
answer.  Their truth is established whether or not we test it, ask it,  
implement it or think it.  They would be either true or false even if  
nothing existed for us to have any hope of answering it.


If you mathematically defined what programs are conscious you could  
even say the question Does program xyz contain conscious entities?  
is a mathematical question.  If it is true, then there exist conscious  
entities.


Your requirement that there be some real implementation for  
computation leads to an infinite regress.  What real computer is our  
universe running on?


Jason




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Re: Numbers in Space

[Craig Weinberg]

On Thursday, September 20, 2012 11:16:19 PM UTC-4, Stephen Paul King wrote:

 On 9/20/2012 9:49 PM, Craig Weinberg wrote: 
 Physical computers are assembled substances which exhibit exceptionally 
 normative, controllable, and observable behaviors. 

 Craig 

  To understand a thing is to control a thing. 


Yes! Sort of. I have this whole concept of how motive participation evolves 
through sense in a linear, strategic way. Think of the panopticon 
perspective, where the control center is the hub of a wheel of cells which 
can be observed by the controllers. This metaphorically elevated position 
mirrors the physically elevated position, like a hilltop in battle, where 
the more terrain you can view, the more you can theoretically control the 
outcome of the battle strategically...

However:

You can still understand that you are going to get your ass kicked. 
Understanding gives you potential to control, and motive to control, but 
the execution of control requires...resources. Which means using your 
motives in a way which causes other beings to cause other beings to 
sympathize with your motives, leverage their own motives against rocks and 
sticks and high explosives, etc.. to be come more *persuasive*. 

Craig

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Re: Numbers in Space

[Craig Weinberg]

On Friday, September 21, 2012 4:18:47 AM UTC-4, Bruno Marchal wrote:


 On 20 Sep 2012, at 19:16, Craig Weinberg wrote:



 On Thursday, September 20, 2012 12:26:07 PM UTC-4, Bruno Marchal wrote:


 On 20 Sep 2012, at 17:02, Craig Weinberg wrote: 

  Here's another reductio ad absurdum illustration of comp. 
  
  If the version of comp we are discussing here is independent of   
  physics, then shouldn't it be possible for us to program universal   
  machines using only empty space? 

 You are quite quick here, but have a good insight, as comp makes space   
 non clonable, indeterministic in the details, and plausibly Turing   
 universal, as QM confirms. The 0-body problem (the quantum vacuum) is   
 already Turing universal (I think). For classical physics you need   
 three bodies at least). 


 What about an ideal vacuum? Just lengths multiplying and adding enumerated 
 bundles of lengths. No quantum. 


 It would not be Turing universal.


If it isn't then that seems to me an argument for primitive physics. 
 




  




  Length can be quantified, so why can't we just use millimeters or   
  Planck lengths as the basis for our enumeration, addition, and   
  multiplication and directly program from our mind to space? 

 Who we? In the universe nearby it costs a lot of energy/money/time to   
 handle matter already gigantic compared to the Planck length.  


 Or are you suggesting we are already simulated by the quantum vacuum.   
 Very plausible, but comp asks for justifying this in arithmetic. 


 I'm saying that whatever program we access when we choose what we think 
 about should be able to run just as easily in space as it does through the 
 brain.


 Or just arithmetic. You don't need space. Only addition and multiplication 
 of integers. Or justapplication and abstraction on lambda terms, etc.


I was going to do another post upping the ante from Numbers in Space to 
Numbers in Xpace (imaginary space). To me this is the fading qualia 
argument that could be a Waterloo for comp. The transition from Turing 
machines executed in matter to execution in space and then xpace would have 
to be consistent to support the claim that arithmetic is independent from 
physics. If that isn't the case, why not? What is different other than 
physical properties between matter, space, and xpace?
 




 I should be able to pick an area of my house and leave a bunch of memories 
 there and then come back to them later just be occupying the same space. 


 Not at all. You are distributed in the whole UD*. You can go back to your 
 memory only if the measure on computations makes such a persistence 
 possible. This needs to be justified with the self-reference logics, and 
 that is what is done with S4Grz1, Z1* and X1*.


I don't know what that means exactly but if I am getting the gist, it still 
doesn't tell me why it is easier for me to remember something in my mind 
than to offload my memories onto objects, places, times of the year, 
whatever. Why not make a Turing machine out of time that uses moments 
instead of tape and tape instead of numbers? It seems to me that the 
universality of UMs is wildly overstated. 




 That's if we define space as relative to my house and not the rotating 
 planet, revolving sun, etc.

 So it sounds like you are not opposed to this idea of computation with no 
 resources whatsoever besides space, 


 No need for spaces. To invoke it is already too much physicalist for comp.


So we can pretty much call comp magic then. It needs nothing whatsoever and 
can ultimately control anything from anywhere.
 




 provided that it could be justified arithmetically (which I don't 
 understand why it wouldn't be. how does comp know if it's running on matter 
 or space?)


 By UDA. Anything physical must be justified with the material 
 hypostases. Up to now, this works, even by giving the shadows of the 
 reason why destructive interference of the computations occurs below our 
 substitution level.


Why doesn't anything arithmetic need to be justified with computational 
hypostases?

Craig
 


 Bruno



  



  
  Of course, it would be hard to know where it was because we would be   
  constantly flying away from a space that was anchored to an absolute   
  position independent of Earth, the solar system, Milky Way, etc, but   
  that shouldn't matter anyhow since whatever method we use to   
  directly program in empty space with our minds should also give us   
  access to the results of the computations. 

 ? 


 I mean if I could stand completely still then the planet would fly off 
 from under my feet and I would be left standing exactly where I was with 
 the Earth revolving past me at 107,000 km/hr. I would occupy the same space 
 while the Earth, Sun, and galaxy sweep away from me.

 If instead of me, it was memories I had stashed away in space, then my 
 body would be soon separated from the absolute position that I had placed 
 them. It shouldn't matter though, since by 

Re: Re: Numbers in Space

[Roger Clough]

Hi Craig Weinberg 

Thwe ideal vacuum is still in spacetime.


Roger Clough, rclo...@verizon.net
9/21/2012 
Forever is a long time, especially near the end. -Woody Allen


- Receiving the following content - 
From: Craig Weinberg 
Receiver: everything-list 
Time: 2012-09-21, 11:27:56
Subject: Re: Numbers in Space




On Friday, September 21, 2012 4:18:47 AM UTC-4, Bruno Marchal wrote:


On 20 Sep 2012, at 19:16, Craig Weinberg wrote:




On Thursday, September 20, 2012 12:26:07 PM UTC-4, Bruno Marchal wrote:

On 20 Sep 2012, at 17:02, Craig Weinberg wrote: 

 Here's another reductio ad absurdum illustration of comp. 
 
 If the version of comp we are discussing here is independent of   
 physics, then shouldn't it be possible for us to program universal   
 machines using only empty space? 

You are quite quick here, but have a good insight, as comp makes space   
non clonable, indeterministic in the details, and plausibly Turing   
universal, as QM confirms. The 0-body problem (the quantum vacuum) is   
already Turing universal (I think). For classical physics you need   
three bodies at least). 



What about an ideal vacuum? Just lengths multiplying and adding enumerated 
bundles of lengths. No quantum. 



It would not be Turing universal.

If it isn't then that seems to me an argument for primitive physics. 
 












 Length can be quantified, so why can't we just use millimeters or   
 Planck lengths as the basis for our enumeration, addition, and   
 multiplication and directly program from our mind to space? 

Who we? In the universe nearby it costs a lot of energy/money/time to   
handle matter already gigantic compared to the Planck length.  


Or are you suggesting we are already simulated by the quantum vacuum.   
Very plausible, but comp asks for justifying this in arithmetic. 


I'm saying that whatever program we access when we choose what we think about 
should be able to run just as easily in space as it does through the brain.


Or just arithmetic. You don't need space. Only addition and multiplication of 
integers. Or justapplication and abstraction on lambda terms, etc.

I was going to do another post upping the ante from Numbers in Space to Numbers 
in Xpace (imaginary space). To me this is the fading qualia argument that could 
be a Waterloo for comp. The transition from Turing machines executed in matter 
to execution in space and then xpace would have to be consistent to support the 
claim that arithmetic is independent from physics. If that isn't the case, why 
not? What is different other than physical properties between matter, space, 
and xpace?
 







I should be able to pick an area of my house and leave a bunch of memories 
there and then come back to them later just be occupying the same space. 


Not at all. You are distributed in the whole UD*. You can go back to your 
memory only if the measure on computations makes such a persistence possible. 
This needs to be justified with the self-reference logics, and that is what is 
done with S4Grz1, Z1* and X1*.

I don't know what that means exactly but if I am getting the gist, it still 
doesn't tell me why it is easier for me to remember something in my mind than 
to offload my memories onto objects, places, times of the year, whatever. Why 
not make a Turing machine out of time that uses moments instead of tape and 
tape instead of numbers? It seems to me that the universality of UMs is wildly 
overstated. 








That's if we define space as relative to my house and not the rotating planet, 
revolving sun, etc.

So it sounds like you are not opposed to this idea of computation with no 
resources whatsoever besides space, 


No need for spaces. To invoke it is already too much physicalist for comp.

So we can pretty much call comp magic then. It needs nothing whatsoever and can 
ultimately control anything from anywhere.
 







provided that it could be justified arithmetically (which I don't understand 
why it wouldn't be. how does comp know if it's running on matter or space?)



By UDA. Anything physical must be justified with the material hypostases. Up 
to now, this works, even by giving the shadows of the reason why destructive 
interference of the computations occurs below our substitution level.

Why doesn't anything arithmetic need to be justified with computational 
hypostases?

Craig
 



Bruno










 
 Of course, it would be hard to know where it was because we would be   
 constantly flying away from a space that was anchored to an absolute   
 position independent of Earth, the solar system, Milky Way, etc, but   
 that shouldn't matter anyhow since whatever method we use to   
 directly program in empty space with our minds should also give us   
 access to the results of the computations. 

? 


I mean if I could stand completely still then the planet would fly off from 
under my feet and I would be left standing exactly where I was with the Earth 
revolving past me at 107,000 km/hr. I

Re: Numbers in Space

[Bruno Marchal]

On 21 Sep 2012, at 16:24, Stephen P. King wrote:


On 9/21/2012 4:10 AM, Bruno Marchal wrote:


On 21 Sep 2012, at 03:28, Stephen P. King wrote:


On 9/20/2012 12:14 PM, Craig Weinberg wrote:



On Thursday, September 20, 2012 11:48:15 AM UTC-4, Jason wrote:


It's not doing the computations that is hard, the computations  
are already there.  The problem is learning their results.


The problem is doing anything in the first place. Computations  
don't do anything at all. The reason that we do things is that we  
are not computations. We use computations. We can program things,  
but we can't thing programs without something to thing them with.  
This is a fatal flaw. If Platonia exists, it makes no sense for  
anything other than Platonia to exist. It would be redundant to  
go through the formality of executing any function is already  
executed non-locally. Why 'do' anything?


Bruno can 't answer that question. He is afraid that it will  
corrupt Olympia.


Not at all, the answer is easy here. In the big picture, that is  
arithmetic, nothing is done. The computations are already done in  
it. doing things is a relative internal notion coming from the  
first person perspectives.


Also, Platonia does not really exist, nor God, as existence is what  
belongs to Platonia. Comp follows Plotinus on this, both God and  
Matter does not belong to the category exist (ontologically). They  
are epistemological beings.


Bruno


Dear Bruno,

OK, but you are ignoring my question: How does the existence  
become decomposed such that there are epistemological beings?


We agree that arithmetical truth is independent of us, or more  
formalistically we assume 0 s(0) ... and the law of addition and  
multiplication.


From that, and only that, we proves the existence of the  
computations, and get notably all the dreams, as with comp we know  
that dreams, subjective experiences, needs to be associated to those  
computations. The epistemological beings appears in the content of  
those dreams, and recover, or not, sharable persistent epistemological  
realities.








So far your explanation is focused on the representation in terms of  
arithmetics and I accept your reasonings: In the big picture, that  
is arithmetic, nothing is done. There is no action, no change,  
all that exists just is. But then what do we make of time?


Time is easy, with comp, as we give an importance to processing, or  
successive manipulation. There is a variety of time since the start:

the order 0, s(0), s(s(0)), ...
The UD time steps,
The particular steps of each computations in the UD,
etc.
None give the physical time, as it needs to be extracted from the  
physics emerging on the dreams.






We can dismiss it as an illusion?


We better not. Immaterial does not mean illusion, unless you are  
fictionalist, in which case comp is meaningless.



But that would be just an evasion of the obvious question: Why does  
the illusion occur?


Comp explains this entirely. Numbers can already explains where the  
illusion comes from, and why the illusion has many incommunicable  
features. This *is* solved.





I am interested in explanation that at least try to answer this  
question: How does the illusion persist?


That is the difficult things. That is what I translated in arithmetic.  
That is the measure problem. Either comp gives a quantum machinery  
below our substitution level, or it fails. The material hypostases  
already show that the measure one obeys to quantum like logics, and we  
got an arithmetical quantization in which we can test if there are  
quantum gate at the universal dream bottom.




What might cause it? Why do special purpose computations occur  
such that we can identify physical systems with them? My proposal is  
to weaken the concept of Computational Universality a tiny bit and  
thus allow room for the possibility of an answer to the questions  
that I have.


CT makes the concept of Turing universality is one of the most solid  
epistemological concept ever ... (cf CT)

Good luck.



Consider this: What happens is there does not exist any physical  
system that can implement a particular computation X?


All computations can be implemented in any Turing universal system.  
*Many* subparts of the known physics are Turing universal, so what you  
say is impossible.




Is it possible for us, humans, or any other sentient physical being  
to know anything about X, such that we might have some model of X  
that is faithfully representative?


We already know many things which are not computable. Recursion theory  
is mainly the study and classification of those non computable things.  
In math, the computable is both pro-eminent in the construction we do,  
and the non computable is majority in the ontology. For example the  
non computable functions from N to N are not enumerable, and the  
computable one are enumerable (even if not mechanically or computably  
enumerable (see my posts 

Re: Numbers in Space

[Stephen P. King]

On 9/21/2012 11:05 AM, Jason Resch wrote:



On Sep 21, 2012, at 6:55 AM, Stephen P. King stephe...@charter.net 
mailto:stephe...@charter.net wrote:



On 9/21/2012 1:19 AM, Jason Resch wrote:



On Thu, Sep 20, 2012 at 8:10 PM, Stephen P. King 
stephe...@charter.net mailto:stephe...@charter.net wrote:


On 9/20/2012 11:48 AM, Jason Resch wrote:



On Thu, Sep 20, 2012 at 10:02 AM, Craig Weinberg
whatsons...@gmail.com mailto:whatsons...@gmail.com wrote:

Here's another reductio ad absurdum illustration of comp.

If the version of comp we are discussing here is
independent of physics, then shouldn't it be possible for
us to program universal machines using only empty space?
Length can be quantified, so why can't we just use
millimeters or Planck lengths as the basis for our
enumeration, addition, and multiplication and directly
program from our mind to space?

Of course, it would be hard to know where it was because we
would be constantly flying away from a space that was
anchored to an absolute position independent of Earth, the
solar system, Milky Way, etc, but that shouldn't matter
anyhow since whatever method we use to directly program in
empty space with our minds should also give us access to
the results of the computations.


Right this is already the case.  That we can use our minds to
access the results.


What do you think? Just as wafers of silicon glass could in
theory be functionally identical to a living brain,
wouldn't it be equally prejudiced to say that empty space
isn't good enough to host the computations of silicon?


We don't even need empty space, we can use thought alone to
figure out the future evolution of computers that already exist
in Platonia and then get the result of any computation.  The
problem is we are slow at doing this, so we build machines that
can tell us what these platonic machines do with greater speed
and accuracy than we ever could.

It's not doing the computations that is hard, the computations
are already there.  The problem is learning their results.

Jason


It takes the consumption of resources to learn the
results. This is what I have been yelling at Bruno about the
entire time since I first read his beautiful papers.
Understanding is never free.


For us (in this universe) to learn the results of a platonic 
computation may take resources, but if you happen to be that very 
platonic computation in question, then you don't need to do anything 
extra to get the result.  You are the result.


Jason

Jason,

That is not the point! I think we all agree on what you remark 
upon! It is how everything gets partitioned up so that we have the 
kind of world we observe. We observe a classical world where things 
don't work with infinite resources or infinite speed or infinite 
connectivity. We are asking for the fact that we observe an illusion 
to be explained!


Does 38 have any factors?

Does program xyz stop in fewer than 10^100 steps?

Both of these are mathematical questions with only one possible 
answer.  Their truth is established whether or not we test it, ask it, 
implement it or think it.  They would be either true or false even if 
nothing existed for us to have any hope of answering it.


Hi Jason,

You are missing the point. There is the Truth and there is the 
ability to know of it. The former is immaterial, independent of any one 
of us. The latter is physical, we must work to have it.




If you mathematically defined what programs are conscious you could 
even say the question Does program xyz contain conscious entities? 
is a mathematical question.  If it is true, then there exist conscious 
entities.


We have to be able to communicate...



Your requirement that there be some real implementation for 
computation leads to an infinite regress.  What real computer is our 
universe running on?


The underlying Quantum's unitary transformation.



Jason




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Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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Re: Re: Numbers in Space

[Craig Weinberg]

On Friday, September 21, 2012 11:51:10 AM UTC-4, rclough wrote:

  Hi Craig Weinberg 
  
 Thwe ideal vacuum is still in spacetime.


It's in ideal spacetime.
 

  
  
 Roger Clough, rclo...@verizon.net javascript:
 9/21/2012 
 Forever is a long time, especially near the end. -Woody Allen
  
  

 - Receiving the following content - 
 *From:* Craig Weinberg javascript: 
 *Receiver:* everything-list javascript: 
 *Time:* 2012-09-21, 11:27:56
 *Subject:* Re: Numbers in Space

  

 On Friday, September 21, 2012 4:18:47 AM UTC-4, Bruno Marchal wrote: 


  On 20 Sep 2012, at 19:16, Craig Weinberg wrote:



 On Thursday, September 20, 2012 12:26:07 PM UTC-4, Bruno Marchal wrote: 


 On 20 Sep 2012, at 17:02, Craig Weinberg wrote: 

  Here's another reductio ad absurdum illustration of comp. 
  
  If the version of comp we are discussing here is independent of   
  physics, then shouldn't it be possible for us to program universal   
  machines using only empty space? 

 You are quite quick here, but have a good insight, as comp makes space   
 non clonable, indeterministic in the details, and plausibly Turing   
 universal, as QM confirms. The 0-body problem (the quantum vacuum) is   
 already Turing universal (I think). For classical physics you need   
 three bodies at least). 


 What about an ideal vacuum? Just lengths multiplying and adding 
 enumerated bundles of lengths. No quantum. 


 It would not be Turing universal.


 If it isn't then that seems to me an argument for primitive physics. 
  

  


  
  




  Length can be quantified, so why can't we just use millimeters or   
  Planck lengths as the basis for our enumeration, addition, and   
  multiplication and directly program from our mind to space? 

 Who we? In the universe nearby it costs a lot of energy/money/time to   
 handle matter already gigantic compared to the Planck length.  


 Or are you suggesting we are already simulated by the quantum vacuum.   
 Very plausible, but comp asks for justifying this in arithmetic. 


 I'm saying that whatever program we access when we choose what we think 
 about should be able to run just as easily in space as it does through the 
 brain.


 Or just arithmetic. You don't need space. Only addition and 
 multiplication of integers. Or justapplication and abstraction on lambda 
 terms, etc.


 I was going to do another post upping the ante from Numbers in Space to 
 Numbers in Xpace (imaginary space). To me this is the fading qualia 
 argument that could be a Waterloo for comp. The transition from Turing 
 machines executed in matter to execution in space and then xpace would have 
 to be consistent to support the claim that arithmetic is independent from 
 physics. If that isn't the case, why not? What is different other than 
 physical properties between matter, space, and xpace?
  

  


  I should be able to pick an area of my house and leave a bunch of 
 memories there and then come back to them later just be occupying the same 
 space. 


 Not at all. You are distributed in the whole UD*. You can go back to your 
 memory only if the measure on computations makes such a persistence 
 possible. This needs to be justified with the self-reference logics, and 
 that is what is done with S4Grz1, Z1* and X1*.


 I don't know what that means exactly but if I am getting the gist, it 
 still doesn't tell me why it is easier for me to remember something in my 
 mind than to offload my memories onto objects, places, times of the year, 
 whatever. Why not make a Turing machine out of time that uses moments 
 instead of tape and tape instead of numbers? It seems to me that the 
 universality of UMs is wildly overstated. 

   


  That's if we define space as relative to my house and not the rotating 
 planet, revolving sun, etc.

 So it sounds like you are not opposed to this idea of computation with no 
 resources whatsoever besides space, 


 No need for spaces. To invoke it is already too much physicalist for comp.


 So we can pretty much call comp magic then. It needs nothing whatsoever 
 and can ultimately control anything from anywhere.
  

  


  provided that it could be justified arithmetically (which I don't 
 understand why it wouldn't be. how does comp know if it's running on matter 
 or space?)


 By UDA. Anything physical must be justified with the material 
 hypostases. Up to now, this works, even by giving the shadows of the 
 reason why destructive interference of the computations occurs below our 
 substitution level.


 Why doesn't anything arithmetic need to be justified with computational 
 hypostases?

 Craig
  

  
 Bruno



  
  



  
  Of course, it would be hard to know where it was because we would be   
  constantly flying away from a space that was anchored to an absolute   
  position independent of Earth, the solar system, Milky Way, etc, but   
  that shouldn't matter anyhow since whatever method we use to   
  directly program in empty space with our minds should also

Re: Numbers in Space

[Jason Resch]

On Fri, Sep 21, 2012 at 11:14 AM, Stephen P. King stephe...@charter.netwrote:

  On 9/21/2012 11:05 AM, Jason Resch wrote:



 On Sep 21, 2012, at 6:55 AM, Stephen P. King stephe...@charter.net
 wrote:

   On 9/21/2012 1:19 AM, Jason Resch wrote:



 On Thu, Sep 20, 2012 at 8:10 PM, Stephen P. King stephe...@charter.netwrote:

   On 9/20/2012 11:48 AM, Jason Resch wrote:



 On Thu, Sep 20, 2012 at 10:02 AM, Craig Weinberg 
 whatsons...@gmail.comwrote:

 Here's another reductio ad absurdum illustration of comp.

 If the version of comp we are discussing here is independent of physics,
 then shouldn't it be possible for us to program universal machines using
 only empty space? Length can be quantified, so why can't we just use
 millimeters or Planck lengths as the basis for our enumeration, addition,
 and multiplication and directly program from our mind to space?

 Of course, it would be hard to know where it was because we would be
 constantly flying away from a space that was anchored to an absolute
 position independent of Earth, the solar system, Milky Way, etc, but that
 shouldn't matter anyhow since whatever method we use to directly program in
 empty space with our minds should also give us access to the results of the
 computations.


  Right this is already the case.  That we can use our minds to access
 the results.



 What do you think? Just as wafers of silicon glass could in theory be
 functionally identical to a living brain, wouldn't it be equally prejudiced
 to say that empty space isn't good enough to host the computations of
 silicon?


  We don't even need empty space, we can use thought alone to figure out
 the future evolution of computers that already exist in Platonia and then
 get the result of any computation.  The problem is we are slow at doing
 this, so we build machines that can tell us what these platonic machines do
 with greater speed and accuracy than we ever could.

  It's not doing the computations that is hard, the computations are
 already there.  The problem is learning their results.

  Jason

   It takes the consumption of resources to learn the results. This
 is what I have been yelling at Bruno about the entire time since I first
 read his beautiful papers. Understanding is never free.


  For us (in this universe) to learn the results of a platonic computation
 may take resources, but if you happen to be that very platonic computation
 in question, then you don't need to do anything extra to get the result.
  You are the result.

  Jason

 Jason,

 That is not the point! I think we all agree on what you remark upon!
 It is how everything gets partitioned up so that we have the kind of world
 we observe. We observe a classical world where things don't work with
 infinite resources or infinite speed or infinite connectivity. We are
 asking for the fact that we observe an illusion to be explained!


  Does 38 have any factors?

  Does program xyz stop in fewer than 10^100 steps?

  Both of these are mathematical questions with only one possible answer.
  Their truth is established whether or not we test it, ask it, implement it
 or think it.  They would be either true or false even if nothing existed
 for us to have any hope of answering it.


 Hi Jason,

 You are missing the point. There is the Truth and there is the ability
 to know of it. The former is immaterial, independent of any one of us. The
 latter is physical, we must work to have it.


If you accept platonism then why do you always give Bruno trouble over
there needing to be a physical universe in which to run the UD?




  If you mathematically defined what programs are conscious you could even
 say the question Does program xyz contain conscious entities? is a
 mathematical question.  If it is true, then there exist conscious entities.


 We have to be able to communicate...


This isn't hard to explain.  Some programs contain multiple interacting
entities.




  Your requirement that there be some real implementation for
 computation leads to an infinite regress.  What real computer is our
 universe running on?


 The underlying Quantum's unitary transformation.



  Jason



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 Stephen
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Re: Numbers in Space

[Bruno Marchal]

On 21 Sep 2012, at 17:05, Stephen P. King wrote:


On 9/21/2012 4:34 AM, Bruno Marchal wrote:


And computationalists are cool as they don't think twice before  
giving the restaurant menu to the puppet who asks politely. They  
don't judge people from their religion, skin color, clothes, or  
if made of wood, or metal or flesh, as long as they behave  
respectfully of course.


  Maybe it is because they are really not people at all! They are  
algorithms hiding in a puppet.


In that case comp is false.



   No, it is not false. Only the strong version of step 8 is false.


All steps follows from comp.

If something more is used in step 8: tell me what, but don't confuse a  
conclusion with an assumption, as you did before.


I suggest a point: which is that step 8 uses:  sup-phys + comp = 323.

Most people up to now agree that this follows from comp. It is hard to  
formalize this, as sup-phys is hard to formalize by itself. Indeed you  
can easily build ad hoc theory of matter which contradicts this. Yet,  
when people effectively define such ad hoc notion of primitive matter,  
without magic, it becomes Turing emulable, and their argument becomes  
an argument either against comp, by making the magic non Turing  
emulable, or an argument for lowering down the level, not for the  
invalidity of sup-phys + comp = 323.


Bruno

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



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Re: Numbers in Space

[meekerdb]

On 9/21/2012 8:05 AM, Jason Resch wrote:



On Sep 21, 2012, at 6:55 AM, Stephen P. King stephe...@charter.net 
mailto:stephe...@charter.net wrote:



On 9/21/2012 1:19 AM, Jason Resch wrote:



On Thu, Sep 20, 2012 at 8:10 PM, Stephen P. King stephe...@charter.net 
mailto:stephe...@charter.net wrote:


On 9/20/2012 11:48 AM, Jason Resch wrote:



On Thu, Sep 20, 2012 at 10:02 AM, Craig Weinberg whatsons...@gmail.com
mailto:whatsons...@gmail.com wrote:

Here's another reductio ad absurdum illustration of comp.

If the version of comp we are discussing here is independent of 
physics, then
shouldn't it be possible for us to program universal machines using only
empty space? Length can be quantified, so why can't we just use 
millimeters
or Planck lengths as the basis for our enumeration, addition, and
multiplication and directly program from our mind to space?

Of course, it would be hard to know where it was because we would be
constantly flying away from a space that was anchored to an absolute 
position
independent of Earth, the solar system, Milky Way, etc, but that 
shouldn't
matter anyhow since whatever method we use to directly program in empty 
space
with our minds should also give us access to the results of the 
computations.


Right this is already the case.  That we can use our minds to access the 
results.


What do you think? Just as wafers of silicon glass could in theory be
functionally identical to a living brain, wouldn't it be equally 
prejudiced
to say that empty space isn't good enough to host the computations of 
silicon?


We don't even need empty space, we can use thought alone to figure out the 
future
evolution of computers that already exist in Platonia and then get the 
result of
any computation.  The problem is we are slow at doing this, so we build 
machines
that can tell us what these platonic machines do with greater speed and 
accuracy
than we ever could.

It's not doing the computations that is hard, the computations are already 
there.
 The problem is learning their results.

Jason


It takes the consumption of resources to learn the results. This is 
what I
have been yelling at Bruno about the entire time since I first read his 
beautiful
papers. Understanding is never free.


For us (in this universe) to learn the results of a platonic computation may take 
resources, but if you happen to be that very platonic computation in question, then 
you don't need to do anything extra to get the result.  You are the result.


Jason

Jason,

That is not the point! I think we all agree on what you remark upon! It is how 
everything gets partitioned up so that we have the kind of world we observe. We observe 
a classical world where things don't work with infinite resources or infinite speed or 
infinite connectivity. We are asking for the fact that we observe an illusion to be 
explained!


Does 38 have any factors?

Does program xyz stop in fewer than 10^100 steps?

Both of these are mathematical questions with only one possible answer.  Their truth is 
established whether or not we test it, ask it, implement it or think it.  They would be 
either true or false even if nothing existed for us to have any hope of answering it.


If you mathematically defined what programs are conscious you could even say the 
question Does program xyz contain conscious entities? is a mathematical question.  If 
it is true, then there exist conscious entities.


But a statement can be true, Sherlock Holmes live on Baker Street. without implying any 
existence.


Brent

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Re: Numbers in Space

[Jason Resch]

On Thu, Sep 20, 2012 at 10:02 AM, Craig Weinberg whatsons...@gmail.comwrote:

 Here's another reductio ad absurdum illustration of comp.

 If the version of comp we are discussing here is independent of physics,
 then shouldn't it be possible for us to program universal machines using
 only empty space? Length can be quantified, so why can't we just use
 millimeters or Planck lengths as the basis for our enumeration, addition,
 and multiplication and directly program from our mind to space?

 Of course, it would be hard to know where it was because we would be
 constantly flying away from a space that was anchored to an absolute
 position independent of Earth, the solar system, Milky Way, etc, but that
 shouldn't matter anyhow since whatever method we use to directly program in
 empty space with our minds should also give us access to the results of the
 computations.


Right this is already the case.  That we can use our minds to access the
results.



 What do you think? Just as wafers of silicon glass could in theory be
 functionally identical to a living brain, wouldn't it be equally prejudiced
 to say that empty space isn't good enough to host the computations of
 silicon?


We don't even need empty space, we can use thought alone to figure out the
future evolution of computers that already exist in Platonia and then get
the result of any computation.  The problem is we are slow at doing this,
so we build machines that can tell us what these platonic machines do with
greater speed and accuracy than we ever could.

It's not doing the computations that is hard, the computations are already
there.  The problem is learning their results.

Jason

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Re: Numbers in Space

[Craig Weinberg]

On Thursday, September 20, 2012 11:48:15 AM UTC-4, Jason wrote:



 On Thu, Sep 20, 2012 at 10:02 AM, Craig Weinberg 
 whats...@gmail.comjavascript:
  wrote:

 Here's another reductio ad absurdum illustration of comp.

 If the version of comp we are discussing here is independent of physics, 
 then shouldn't it be possible for us to program universal machines using 
 only empty space? Length can be quantified, so why can't we just use 
 millimeters or Planck lengths as the basis for our enumeration, addition, 
 and multiplication and directly program from our mind to space? 

 Of course, it would be hard to know where it was because we would be 
 constantly flying away from a space that was anchored to an absolute 
 position independent of Earth, the solar system, Milky Way, etc, but that 
 shouldn't matter anyhow since whatever method we use to directly program in 
 empty space with our minds should also give us access to the results of the 
 computations.


 Right this is already the case.  That we can use our minds to access the 
 results.


Why do you say this is the case? We aren't storing memories in space. When 
we lose our memory capacity it isn't because the universe is running out of 
space. We access experience through what we are, not through nothingness.
 

  


 What do you think? Just as wafers of silicon glass could in theory be 
 functionally identical to a living brain, wouldn't it be equally prejudiced 
 to say that empty space isn't good enough to host the computations of 
 silicon?


 We don't even need empty space, we can use thought alone to figure out the 
 future evolution of computers that already exist in Platonia and then get 
 the result of any computation.  The problem is we are slow at doing this, 


Why is being 'slow' a problem? What's the rush? What time is it in 
Platonia? Why aren't we in Platonia now?
 

 so we build machines that can tell us what these platonic machines do with 
 greater speed and accuracy than we ever could.


Why would speed and accuracy matter, objectively? What is speed?
 


 It's not doing the computations that is hard, the computations are already 
 there.  The problem is learning their results.


The problem is doing anything in the first place. Computations don't do 
anything at all. The reason that we do things is that we are not 
computations. We use computations. We can program things, but we can't 
thing programs without something to thing them with. This is a fatal flaw. 
If Platonia exists, it makes no sense for anything other than Platonia to 
exist. It would be redundant to go through the formality of executing any 
function is already executed non-locally. Why 'do' anything?

Craig


 Jason



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Re: Numbers in Space

[Bruno Marchal]

On 20 Sep 2012, at 17:02, Craig Weinberg wrote:


Here's another reductio ad absurdum illustration of comp.

If the version of comp we are discussing here is independent of  
physics, then shouldn't it be possible for us to program universal  
machines using only empty space?


You are quite quick here, but have a good insight, as comp makes space  
non clonable, indeterministic in the details, and plausibly Turing  
universal, as QM confirms. The 0-body problem (the quantum vacuum) is  
already Turing universal (I think). For classical physics you need  
three bodies at least).





Length can be quantified, so why can't we just use millimeters or  
Planck lengths as the basis for our enumeration, addition, and  
multiplication and directly program from our mind to space?


Who we? In the universe nearby it costs a lot of energy/money/time to  
handle matter already gigantic compared to the Planck length.


Or are you suggesting we are already simulated by the quantum vacuum.  
Very plausible, but comp asks for justifying this in arithmetic.





Of course, it would be hard to know where it was because we would be  
constantly flying away from a space that was anchored to an absolute  
position independent of Earth, the solar system, Milky Way, etc, but  
that shouldn't matter anyhow since whatever method we use to  
directly program in empty space with our minds should also give us  
access to the results of the computations.


?




What do you think? Just as wafers of silicon glass could in theory  
be functionally identical to a living brain, wouldn't it be equally  
prejudiced to say that empty space isn't good enough to host the  
computations of silicon?


Empty space, in any turing universal theory, is equivalent with  
universal dovetailing. It is a trivial theory, as when we assume comp,  
the space and belief in spaces have to be justified through number  
dreams statistics.


The advantage of comp is that we can use math and more easily reason  
clearly. We can formulate key parts of the mind body problem  
mathematically.


And computationalists are cool as they don't think twice before giving  
the restaurant menu to the puppet who asks politely. They don't judge  
people from their religion, skin color, clothes, or if made of wood,  
or metal or flesh, as long as they behave respectfully of course.


Bruno



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



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Re: Numbers in Space

[Craig Weinberg]

On Thursday, September 20, 2012 12:26:07 PM UTC-4, Bruno Marchal wrote:


 On 20 Sep 2012, at 17:02, Craig Weinberg wrote: 

  Here's another reductio ad absurdum illustration of comp. 
  
  If the version of comp we are discussing here is independent of   
  physics, then shouldn't it be possible for us to program universal   
  machines using only empty space? 

 You are quite quick here, but have a good insight, as comp makes space   
 non clonable, indeterministic in the details, and plausibly Turing   
 universal, as QM confirms. The 0-body problem (the quantum vacuum) is   
 already Turing universal (I think). For classical physics you need   
 three bodies at least). 


What about an ideal vacuum? Just lengths multiplying and adding enumerated 
bundles of lengths. No quantum. 
 




  Length can be quantified, so why can't we just use millimeters or   
  Planck lengths as the basis for our enumeration, addition, and   
  multiplication and directly program from our mind to space? 

 Who we? In the universe nearby it costs a lot of energy/money/time to   
 handle matter already gigantic compared to the Planck length.  


 Or are you suggesting we are already simulated by the quantum vacuum.   
 Very plausible, but comp asks for justifying this in arithmetic. 


I'm saying that whatever program we access when we choose what we think 
about should be able to run just as easily in space as it does through the 
brain. I should be able to pick an area of my house and leave a bunch of 
memories there and then come back to them later just be occupying the same 
space. That's if we define space as relative to my house and not the 
rotating planet, revolving sun, etc.

So it sounds like you are not opposed to this idea of computation with no 
resources whatsoever besides space, provided that it could be justified 
arithmetically (which I don't understand why it wouldn't be. how does comp 
know if it's running on matter or space?)
 



  
  Of course, it would be hard to know where it was because we would be   
  constantly flying away from a space that was anchored to an absolute   
  position independent of Earth, the solar system, Milky Way, etc, but   
  that shouldn't matter anyhow since whatever method we use to   
  directly program in empty space with our minds should also give us   
  access to the results of the computations. 

 ? 


I mean if I could stand completely still then the planet would fly off from 
under my feet and I would be left standing exactly where I was with the 
Earth revolving past me at 107,000 km/hr. I would occupy the same space 
while the Earth, Sun, and galaxy sweep away from me.

If instead of me, it was memories I had stashed away in space, then my body 
would be soon separated from the absolute position that I had placed them. 
It shouldn't matter though, since by the same method of thinking numbers 
into space, I should be able to retrieve them too, regardless of the 
distance between my body and the numbers.



  
  What do you think? Just as wafers of silicon glass could in theory   
  be functionally identical to a living brain, wouldn't it be equally   
  prejudiced to say that empty space isn't good enough to host the   
  computations of silicon? 

 Empty space, in any turing universal theory, is equivalent with   
 universal dovetailing. It is a trivial theory, as when we assume comp,   
 the space and belief in spaces have to be justified through number   
 dreams statistics. 


So you are saying yes to the space doctor?
 


 The advantage of comp is that we can use math and more easily reason   
 clearly. We can formulate key parts of the mind body problem   
 mathematically. 


I don't question that, and I think that it may ultimately be the only way 
of engineering mind body solutions - but I still think that if we really 
want to know the truth about mind body, we can only find that in the 
un-numbered, un-named meta-juxtapostions of experienced sense.
 


 And computationalists are cool as they don't think twice before giving   
 the restaurant menu to the puppet who asks politely. They don't judge   
 people from their religion, skin color, clothes, or if made of wood,   
 or metal or flesh, as long as they behave respectfully of course. 


I can behave respectfully to a puppet too, but I feel hypocritical because 
I wouldn't change places with them for any reason. 


 Bruno 



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





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Re: Numbers in Space

[Stephen P. King]

On 9/20/2012 11:02 AM, Craig Weinberg wrote:

Here's another reductio ad absurdum illustration of comp.

If the version of comp we are discussing here is independent of 
physics, then shouldn't it be possible for us to program universal 
machines using only empty space? Length can be quantified, so why 
can't we just use millimeters or Planck lengths as the basis for our 
enumeration, addition, and multiplication and directly program from 
our mind to space?


Of course, it would be hard to know where it was because we would be 
constantly flying away from a space that was anchored to an absolute 
position independent of Earth, the solar system, Milky Way, etc, but 
that shouldn't matter anyhow since whatever method we use to directly 
program in empty space with our minds should also give us access to 
the results of the computations.


What do you think? Just as wafers of silicon glass could in theory be 
functionally identical to a living brain, wouldn't it be equally 
prejudiced to say that empty space isn't good enough to host the 
computations of silicon?



Craig


Hey Craig,

What do you think physical computers actually are? universal 
machines using only empty space. But Nature hates a vacuum...


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Onward!

Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html


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Re: Numbers in Space

[Stephen P. King]

On 9/20/2012 11:48 AM, Jason Resch wrote:



On Thu, Sep 20, 2012 at 10:02 AM, Craig Weinberg 
whatsons...@gmail.com mailto:whatsons...@gmail.com wrote:


Here's another reductio ad absurdum illustration of comp.

If the version of comp we are discussing here is independent of
physics, then shouldn't it be possible for us to program universal
machines using only empty space? Length can be quantified, so why
can't we just use millimeters or Planck lengths as the basis for
our enumeration, addition, and multiplication and directly program
from our mind to space?

Of course, it would be hard to know where it was because we would
be constantly flying away from a space that was anchored to an
absolute position independent of Earth, the solar system, Milky
Way, etc, but that shouldn't matter anyhow since whatever method
we use to directly program in empty space with our minds should
also give us access to the results of the computations.


Right this is already the case.  That we can use our minds to access 
the results.



What do you think? Just as wafers of silicon glass could in theory
be functionally identical to a living brain, wouldn't it be
equally prejudiced to say that empty space isn't good enough to
host the computations of silicon?


We don't even need empty space, we can use thought alone to figure out 
the future evolution of computers that already exist in Platonia and 
then get the result of any computation.  The problem is we are slow at 
doing this, so we build machines that can tell us what these platonic 
machines do with greater speed and accuracy than we ever could.


It's not doing the computations that is hard, the computations are 
already there.  The problem is learning their results.


Jason

It takes the consumption of resources to learn the results. This 
is what I have been yelling at Bruno about the entire time since I first 
read his beautiful papers. Understanding is never free.


--
Onward!

Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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Re: Numbers in Space

[Stephen P. King]

On 9/20/2012 12:14 PM, Craig Weinberg wrote:



On Thursday, September 20, 2012 11:48:15 AM UTC-4, Jason wrote:



On Thu, Sep 20, 2012 at 10:02 AM, Craig Weinberg
whats...@gmail.com javascript: wrote:

Here's another reductio ad absurdum illustration of comp.

If the version of comp we are discussing here is independent
of physics, then shouldn't it be possible for us to program
universal machines using only empty space? Length can be
quantified, so why can't we just use millimeters or Planck
lengths as the basis for our enumeration, addition, and
multiplication and directly program from our mind to space?

Of course, it would be hard to know where it was because we
would be constantly flying away from a space that was anchored
to an absolute position independent of Earth, the solar
system, Milky Way, etc, but that shouldn't matter anyhow since
whatever method we use to directly program in empty space with
our minds should also give us access to the results of the
computations.


Right this is already the case.  That we can use our minds to
access the results.


Why do you say this is the case? We aren't storing memories in space. 
When we lose our memory capacity it isn't because the universe is 
running out of space. We access experience through what we are, not 
through nothingness.



What do you think? Just as wafers of silicon glass could in
theory be functionally identical to a living brain, wouldn't
it be equally prejudiced to say that empty space isn't good
enough to host the computations of silicon?


We don't even need empty space, we can use thought alone to figure
out the future evolution of computers that already exist in
Platonia and then get the result of any computation.  The problem
is we are slow at doing this,


Why is being 'slow' a problem? What's the rush? What time is it in 
Platonia? Why aren't we in Platonia now?

Hi Craig,

We are! We just don't feel it...


so we build machines that can tell us what these platonic machines
do with greater speed and accuracy than we ever could.


Why would speed and accuracy matter, objectively? What is speed?


What is the speed of light? Same question!




It's not doing the computations that is hard, the computations are
already there.  The problem is learning their results.


The problem is doing anything in the first place. Computations don't 
do anything at all. The reason that we do things is that we are not 
computations. We use computations. We can program things, but we can't 
thing programs without something to thing them with. This is a fatal 
flaw. If Platonia exists, it makes no sense for anything other than 
Platonia to exist. It would be redundant to go through the formality 
of executing any function is already executed non-locally. Why 'do' 
anything?


Bruno can 't answer that question. He is afraid that it will 
corrupt Olympia.



--
Onward!

Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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Re: Numbers in Space

[Stephen P. King]

On 9/20/2012 12:26 PM, Bruno Marchal wrote:


On 20 Sep 2012, at 17:02, Craig Weinberg wrote:


Here's another reductio ad absurdum illustration of comp.

If the version of comp we are discussing here is independent of 
physics, then shouldn't it be possible for us to program universal 
machines using only empty space?


You are quite quick here, but have a good insight, as comp makes space 
non clonable, indeterministic in the details, and plausibly Turing 
universal, as QM confirms. The 0-body problem (the quantum vacuum) is 
already Turing universal (I think). For classical physics you need 
three bodies at least).




Dear Bruno,

I agree 100% with you. That the quantum vacuum is TU, is obvious to 
me. I think that Svozil has something written on this.. maybe or 't Hoft.






Length can be quantified, so why can't we just use millimeters or 
Planck lengths as the basis for our enumeration, addition, and 
multiplication and directly program from our mind to space?


Who we? In the universe nearby it costs a lot of energy/money/time to 
handle matter already gigantic compared to the Planck length.


Only because we are trying to do things the classical way...



Or are you suggesting we are already simulated by the quantum vacuum. 
Very plausible, but comp asks for justifying this in arithmetic.


I am not sure if that is possible because it seems to me that that 
requires the specification of an uncountable infinity.






Of course, it would be hard to know where it was because we would be 
constantly flying away from a space that was anchored to an absolute 
position independent of Earth, the solar system, Milky Way, etc, but 
that shouldn't matter anyhow since whatever method we use to directly 
program in empty space with our minds should also give us access to 
the results of the computations.


?




What do you think? Just as wafers of silicon glass could in theory be 
functionally identical to a living brain, wouldn't it be equally 
prejudiced to say that empty space isn't good enough to host the 
computations of silicon?


Empty space, in any turing universal theory, is equivalent with 
universal dovetailing. It is a trivial theory, as when we assume comp, 
the space and belief in spaces have to be justified through number 
dreams statistics.


But the numbers build an arithmetic body and then populate a 
space with multiple copies of it... so that they can implement the UD. 
Their dreaming is this! http://en.wikipedia.org/wiki/Dreamlands




The advantage of comp is that we can use math and more easily reason 
clearly. We can formulate key parts of the mind body problem 
mathematically.


I disagree. We can only formalize the mind, never the body, if we 
wish to never be inconsistent.




And computationalists are cool as they don't think twice before giving 
the restaurant menu to the puppet who asks politely. They don't judge 
people from their religion, skin color, clothes, or if made of wood, 
or metal or flesh, as long as they behave respectfully of course.


Maybe it is because they are really not people at all! They are 
algorithms hiding in a puppet.



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Re: Numbers in Space

[Craig Weinberg]

On Thursday, September 20, 2012 8:50:20 PM UTC-4, Stephen Paul King wrote:

 On 9/20/2012 11:02 AM, Craig Weinberg wrote: 
  Here's another reductio ad absurdum illustration of comp. 
  
  If the version of comp we are discussing here is independent of 
  physics, then shouldn't it be possible for us to program universal 
  machines using only empty space? Length can be quantified, so why 
  can't we just use millimeters or Planck lengths as the basis for our 
  enumeration, addition, and multiplication and directly program from 
  our mind to space? 
  
  Of course, it would be hard to know where it was because we would be 
  constantly flying away from a space that was anchored to an absolute 
  position independent of Earth, the solar system, Milky Way, etc, but 
  that shouldn't matter anyhow since whatever method we use to directly 
  program in empty space with our minds should also give us access to 
  the results of the computations. 
  
  What do you think? Just as wafers of silicon glass could in theory be 
  functionally identical to a living brain, wouldn't it be equally 
  prejudiced to say that empty space isn't good enough to host the 
  computations of silicon? 
  
  
  Craig 

 Hey Craig, 

  What do you think physical computers actually are? universal 
 machines using only empty space. But Nature hates a vacuum... 


Physical computers are assembled substances which exhibit exceptionally 
normative, controllable, and observable behaviors.

Craig


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 Onward! 

 Stephen 

 http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html 




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Re: Numbers in Space

[Craig Weinberg]

On Thursday, September 20, 2012 9:10:39 PM UTC-4, Stephen Paul King wrote:

  On 9/20/2012 11:48 AM, Jason Resch wrote:
  


 On Thu, Sep 20, 2012 at 10:02 AM, Craig Weinberg 
 whats...@gmail.comjavascript:
  wrote:

 Here's another reductio ad absurdum illustration of comp.

 If the version of comp we are discussing here is independent of physics, 
 then shouldn't it be possible for us to program universal machines using 
 only empty space? Length can be quantified, so why can't we just use 
 millimeters or Planck lengths as the basis for our enumeration, addition, 
 and multiplication and directly program from our mind to space? 

 Of course, it would be hard to know where it was because we would be 
 constantly flying away from a space that was anchored to an absolute 
 position independent of Earth, the solar system, Milky Way, etc, but that 
 shouldn't matter anyhow since whatever method we use to directly program in 
 empty space with our minds should also give us access to the results of the 
 computations.


  Right this is already the case.  That we can use our minds to access the 
 results.
  


 What do you think? Just as wafers of silicon glass could in theory be 
 functionally identical to a living brain, wouldn't it be equally prejudiced 
 to say that empty space isn't good enough to host the computations of 
 silicon?


  We don't even need empty space, we can use thought alone to figure out 
 the future evolution of computers that already exist in Platonia and then 
 get the result of any computation.  The problem is we are slow at doing 
 this, so we build machines that can tell us what these platonic machines do 
 with greater speed and accuracy than we ever could.

  It's not doing the computations that is hard, the computations are 
 already there.  The problem is learning their results.

  Jason

  It takes the consumption of resources to learn the results. This 
 is what I have been yelling at Bruno about the entire time since I first 
 read his beautiful papers. Understanding is never free.


Exactly, and I was trying to show why. Without that resource cost, there is 
no reason for anything to have a cost and no reason to leave Platonia. 
Castles in the clouds ahoy!

Craig

 

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 Stephen
 http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

  

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Re: Numbers in Space

[Stephen P. King]

On 9/20/2012 1:16 PM, Craig Weinberg wrote:



On Thursday, September 20, 2012 12:26:07 PM UTC-4, Bruno Marchal wrote:


On 20 Sep 2012, at 17:02, Craig Weinberg wrote:

 Here's another reductio ad absurdum illustration of comp.

 If the version of comp we are discussing here is independent of
 physics, then shouldn't it be possible for us to program universal
 machines using only empty space?

You are quite quick here, but have a good insight, as comp makes
space
non clonable, indeterministic in the details, and plausibly Turing
universal, as QM confirms. The 0-body problem (the quantum vacuum) is
already Turing universal (I think). For classical physics you need
three bodies at least).


What about an ideal vacuum? Just lengths multiplying and adding 
enumerated bundles of lengths. No quantum.

Hey!


Do you mean like a measure with nothing to rule on? Or a nothing 
without a measure?







 Length can be quantified, so why can't we just use millimeters or
 Planck lengths as the basis for our enumeration, addition, and
 multiplication and directly program from our mind to space?

Who we? In the universe nearby it costs a lot of energy/money/time to
handle matter already gigantic compared to the Planck length.


Or are you suggesting we are already simulated by the quantum vacuum.
Very plausible, but comp asks for justifying this in arithmetic.


I'm saying that whatever program we access when we choose what we 
think about should be able to run just as easily in space as it does 
through the brain. I should be able to pick an area of my house and 
leave a bunch of memories there and then come back to them later just 
be occupying the same space. That's if we define space as relative to 
my house and not the rotating planet, revolving sun, etc.


So it sounds like you are not opposed to this idea of computation with 
no resources whatsoever besides space, provided that it could be 
justified arithmetically (which I don't understand why it wouldn't be. 
how does comp know if it's running on matter or space?)




Space is the only resource needed.





 Of course, it would be hard to know where it was because we
would be
 constantly flying away from a space that was anchored to an
absolute
 position independent of Earth, the solar system, Milky Way, etc,
but
 that shouldn't matter anyhow since whatever method we use to
 directly program in empty space with our minds should also give us
 access to the results of the computations.

?


I mean if I could stand completely still then the planet would fly off 
from under my feet and I would be left standing exactly where I was 
with the Earth revolving past me at 107,000 km/hr. I would occupy the 
same space while the Earth, Sun, and galaxy sweep away from me.


If instead of me, it was memories I had stashed away in space, then my 
body would be soon separated from the absolute position that I had 
placed them. It shouldn't matter though, since by the same method of 
thinking numbers into space, I should be able to retrieve them too, 
regardless of the distance between my body and the numbers.





 What do you think? Just as wafers of silicon glass could in theory
 be functionally identical to a living brain, wouldn't it be equally
 prejudiced to say that empty space isn't good enough to host the
 computations of silicon?

Empty space, in any turing universal theory, is equivalent with
universal dovetailing. It is a trivial theory, as when we assume
comp,
the space and belief in spaces have to be justified through number
dreams statistics.


So you are saying yes to the space doctor?


YES! I do! Over and over and over and over!




The advantage of comp is that we can use math and more easily reason
clearly. We can formulate key parts of the mind body problem
mathematically.


I don't question that, and I think that it may ultimately be the only 
way of engineering mind body solutions - but I still think that if we 
really want to know the truth about mind body, we can only find that 
in the un-numbered, un-named meta-juxtapostions of experienced sense.



And computationalists are cool as they don't think twice before
giving
the restaurant menu to the puppet who asks politely. They don't judge
people from their religion, skin color, clothes, or if made of wood,
or metal or flesh, as long as they behave respectfully of course.


I can behave respectfully to a puppet too, but I feel hypocritical 
because I wouldn't change places with them for any reason.





How would you know that it happened?

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Re: Numbers in Space

[Stephen P. King]

On 9/20/2012 9:49 PM, Craig Weinberg wrote:
Physical computers are assembled substances which exhibit exceptionally 
normative, controllable, and observable behaviors.


Craig

To understand a thing is to control a thing.

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Re: Numbers in Space

[Jason Resch]

On Thu, Sep 20, 2012 at 8:10 PM, Stephen P. King stephe...@charter.netwrote:

  On 9/20/2012 11:48 AM, Jason Resch wrote:



 On Thu, Sep 20, 2012 at 10:02 AM, Craig Weinberg whatsons...@gmail.comwrote:

 Here's another reductio ad absurdum illustration of comp.

 If the version of comp we are discussing here is independent of physics,
 then shouldn't it be possible for us to program universal machines using
 only empty space? Length can be quantified, so why can't we just use
 millimeters or Planck lengths as the basis for our enumeration, addition,
 and multiplication and directly program from our mind to space?

 Of course, it would be hard to know where it was because we would be
 constantly flying away from a space that was anchored to an absolute
 position independent of Earth, the solar system, Milky Way, etc, but that
 shouldn't matter anyhow since whatever method we use to directly program in
 empty space with our minds should also give us access to the results of the
 computations.


  Right this is already the case.  That we can use our minds to access the
 results.



 What do you think? Just as wafers of silicon glass could in theory be
 functionally identical to a living brain, wouldn't it be equally prejudiced
 to say that empty space isn't good enough to host the computations of
 silicon?


  We don't even need empty space, we can use thought alone to figure out
 the future evolution of computers that already exist in Platonia and then
 get the result of any computation.  The problem is we are slow at doing
 this, so we build machines that can tell us what these platonic machines do
 with greater speed and accuracy than we ever could.

  It's not doing the computations that is hard, the computations are
 already there.  The problem is learning their results.

  Jason

  It takes the consumption of resources to learn the results. This
 is what I have been yelling at Bruno about the entire time since I first
 read his beautiful papers. Understanding is never free.


For us (in this universe) to learn the results of a platonic computation
may take resources, but if you happen to be that very platonic computation
in question, then you don't need to do anything extra to get the result.
 You are the result.

Jason

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Re: numbers?

[Bruno Marchal]

On 07 Aug 2010, at 00:05, Brian Tenneson wrote:


Bruno Marchal wrote:
Tegmark argues that reality is a mathematical structure and states  
that an open problem is finding a mathematical structure which is  
isomorphic to reality.  This might or might not be clear: the  
mathematical structure with the property that all mathematical  
structures can be embedded within it is precisely the mathematical  
structure we are looking for.


The problem is in defining embedded. I am not sure it makes set  
theoretical sense, unless you believe in Quine's New foundation  
(NF). I am neutral on the consistency of NF. With a large sense of  
embedded I may argue that the mathematical structure you are  
looking for is just the (mathematical) universal machine. In which  
case Robinson arithmetic (a tiny fragment of arithmetical truth, on  
which both platonist and non platonist (intuitionist) is enough.  
Indeed, I argue with comp that Robinson arithmetic, or any first  
order specification of a (Turing) universal theory is enough to  
derive the appearance of quanta and qualia.
Actually, I'm using what's called NF with urelements (NFU) which  
according to what I've read is consistent.
http://plato.stanford.edu/archives/sum2009/entries/quine-nf/   
(section 7. Coda).


I know my late colleague Boffa proved the consistency of variant of  
NF, like Crabbe (there is belgium school on NF!). But can we have a  
universal set in those variants? Don't we lose extensionnality with  
NFU? I should revise my NF!
I think that I remember you are using NF motivated by such a universal  
set, am I right?





Where would I go about finding out a survey of concepts including  
universal machine?  Are they known to exist?


Yes, and 'real' computers provide concrete examples. They are the  
pillar of recursion theory and theoretical computer science. Of  
course, mathematically we can debate on their best definition. Martin  
Davis(*) gave the old definition (similar to Turing, Post, ...) in  
1956, and corrected it in a 1957 paper(*). Usually recursion theorist  
use the new one, because it leads to a mathematically clean notion of  
recursive equivalence (see the book by Rogers(**)). But in the context  
of applying this to biology, or to theoretical artificial  
intelligence, or to machine theology, the old, larger definition, is  
better, because those applications are more intensional in nature  
(coding play a role). The old definition is also equivalent with Emil  
Post notion of creative set (a recursively enumerable set with a  
productive complement, and a set is productive if for all Wi included  
in it, you can find effectively a counterexample, that is a k in the  
set but not in Wi (Wi is the domain of Phi_i, the ith partial  
recursive function in some universal programming language). The notion  
of creative set is the set-theoretical notion of universal machine.  
This is not obvious and has been proved by some people like John  
Myhill. The set of (gödel numbers) of provable sentences of a sigma_1  
complete theory is creative, for example, and you can use that for  
making them emulating any universal machine. The best book is the book  
by Rogers(**), but Cutland wrote a nice introduction(***).



(*)
DAVIS, M., 1956, A note on universal Turing machines, Automata  
Studies, Annals of

mathematics studies, no 34, pp. 167-175, Princeton, N.Y.
DAVIS, M., 1957, The definition of universal Turing machines,  
Proceedings of the

American Mathematical Society, Vol 8, pp. 1125-1126.
(**)
ROGERS H.,1967, Theory of Recursive Functions and Effective  
Computability, McGraw-

Hill, 1967. (2ed, MIT Press, Cambridge, Massachusetts 1987).
(***)
CUTLAND N. J., 1980, Computability An introduction to recursive  
function theory,

Cambridge University Press.


  How are they defined?  It would be much easier if I didn't have to  
reinvent the wheel.
The last sentence in the quote excites me: The leap from mathematics  
to things such as quanta and qualia is something I haven't really  
understood.


Well, alas, for almost precise historical reasons(:), you will not  
find many logicians interested in qualia. Thanks to quantum computer  
science, slowly but surely a growing number of logicians begin to see  
the interest of learning quantum mechanics.
It is mainly my own work which shows that quanta can be a particular  
case of sharable qualia. I obtained this by using the work in  
(arithmetical, set-theoretical, analytical) self-reference logics  
(build on Gödel and Löb's results).


(:) for historical reasons, logicians have fought to be recognized as  
pure mathematicians, and most really dislike we remind them of the  
theo/philosophical origin/motivation of logic.




Digital mechanism (the tiny arithmetic TOE) entails already a large  
part of Quantum Mechanics, and then group or category theoretic  
considerations (and knot theory) might explain the 'illusions' of  
time, space, particle, and (symmetrical) 

Re: numbers?

[Brian Tenneson]

John Mikes wrote:


 
...Rectangles are not found in nature and not are numbers; both are 
abstractions of things we see in nature...
Pray: what things? and how are they 'abstracted into numbers? 
(Rectangles etc. - IMO - are artifacts made (upon/within) a system of 
human application).
Yet numbers and rectangles (and many other abstractions) have a 
suspiciously good use for modeling in nature

   ---   - u s e - . (?) -
Number systems like the one asserted by the Peano axioms are 
abstractions of the process of counting.  The box has no apples, the box 
has one apple, etc..  The numbers 0, 1, etc., are abstracted so that 0 
can universally mean none of anything, 1 can universally mean 1 of 
anything, etc..  When we say 3+4=7, it is an abstraction because it 
universally means 3 of anything added to 4 of that anything is 7 of that 
anything. 

A rectangle traditionally is a set of points with special additional 
requirements.  You will never find a rectangle in nature because points 
are smaller than particles and the edge of a rectangle is more dense 
than any physical arrangement.  Dense meaning that between any two 
points there is another point in between the two.  This is not true of 
naturally occurring arrangement of things: it is not the case that you 
can always find a third object between two other objects.  Physical 
arrangements are not infinitely fine, they are coarse even if only 
discernibly coarse on a very small scale.


Numbers are good models and have a use in a variety of applications such 
as finance and rectangles are good models for architecture and a whole 
lot more.
 
Equivalence of III + IV as VII? Or in other numbering systems 
(letters, etc.) used in various languages? In Bruno's example some 
time ago the II + I = III definitely referred to the quantity of the 
I lines. He even went up to some 
I or similar. Now in my 
feeble mind to construct 'symbols' for expressing /_how many Is 
there are_/ is not the other way around. 3 stands for III, the 
COUNTED amount of the lines and not vice versa.
 
So: what are those _naturally occurring_ things that serve for being 
abstracted into numbers?

*
 
Seems like the concept of number system is getting mixed up with the 
concept of numeral system.  It does not matter if you use III, 3, three, 
@@@, etc.  It does not matter that III can be written 7 or seven.  
The numeral system is the notation and the number system are what the 
symbols in the numeral system point to.  So while we may write III or 3 
or three, what those symbols point to is a number.  If you will, imagine 
two domains: one domain is of symbols and the other domain is what those 
symbols point to.  Numeral systems are of the first domain and number 
systems are of the second domain.


Counting inspired number systems.  Numeral systems are used to describe 
counting.
Axioms are statements - not controversial to what I stated. And 
please, do not divert into quite different topics, where you may have 
a point in some other aspect. We are talking about numbers, not the 
masculinity of the US president.
Fine, not controversial.   My examples, admittedly not all drawn from 
mathematics, were just illustrations of my point that statements exist 
independently of humans.  What you said was this:
/_Axioms_/ however sounds to my vocabulary like inventions helping to 
justify our theories. Sometimes quite weird.
Yet axioms exist independently of humans.  What a human does is select 
axioms to his or her liking to momentarily assume for some purpose or 
another.  Basically, because axioms exist independently of humans (as do 
all statements), they are not inventions of humans.
Not inventions but a human will choose which axioms to assume 
momentarily for some purpose.  Choose, not invent.


 
Exist is something to be identified. IMO physical existence is a 
figment pertinent to the figment of a physical world - quite outside 
of my position. I don't permit physical existence.
Well then perhaps numbers exist for you.  I do not put the physical 
condition on existence; for me numbers do indeed exist.
If I may repeat: so WHAT ARE NUMBERS? (symbols for what? how do they 
apply them to quantitative considerations? what if another 'logic' 
uses them in a different math (e.g. where 17 is not identifiable as a 
prime number? Is it likely that more will be found - as was the zero, 
or are we in a mathematical omniscience already? Is our restriction 
to the 'naturals' - natural, or just a consequence of our insufficient 
knowledge (caabilities)?
 
May I quote a smart person: there are no stupid questions, only stupid 
answers. I ask them.
 
John Mikes
 

When considering number systems such as naturals, rationals, and (finite 
or infinite) cardinal numbers, it seems to me to not be a question with 
a quick answer.  Division is not possible in all number systems, so I 
would have to say that in order to count (no pun intended) as 

Re: numbers?

[Brian Tenneson]

 Bruno Marchal wrote:

Tegmark argues that reality is a mathematical structure and states that an
open problem is finding a mathematical structure which is isomorphic to
reality.  This might or might not be clear: the mathematical structure with
the property that all mathematical structures can be embedded within it is
precisely the mathematical structure we are looking for.

The problem is in defining embedded. I am not sure it makes set
theoretical sense, unless you believe in Quine's New foundation (NF). I am
neutral on the consistency of NF. With a large sense of embedded I may
argue that the mathematical structure you are looking for is just the
(mathematical) universal machine. In which case Robinson arithmetic (a tiny
fragment of arithmetical truth, on which both platonist and non platonist
(intuitionist) is enough. Indeed, I argue with comp that Robinson
arithmetic, or any first order specification of a (Turing) universal theory
is enough to derive the appearance of quanta and qualia.

Actually, I'm using what's called NF with urelements (NFU) which according
to what I've read is consistent.
http://plato.stanford.edu/archives/sum2009/entries/quine-nf/  (section 7.
Coda).
Where would I go about finding out a survey of concepts including universal
machine?  Are they known to exist?  How are they defined?  It would be much
easier if I didn't have to reinvent the wheel.
The last sentence in the quote excites me: The leap from mathematics to
things such as quanta and qualia is something I haven't really understood.

Digital mechanism (the tiny arithmetic TOE) entails already a large part of
Quantum Mechanics, and then group or category theoretic considerations (and
knot theory) might explain the 'illusions' of time, space, particle, and
(symmetrical) hamiltonians, and why indeed physical reality should appear as
an indeterminate state of a physical vacuum. But the logic-math problems
remaining are not easy to solve. That is normal in a such top down,
mind-body problem driven, approach to physics (and
psychology/theology/biology).

Interesting!

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Re: numbers?

[John Mikes]

I am not sure whether I reply to Brian, or to Bruno? there are remarks on *my
texts to Brian* without marking the replier and at the end it reads: *
Bruno* with no further ado.
Never mind, I want to be short.

...Rectangles are not found in nature and not are numbers; both are
abstractions of things we see in nature...
Pray: what things? and how are they 'abstracted into numbers? (Rectangles
etc. - IMO - are artifacts made (upon/within) a system of human
application).
Yet numbers and rectangles (and many other abstractions) have a
suspiciously good use for modeling in nature
   ---   - u s e - . (?) -

Equivalence of III + IV as VII? Or in other numbering systems (letters,
etc.) used in various languages? In Bruno's example some time ago the II + I
= III definitely referred to the quantity of the I lines. He even went up
to some I or similar. Now in my
feeble mind to construct 'symbols' for expressing *how many Is there
are*is not the other way around. 3 stands for III, the COUNTED
amount of the
lines and not vice versa.

So: what are those *naturally occurring* things that serve for being
abstracted into numbers?
*

Axioms are statements - not controversial to what I stated. And please, do
not divert into quite different topics, where you may have a point in some
other aspect. We are talking about numbers, not the masculinity of the US
president.

Exist is something to be identified. IMO physical existence is a figment
pertinent to the figment of a physical world - quite outside of my
position. I don't permit physical existence.

To your(?) question after my signature (whoever asked it) I gave already my
apologetic deference conceding to Quentin's retort on that badly applied
sentence of mine. So I repeat it now: sorry, it does not make sense.
Satisfied?

I have no comment on those paragraphs after the - line.

If I may repeat: so WHAT ARE NUMBERS? (symbols for what? how do they apply
them to quantitative considerations? what if another 'logic' uses them in a
different math (e.g. where 17 is not identifiable as a prime number? Is it
likely that more will be found - as was the zero, or are we in a
mathematical omniscience already? Is our restriction to the 'naturals' -
natural, or just a consequence of our insufficient knowledge (caabilities)?

May I quote a smart person: there are no stupid questions, only stupid
answers. I ask them.

John Mikes



On 8/4/10, Brian Tenneson tenn...@gmail.com wrote:

 John Mikes wrote:

 Brian,
 nothing could be more remote for me than to argue 'math' (number's
 application and theories) with you. I thinkyou mix up* 'counting'* for the
 stuff that serves it. As I usually do, I looked up Google for the Peano
 axioms and found nothing in them that pertains to the origination of
 numbers. They USE them and EXPLAIN sich usage. Use what

 Indeed, counting and what I'm referring to as numbers are different.
 Counting is a mental process while numbers have nothing to do with mind
 though the mind may apprehend and understand numbers to some extent.

 Counting is not the origin of numbers.  Counting inspired the discovery of
 numbers as elucidated by people like Peano.  Numbers are idealized models
 for the process of counting much like how a rectangle is an idealized model
 for the blueprint of an architectural  structure's foundation.  Rectangles
 are not found in nature and neither are numbers; both are abstractions of
 things we see in nature.

 Yet numbers and rectangles (and many other abstractions) have a
 suspiciously good use for modeling things in nature.


  I wonder if you have an example where application of numbers is
 extractable from ANY quantity the numbers refer to?
 Three plus four is not different from blue plus loud, sound plus
 speed, *whatever*, meaningless words bound together. UNless - of course -
 you as a human, with human logic and complexity, UNDERSTAND the amount *
 three* added to a *comparable* amount of *four *and RESULT in 
 *sevenpertaining to the same kind of amount.
 *

 I only mean to reference the difference between numbers and the quantity
 they point to.  In an important way, 3+4 is different from your other
 examples in that 3+4 can be translated into a language devoid of human
 baggage and symbolically manipulated so as to show an equivalence between
 the symbols 3+4 and 7.


  **
 **
 *Axioms* however sounds to my vocabulary like inventions helping to
 justify our theories. Sometimes quite weird.
 And *Brent* was so right:  *...I don't think the existence of some number
 of distinct things is the same as the existence of numbers*  -
 Tegmark's quoted accounted for... is not consists of.
 *To 'explain'   *something by a conceptualization does not substitute for
 the existence and justification of such conceptualization.

 Axioms are statements.  Do humans need to exist in order for the statement
 the galaxy is approximately a spiral shape to exist?  How about 

Re: numbers?

[Bruno Marchal]

On 05 Aug 2010, at 01:18, Brian Tenneson wrote:


Hmm... Lawvere has tried to build an all encompassing universal  
mathematical structure, but he failed. It was an interesting failure  
as he discovered the notion of topos, (discovered also independently  
by Groethendieck) which is more a mathematical mathematician than a  
mathematical universe.
Also Tegmark is not aware that Digital Mechanism entails the non  
locality, the indeterminacy and the non cloning of matter, and that  
DM makes the physical into a person-modality due to the presence of  
the mathematician in the arithmetical reality.

Quanta are special case of first person plural sharable qualia.

-

I'm not looking for a truly all-encompassing mathematical  
structure.  What I'm looking for is a mathematical structure in  
which all mathematical structures can be embedded.  By mathematical  
structure, I mean there is a symbol set S consisting of constant  
symbols, relation symbols, and function symbols, and the pairing of  
a set with a list of rules that interpret the symbols.  In Tegmark's  
papers on ultimate ensemble TOE and the mathematical universe,  
he refers to what I call a mathematical structure as a formal  
system (and also mathematical structure).


The structure I'm looking for wouldn't encompass anything that isn't  
a mathematical structure, like a category with no objects/elements.


You may encounter a problem with the notion of 1-person, and  
'material' bodies.





Tegmark argues that reality is a mathematical structure.  What's  
cute about his argument is that while invoking the concept of a TOE,  
his argument is independent of what that TOE might be.  He defines a  
TOE to be a complete description of reality.  Whether or not this  
can be expressed in a finite string is an open problem as far as I  
know.  (I doubt it can.)  He argues that a complete description of  
reality must be expressible in a form that has no human baggage and  
I would add to that is something that exists independent of humans  
in the sense that while the symbols used to provide that complete  
description will depend on humans, what is pointed to by the symbols  
is not.


Computationalism entails something very near such view indeed. It  
entails also that if such structure make sense, then its cardinality  
is unknowable by the self-aware beings that could be generated inside.  
The statement that the cardinality of the mathematical universe is  
countable or not is absolutely undecidable, from 'inside'.






Tegmark argues that reality is a mathematical structure and states  
that an open problem is finding a mathematical structure which is  
isomorphic to reality.  This might or might not be clear: the  
mathematical structure with the property that all mathematical  
structures can be embedded within it is precisely the mathematical  
structure we are looking for.


The problem is in defining embedded. I am not sure it makes set  
theoretical sense, unless you believe in Quine's New foundation (NF).  
I am neutral on the consistency of NF.
With a large sense of embedded I may argue that the mathematical  
structure you are looking for is just the (mathematical) universal  
machine. In which case Robinson arithmetic (a tiny fragment of  
arithmetical truth, on which both platonist and non platonist  
(intuitionist) is enough. Indeed, I argue with comp that Robinson  
arithmetic, or any first order specification of a (Turing) universal  
theory is enough to derive the appearance of quanta and qualia.




I am confident that I have found such a structure but only over a  
fixed symbol set; I need such a structure to be inclusive of all  
symbol sets so as to cast away the need to refer to a symbol set.


This again follows from Church thesis, for the 'computationalist' TOE.



The technique I used was to use NFU, new foundations set theory with  
urelements--which is known to be a consistent set theory, to first  
find the set of all S-structures.


All right, then.


Then I take what I believe is called the reduced product of all S- 
structures.  Then I show that all S-structures can be embedded  
within the reduced product of all S-structures.  Admittedly, there  
is nothing at all deep about this; none of my arguments are deeper  
than typical homework problems in a math logic course.


That may be already a lot for non mathematical logicians ...




My next move is to find justification for the existence of a math  
structure with the important property that all structures can be  
embedded within it --independent of the symbol set-- and thus  
eliminating the need to refer to it.


One thing I wonder is how to define all your notions such as  
mathematician, n-brains, n-minds, and digital mechanism in  
terms of mathematical structures.


This is done. Everything is defined in term of number and number  
relation. But it is not asked that the relation is arithmeticaly  
definable. For example, the ONE of Plotinus 

Re: numbers?

[Brian Tenneson]

John Mikes wrote:

Brian,
nothing could be more remote for me than to argue 'math' (number's 
application and theories) with you. I thinkyou mix up* 'counting'* for 
the stuff that serves it. As I usually do, I looked up Google for the 
Peano axioms and found nothing in them that pertains to the 
origination of numbers. They USE them and EXPLAIN sich usage. Use what
Indeed, counting and what I'm referring to as numbers are different.  
Counting is a mental process while numbers have nothing to do with mind 
though the mind may apprehend and understand numbers to some extent.


Counting is not the origin of numbers.  Counting inspired the discovery 
of numbers as elucidated by people like Peano.  Numbers are idealized 
models for the process of counting much like how a rectangle is an 
idealized model for the blueprint of an architectural  structure's 
foundation.  Rectangles are not found in nature and neither are numbers; 
both are abstractions of things we see in nature.


Yet numbers and rectangles (and many other abstractions) have a 
suspiciously good use for modeling things in nature.



I wonder if you have an example where application of numbers is 
extractable from ANY quantity the numbers refer to?
Three plus four is not different from blue plus loud, sound plus 
speed, /_whatever_/, meaningless words bound together. UNless - of 
course - you as a human, with human logic and complexity, UNDERSTAND 
the amount *three* added to a _comparable_ amount of *four *and RESULT 
in /_*seven* pertaining to the same kind of amount._/
I only mean to reference the difference between numbers and the quantity 
they point to.  In an important way, 3+4 is different from your other 
examples in that 3+4 can be translated into a language devoid of human 
baggage and symbolically manipulated so as to show an equivalence 
between the symbols 3+4 and 7. 




/_ _/
// 
/_Axioms_/ however sounds to my vocabulary like inventions helping to 
justify our theories. Sometimes quite weird.
And *Brent* was so right:  /...I don't think the existence of some 
number of distinct things is the same as the existence of 
numbers/  - Tegmark's quoted accounted for... is not consists 
of.
/_To 'explain'   _/something by a conceptualization does not 
substitute for the existence and justification of such conceptualization.
Axioms are statements.  Do humans need to exist in order for the 
statement the galaxy is approximately a spiral shape to exist?  How 
about 3+4=7, does that require humans to exist in order for the 
statement to exist?  What about the existence of the statement the 
president of the US is male; if all the humans were to die out, that 
statement would still exist.  Statements are uttered by humans but do 
not depend on humans for their existence.  This is how axioms exist 
independent of humans, because they are statements.  The notation 
differs and are invented but what is being referred to by the symbols is 
independent of humans.  Moreover, I'm not talking about the truth of 
statements; I'm talking about the statements themselves not requiring 
anyone to utter them in order to exist.


Numbers do not physically exist; so if physical existence is the only 
form of existence you permit, then numbers do not exist... in the same 
sense that math might as well be about Luke Skywalker, who does not 
exist physically.  However, math has a suspiciously good use in nature 
like I said, unlike a novel about Luke Skywalker.



 
Does it make sense that 'numbers existed' when nobody was around to 
*/_K N O W  or  U S E??_/*
Especially when they did not/_  *C O U N T*_/  anything? BTW: what are 
those abstract symbols you refer to as numbers?
(and this question is understood for times way before humans and human 
thinking).

Sorry I asked
 
John M




Does it make sense?  Let me ask you a question.  Way back when, in the 
earliest stages of counting, let's assume there was a point at which a 
hundred thousand was the furthest anyone had counted to.  Now.. Did the 
number 1,000,000 exist at this stage of counting?  I think it did.  A 
million and all of its successors.



Bruno,
-

Hmm... Lawvere has tried to build an all encompassing universal 
mathematical structure, but he failed. It was an interesting failure as 
he discovered the notion of topos, (discovered also independently by 
Groethendieck) which is more a mathematical mathematician than a 
mathematical universe.
Also Tegmark is not aware that Digital Mechanism entails the non 
locality, the indeterminacy and the non cloning of matter, and that DM 
makes the physical into a person-modality due to the presence of the 
mathematician in the arithmetical reality.

Quanta are special case of first person plural sharable qualia.

-

I'm not looking for a truly all-encompassing mathematical structure.  
What I'm looking for is a mathematical structure in which all 
mathematical structures can be embedded.  By mathematical structure, I 
mean 

Re: numbers?

[Bruno Marchal]

On 02 Aug 2010, at 00:30, Brian Tenneson wrote:

As a corollary to some of Tegmark's theory I believe it will be  
possible to prove that the level 4 multiverse is accounted for by  
a mathematical structure..


Hmm... Lawvere has tried to build an all encompassing universal  
mathematical structure, but he failed. It was an interesting failure  
as he discovered the notion of topos, (discovered also independently  
by Groethendieck) which is more a mathematical mathematician than a  
mathematical universe.
Also Tegmark is not aware that Digital Mechanism entails the non  
locality, the indeterminacy and the non cloning of matter, and that DM  
makes the physical into a person-modality due to the presence of the  
mathematician in the arithmetical reality.

Quanta are special case of first person plural sharable qualia.



It's a project I've been working on which assumes that the reality  
hypothesis implies the mathematical universe hypothesis.


I can only encourage you to proceed, but it may be nice to try using  
the already existing results in the field. Tegmark is not aware of the  
importance of the mind-body problem when searching a toe. He uses  
implicitly the brain-mind identity thesis which breaks down with  
digital mechanism (and plausibly with any form of reasonable mechanist  
assumption). You can ascribe an  1-mind to a 3-brain, but you can only  
ascribe a whole infinite set of 3-brain to a 1-mind.


- Bruno Marchal





Bruno Marchal wrote:



... and if you believe that the universe can be accounted for by a  
some consistent mathematical structure. Which is an open problem.  
Assuming mechanism, physical universes have no real existence at  
all, except as first person sharable experience by machines  
(mathematical digital machines).






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Re: numbers?

[John Mikes]

Quentin:
excellent. Your Voltairian acridity showed perfectly how bad my argument
was. A typical gotcha.
Now aout existence: that (noun!) concept is the target of my frequent
question, I used the topic as: to exist, a verb, in the widest sense.
What may lead to desperate argumentation about the meaning. I extended it
into
whatever emerged in any mind DOES exist. I semingly restriceted the numbers
into human minds (human logic) not knowing about better applications than
the human counting-related quantizing.
Maybe you know about 'number-roles' in pre-human times substituting for
many/few in the extremely diverse scales for (humanly) unidentified
features.
As you see, I accept a good argument.

Thanks

John M


On 8/2/10, Quentin Anciaux allco...@gmail.com wrote:



 2010/8/2 John Mikes jami...@gmail.com

 Brian,
 nothing could be more remote for me than to argue 'math' (number's
 application and theories) with you. I thinkyou mix up* 'counting'* for
 the stuff that serves it. As I usually do, I looked up Google for the Peano
 axioms and found nothing in them that pertains to the origination of
 numbers. They USE them and EXPLAIN sich usage. Use what
 I wonder if you have an example where application of numbers is
 extractable from ANY quantity the numbers refer to?
 Three plus four is not different from blue plus loud, sound plus
 speed, *whatever*, meaningless words bound together. UNless - of course
 - you as a human, with human logic and complexity, UNDERSTAND the amount
 *three* added to a *comparable* amount of *four *and RESULT in 
 *sevenpertaining to the same kind of amount.
 *
 **
 *Axioms* however sounds to my vocabulary like inventions helping to
 justify our theories. Sometimes quite weird.
 And *Brent* was so right:  *...I don't think the existence of some
 number of distinct things is the same as the existence of numbers*
 - Tegmark's quoted accounted for... is not consists of.
 *To 'explain'   *something by a conceptualization does not substitute for
 the existence and justification of such conceptualization.

 Does it make sense that 'numbers existed' when nobody was around to *K N
 O W  or  U S E??*


 Yes... provided you use the same meaning as me for existence...

 All of this is linked to what you mean by existed...  asked otherwise,

 Does it make sense to say that 'the universe existed' when nobody was
 around to *K N O W  it existed ??*

 Quentin


 Especially when they did not*  C O U N T*  anything? BTW: what are those
 abstract symbols you refer to as numbers?
 (and this question is understood for times way before humans and human
 thinking).
 Sorry I asked

 John M


 On 8/1/10, Brian Tenneson tenn...@gmail.com wrote:

 I quite agree that counting and the existence of numbers are different.

 The Peano axioms for numbers makes it seem like numbers are not dependent
 on us humans to exist which entails that there are infinite sets by assuming
 an induction property held by (sets of) numbers.

 So while counting may not have been around forever, numbers have,
 independent of us humans.  The Peano axioms are totally free of human
 baggage and did not need Peano to utter them in order for numbers to exist.
 Consequently, I believe most if not all of math is discovered.

 The formalism for counting as describing a one-to-one correspondence to a
 (formally defined) finite set of numbers also exists independent of humans
 in the same way that the unit circle exists.  The formalism for counting is
 of course not how biological machines such as we count; the formalism is
 just meant to intuitively express what we actually do when we count.


 Brent Meeker wrote:

 On 7/29/2010 3:28 PM, Mark Buda wrote:

 Quantum mechanics suggests maybe not. If there were no conscious
 observers to collapse the wave function of the universe after the big bang,
 then what, pray tell, would constitute an atom that might be counted?

 This assumes that conscious observers are necessary to collapse the wave
 function, of course.
 --
 Mark Buda her...@acm.org
 I get my monkeys for nothing and my chimps for free.



 --
 On Jul 29, 2010 2:01 PM, Brian Tenneson 
 tenn...@gmail.comtenn...@gmail.comwrote:

 Numbers existed before people on this rock began to understand them.  If
 not number of atoms in the universe, then the number of cells in organisms
 one day prior to 10,000 years ago. or anything really, that had the
 potential to be counted, one day prior to 10,000 years ago.


 I don't think the existence of some number of distinct things is the same
 as the existence of numbers.  Numbers are defined by order and successor -
 neither of which are present or implicit in a mere collection of atoms or
 anything else.

 Brent
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Re: numbers?

[Quentin Anciaux]

2010/8/2 Brent Meeker meeke...@dslextreme.com

  On 8/1/2010 3:42 PM, Quentin Anciaux wrote:



 2010/8/2 Brent Meeker meeke...@dslextreme.com

  On 8/1/2010 3:24 PM, Brian Tenneson wrote:

 I quite agree that counting and the existence of numbers are different.

 The Peano axioms for numbers makes it seem like numbers are not dependent
 on us humans to exist which entails that there are infinite sets by assuming
 an induction property held by (sets of) numbers.

 So while counting may not have been around forever, numbers have,
 independent of us humans.  The Peano axioms are totally free of human
 baggage


  I don't think so.  Where's the natural instance of successor. This is
 a successor of that seems to me a human conceptualization based on the
 mental equivalent of moving pebbles into a group.  That it can be done
 indefinitely is merely a convenient assumption.

 Brent


 The only problem is if numbers were a human invention... other humans could
 come with a prime number that is even and not 2... There would exists a
 biggest number, 1+1=2 could be false somewhere sometime (even by following
 the rules that makes 1+1=2 true always)...


 They can and do.  In modulo two arithmetic 1+1=0.  You can invent all kinds
 of number systems or other logics and axiomatic systems.


You did not read entirely... quoting: 'even by following the rules that
makes 1+1=2 true always'

rules == axiomatic systems. So if you use the standard definition of
addition in base 10.. 1+1=2 always, if it's a human invention, it can be
otherwise somewhere sometimes even if you use the standard definition of
addition in base 10.




 Mathematical truth are independent of humans, life and the universe and the
 rest, it's nonsense if it's otherwise.


 What's it's in the above sentence?


It's, is the fact that mathematical truths are independent of humans.

Quentin



 Brent



 Quentin




 and did not need Peano to utter them in order for numbers to exist.
 Consequently, I believe most if not all of math is discovered.

 The formalism for counting as describing a one-to-one correspondence to a
 (formally defined) finite set of numbers also exists independent of humans
 in the same way that the unit circle exists.  The formalism for counting is
 of course not how biological machines such as we count; the formalism is
 just meant to intuitively express what we actually do when we count.

 Brent Meeker wrote:

 On 7/29/2010 3:28 PM, Mark Buda wrote:

 Quantum mechanics suggests maybe not. If there were no conscious observers
 to collapse the wave function of the universe after the big bang, then what,
 pray tell, would constitute an atom that might be counted?

 This assumes that conscious observers are necessary to collapse the wave
 function, of course.
  --
 Mark Buda her...@acm.org
 I get my monkeys for nothing and my chimps for free.


  --
 On Jul 29, 2010 2:01 PM, Brian Tenneson 
 tenn...@gmail.comtenn...@gmail.comwrote:

 Numbers existed before people on this rock began to understand them.  If
 not number of atoms in the universe, then the number of cells in organisms
 one day prior to 10,000 years ago. or anything really, that had the
 potential to be counted, one day prior to 10,000 years ago.


 I don't think the existence of some number of distinct things is the same
 as the existence of numbers.  Numbers are defined by order and successor -
 neither of which are present or implicit in a mere collection of atoms or
 anything else.

 Brent
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Re: numbers?

[Brent Meeker]

On 8/2/2010 12:13 AM, Quentin Anciaux wrote:



2010/8/2 Brent Meeker meeke...@dslextreme.com 
mailto:meeke...@dslextreme.com


On 8/1/2010 3:42 PM, Quentin Anciaux wrote:



2010/8/2 Brent Meeker meeke...@dslextreme.com
mailto:meeke...@dslextreme.com

On 8/1/2010 3:24 PM, Brian Tenneson wrote:

I quite agree that counting and the existence of numbers are
different.

The Peano axioms for numbers makes it seem like numbers are
not dependent on us humans to exist which entails that there
are infinite sets by assuming an induction property held by
(sets of) numbers.

So while counting may not have been around forever, numbers
have, independent of us humans.  The Peano axioms are
totally free of human baggage 


I don't think so.  Where's the natural instance of
successor. This is a successor of that seems to me a
human conceptualization based on the mental equivalent of
moving pebbles into a group.  That it can be done
indefinitely is merely a convenient assumption.

Brent


The only problem is if numbers were a human invention... other
humans could come with a prime number that is even and not 2...
There would exists a biggest number, 1+1=2 could be false
somewhere sometime (even by following the rules that makes 1+1=2
true always)...


They can and do.  In modulo two arithmetic 1+1=0.  You can invent
all kinds of number systems or other logics and axiomatic systems.


You did not read entirely... quoting: 'even by following the rules 
that makes 1+1=2 true always'


rules == axiomatic systems. So if you use the standard definition of 
addition in base 10.. 1+1=2 always, if it's a human invention, it can 
be otherwise somewhere sometimes even if you use the standard 
definition of addition in base 10.


But that's like saying if you speak according to the rules of English 
you will utter English sentences.  It doesn't make English a fact of nature.






Mathematical truth are independent of humans, life and the
universe and the rest, it's nonsense if it's otherwise.


What's it's in the above sentence?


It's, is the fact that mathematical truths are independent of humans.


Ah.  The point in question is asserted.

Brent

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Re: numbers?

[Quentin Anciaux]

2010/8/2 Brent Meeker meeke...@dslextreme.com

  On 8/2/2010 12:13 AM, Quentin Anciaux wrote:



 2010/8/2 Brent Meeker meeke...@dslextreme.com

  On 8/1/2010 3:42 PM, Quentin Anciaux wrote:



 2010/8/2 Brent Meeker meeke...@dslextreme.com

  On 8/1/2010 3:24 PM, Brian Tenneson wrote:

 I quite agree that counting and the existence of numbers are different.

 The Peano axioms for numbers makes it seem like numbers are not dependent
 on us humans to exist which entails that there are infinite sets by assuming
 an induction property held by (sets of) numbers.

 So while counting may not have been around forever, numbers have,
 independent of us humans.  The Peano axioms are totally free of human
 baggage


  I don't think so.  Where's the natural instance of successor. This is
 a successor of that seems to me a human conceptualization based on the
 mental equivalent of moving pebbles into a group.  That it can be done
 indefinitely is merely a convenient assumption.

 Brent


 The only problem is if numbers were a human invention... other humans
 could come with a prime number that is even and not 2... There would exists
 a biggest number, 1+1=2 could be false somewhere sometime (even by following
 the rules that makes 1+1=2 true always)...


  They can and do.  In modulo two arithmetic 1+1=0.  You can invent all
 kinds of number systems or other logics and axiomatic systems.


 You did not read entirely... quoting: 'even by following the rules that
 makes 1+1=2 true always'

 rules == axiomatic systems. So if you use the standard definition of
 addition in base 10.. 1+1=2 always, if it's a human invention, it can be
 otherwise somewhere sometimes even if you use the standard definition of
 addition in base 10.


 But that's like saying if you speak according to the rules of English you
 will utter English sentences.  It doesn't make English a fact of nature.


Meaning of words can change and do change. Meaning of english words are
dependant of humans. Meaning of mathematical thruths aren't.







 Mathematical truth are independent of humans, life and the universe and
 the rest, it's nonsense if it's otherwise.


  What's it's in the above sentence?


 It's, is the fact that mathematical truths are independent of humans.


 Ah.  The point in question is asserted.

 Brent


No, it's about the meaning. If mathematical truth are dependant on humans
they mean utlimately nothing at all. So it's nonsensical.

Quentin

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Re: numbers?

[Bruno Marchal]

Hi John,


On 01 Aug 2010, at 00:05, John Mikes wrote:


Bruno and David:

there are concepts in your extremely interesting and informative  
discussion - 'beyond me':


First the real existence (beyond Bruno's 1st person sharable  
experience by machines).
I call 'existence' everything that emerges in (any) 'mind' without  
calling it real, or unreal. Who has the means to distinguish the  
reality of an existence? we can think only in our human  mini- 
solipsism (cf. Colin Hales) ABOUT some 'reality' what we MAY assume.



OK





Physical existence is IMO a figment by our explanatory skills (aided  
by math/physics etc.) of the gradually disclosed items in phenomena  
- poorly understood - over the millennia of human development. (Cf:  
the conventional sciences).


... and the thousands of millennia of life development.
We don't know if there does not even exist build-in prejudices in the  
big bang!
Evidences are that some kind of prejudices may be build in in  
arithmetical truth, already.

But we can build only from what we have ...





Then again: CTM testable? by what rules? by the conventional  
(reductionist) science figments? Who can identify the MIND to test  
it?


The key here is that machine theology explains both qualia and quanta.  
So we can compare the quanta derived from machine's theology with  
the nature observable quanta (quantum mechanics, chemistry, etc.)

Testable just means refutable. It never means prove.



Computational also depends on the Comp applied unless we use(?) the  
Loebian omniscient super machine,


Oh!  I would not apply the adjective omniscient to Löbian machine.  
Universal machine knows about nothing, and all Löbian machines knows  
mainly one thing more: that they know about nothing. We can only  
scratch the surface, somehow. Löbian machine are 'terribly humble and  
modest'.



as I deducted from Brunos words lately (for being 'computer- 
emulable').


I guess I have been unclear. Don't confuse the universality bearing on  
computability and emulability, and the absence of universality  
concerning notion like belief, knowdlege, provability, etc.




I fear: if we position CTM above the physical sciences, we cannot  
judge it by physicality (the physically based scientific testability).


Why not? If CTM predicts that the mass of the electron is above one  
ton, we may consider that CTM is refuted.





I apologize for my agnostic position based on an unlimited  
complexity and its relations of which we know only a fragment by a  
gradual epistemic enrichment still going on.



Sure. You don't have to apologize for an agnostic position. Honest  
science is agnostic. Always. Nobody pretends that CTM is true. On the  
contrary, the goal is to make it precise so that we can test/refute it.




It reduces CTM in both its C (ordinary computer-applications) to  
the data-base and capabilities of the machine in question and the  
M to the figment represented in the reductionistic philosophy  
(including neurosciences, psychology, even religious beliefs).


It is not necessarily reductionist. In particular CTM provides a sort  
of vaccine against reductionism. Löbian machines already  defeat all  
complete theories about them. They point to the fact that we are much  
more ignorant than some conventional science/religion makes some  
people believe.






I am all for the First Person Sharable Experience. That's all we  
got and that's all we can use.


Indeed.



Even pertaining to communicated (3rd pers.?) information, which  
first gets - adjusted to our personal indiviual mindset - OUR 1st  
pers. experience.



I agree,



Bruno



On 7/31/10, Bruno Marchal marc...@ulb.ac.be wrote:

On 31 Jul 2010, at 00:49, David Nyman wrote:

On 30 July 2010 17:35, Bruno Marchal marc...@ulb.ac.be wrote:

... and if you believe that the universe can be accounted for by a  
some

consistent mathematical structure. Which is an open problem. Assuming
mechanism, physical universes have no real existence at all, except  
as first
person sharable experience by machines (mathematical digital  
machines).


Bruno, consideration of the particular way you expressed this above
led to the following thoughts.  Let us leave aside for the moment the
question of whether the universe can be accounted for by some
consistent mathematical structure.  I am aware, of course, of your
detailed disproof per absurdum of the logical possibility of a
physical basis for the computational theory of mind (CTM).  It is
noteworthy, nonetheless, that even in its physicalist version, CTM
seeks to explain first person sharable experience as a virtual
mechanism, albeit here assumed to be capable of justification in
terms of the relations of fundamentally physical tokens of some
sort.  Leaving aside for the moment whether this is ultimately a
correct account or not, my point here is that it is already implicit,
per such a physicalist version of CTM, that the physical universe -
above whatever lowest level is 

Re: numbers?

[Quentin Anciaux]

2010/8/2 Brent Meeker meeke...@dslextreme.com

  On 8/2/2010 1:39 AM, Quentin Anciaux wrote:


 ...

  Meaning of words can change and do change. Meaning of english words are
 dependant of humans. Meaning of mathematical thruths aren't.


 Mathematical truths don't have meaning.



Well I must be too dumb or have too much prejudice with programming a
computer...

The fact that there is or isn't a biggest prime or a biggest number does not
depend on human, consciousness or whatever.

We do not invent that... we can't choose the result, either it is true or it
is false.

Do I have to think about something for it to exists ?

And yes if you choose other axioms, you find other results, still it's not
invented, the result are according to the rules. If you change definition
of words, yes it means something different, so what ?

The truthness of a statement is not decided when you choose the rules... it
was true or false according to the rules even before someone thought of that
particular rules or even if no one ever had and never will.

The fact is that in every possible language, following the rules of addition
in base 10, will always give you 1 + 1 = 2. Even if you speak martian. Even
if you come from another place of the universe or from another universe.











 Mathematical truth are independent of humans, life and the universe and
 the rest, it's nonsense if it's otherwise.


  What's it's in the above sentence?


 It's, is the fact that mathematical truths are independent of humans.


  Ah.  The point in question is asserted.

 Brent


 No, it's about the meaning. If mathematical truth are dependant on humans
 they mean utlimately nothing at all. So it's nonsensical.



 Truth is property of sentences.  In mathematics it's just a token T you
 attach to some sentences (the axioms) and then applying some rules of
 inference that are assumed to preserve T you see which other sentences get
 T.  It is nonsense, in the sense that pure mathematics is not about
 anything.  It is useful for creating models of things because it guarantees
 that the model will not be inconsistent, i.e. lead to the inference of every
 statement.  Mathematics attains certainty by giving up meaning.

 Brent
 In mathematics we never know what we are talking about or whether what we
 say is true or false.
 --- Bertrand Russell


I don't understand what you're trying to say... maybe I don't understand
what you mean by 'inventing'...

Quentin



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Re: numbers?

[Mark Buda]

Brent Meeker meeke...@dslextreme.com writes:

 On 8/1/2010 3:42 PM, Quentin Anciaux wrote:

 The only problem is if numbers were a human invention... other
 humans could come with a prime number that is even and not
 2... There would exists a biggest number, 1+1=2 could be false
 somewhere sometime (even by following the rules that makes 1+1=2
 true always)...

 They can and do.  In modulo two arithmetic 1+1=0.  You can invent all
 kinds of number systems or other logics and axiomatic systems.

No. You can define your terms, and you can use your terms, but you can't
redefine your terms while you're using them and end up with a valid
argument. When Quentin says 1+1=2 always, he has a meaning behind those
symbols. He's talking about the idea in his mind underlying the
utterance 1+1=2 being true always. You can't take a different idea
that happens to be expressed using the same symbols and then assert that
that has any bearing on the truth of Quentin's original idea.

You could do that if he were writing a formal mathematical proof,
because then you would be explicitly bound by the same
symbol-manipulating rules he is.

So what you said above is perfectly true, but doesn't make your case
that numbers are a human invention. The symbols and words we use to talk
about numbers are a human invention. Not the numbers.
-- 
Mark Buda her...@acm.org
I get my monkeys for nothing and my chimps for free.

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Re: numbers?

[Brent Meeker]

On 8/2/2010 11:14 AM, Mark Buda wrote:

Brent Meekermeeke...@dslextreme.com  writes:

   

On 8/1/2010 3:42 PM, Quentin Anciaux wrote:

 The only problem is if numbers were a human invention... other
 humans could come with a prime number that is even and not
 2... There would exists a biggest number, 1+1=2 could be false
 somewhere sometime (even by following the rules that makes 1+1=2
 true always)...

They can and do.  In modulo two arithmetic 1+1=0.  You can invent all
kinds of number systems or other logics and axiomatic systems.
 

No. You can define your terms, and you can use your terms, but you can't
redefine your terms while you're using them and end up with a valid
argument. When Quentin says 1+1=2 always, he has a meaning behind those
symbols.


But the meaning isn't mathematical - it's the idea of putting pebbles 
together and counting them.  He
abstracts away the pebbles and supposes that he has discovered a 
Platonic realm in which the numbers
exist without anything to count or succeed.  But I think that meaning 
(i.e. reference) only comes from
action, or at least potential action, within an environment.  It's fine 
to abstract away particulars for purposes of inference - but to say that 
discovers new existences seems to me simply inventing a new kind of 
existence that could as well be called non-existence or imaginary 
existence.



He's talking about the idea in his mind underlying the
utterance 1+1=2 being true always. You can't take a different idea
that happens to be expressed using the same symbols and then assert that
that has any bearing on the truth of Quentin's original idea.
   


But his original idea existed in his brain - at least that's the 
physicalist theory.



You could do that if he were writing a formal mathematical proof,
because then you would be explicitly bound by the same
symbol-manipulating rules he is.

So what you said above is perfectly true, but doesn't make your case
that numbers are a human invention. The symbols and words we use to talk
about numbers are a human invention. Not the numbers.
   


My point was that since we can invent other mathematical structures - 
including number systems.  Why should we suppose the natural numbers 
exist and the others don't.  Or do you contend that all mathematical 
systems exist and are discovered, not invented.  In which case what 
distinguishes them from all Sherlock Holmes stories - were they to 
discovered?


Brent

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Re: numbers?

[John Mikes]

Brian,
nothing could be more remote for me than to argue 'math' (number's
application and theories) with you. I thinkyou mix up* 'counting'* for the
stuff that serves it. As I usually do, I looked up Google for the Peano
axioms and found nothing in them that pertains to the origination of
numbers. They USE them and EXPLAIN sich usage. Use what
I wonder if you have an example where application of numbers is extractable
from ANY quantity the numbers refer to?
Three plus four is not different from blue plus loud, sound plus
speed, *whatever*, meaningless words bound together. UNless - of course -
you as a human, with human logic and complexity, UNDERSTAND the amount *
three* added to a *comparable* amount of *four *and RESULT in
*sevenpertaining to the same kind of amount.
*
**
*Axioms* however sounds to my vocabulary like inventions helping to justify
our theories. Sometimes quite weird.
And *Brent* was so right:  *...I don't think the existence of some number
of distinct things is the same as the existence of numbers*  -
Tegmark's quoted accounted for... is not consists of.
*To 'explain'   *something by a conceptualization does not substitute for
the existence and justification of such conceptualization.

Does it make sense that 'numbers existed' when nobody was around to *K N O
W  or  U S E??*
Especially when they did not*  C O U N T*  anything? BTW: what are those
abstract symbols you refer to as numbers?
(and this question is understood for times way before humans and human
thinking).
Sorry I asked

John M


On 8/1/10, Brian Tenneson tenn...@gmail.com wrote:

 I quite agree that counting and the existence of numbers are different.

 The Peano axioms for numbers makes it seem like numbers are not dependent
 on us humans to exist which entails that there are infinite sets by assuming
 an induction property held by (sets of) numbers.

 So while counting may not have been around forever, numbers have,
 independent of us humans.  The Peano axioms are totally free of human
 baggage and did not need Peano to utter them in order for numbers to exist.
 Consequently, I believe most if not all of math is discovered.

 The formalism for counting as describing a one-to-one correspondence to a
 (formally defined) finite set of numbers also exists independent of humans
 in the same way that the unit circle exists.  The formalism for counting is
 of course not how biological machines such as we count; the formalism is
 just meant to intuitively express what we actually do when we count.


 Brent Meeker wrote:

 On 7/29/2010 3:28 PM, Mark Buda wrote:

 Quantum mechanics suggests maybe not. If there were no conscious observers
 to collapse the wave function of the universe after the big bang, then what,
 pray tell, would constitute an atom that might be counted?

 This assumes that conscious observers are necessary to collapse the wave
 function, of course.
 --
 Mark Buda her...@acm.org
 I get my monkeys for nothing and my chimps for free.



 --
 On Jul 29, 2010 2:01 PM, Brian Tenneson 
 tenn...@gmail.comtenn...@gmail.comwrote:

 Numbers existed before people on this rock began to understand them.  If
 not number of atoms in the universe, then the number of cells in organisms
 one day prior to 10,000 years ago. or anything really, that had the
 potential to be counted, one day prior to 10,000 years ago.


 I don't think the existence of some number of distinct things is the same
 as the existence of numbers.  Numbers are defined by order and successor -
 neither of which are present or implicit in a mere collection of atoms or
 anything else.

 Brent
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Re: numbers?

[Quentin Anciaux]

2010/8/2 John Mikes jami...@gmail.com

 Brian,
 nothing could be more remote for me than to argue 'math' (number's
 application and theories) with you. I thinkyou mix up* 'counting'* for the
 stuff that serves it. As I usually do, I looked up Google for the Peano
 axioms and found nothing in them that pertains to the origination of
 numbers. They USE them and EXPLAIN sich usage. Use what
 I wonder if you have an example where application of numbers is extractable
 from ANY quantity the numbers refer to?
 Three plus four is not different from blue plus loud, sound plus
 speed, *whatever*, meaningless words bound together. UNless - of course -
 you as a human, with human logic and complexity, UNDERSTAND the amount *
 three* added to a *comparable* amount of *four *and RESULT in 
 *sevenpertaining to the same kind of amount.
 *
 **
 *Axioms* however sounds to my vocabulary like inventions helping to
 justify our theories. Sometimes quite weird.
 And *Brent* was so right:  *...I don't think the existence of some number
 of distinct things is the same as the existence of numbers*  -
 Tegmark's quoted accounted for... is not consists of.
 *To 'explain'   *something by a conceptualization does not substitute for
 the existence and justification of such conceptualization.

 Does it make sense that 'numbers existed' when nobody was around to *K N O
 W  or  U S E??*


Yes... provided you use the same meaning as me for existence...

All of this is linked to what you mean by existed...  asked otherwise,

Does it make sense to say that 'the universe existed' when nobody was around
to *K N O W  it existed ??*

Quentin


 Especially when they did not*  C O U N T*  anything? BTW: what are those
 abstract symbols you refer to as numbers?
 (and this question is understood for times way before humans and human
 thinking).
 Sorry I asked

 John M


 On 8/1/10, Brian Tenneson tenn...@gmail.com wrote:

 I quite agree that counting and the existence of numbers are different.

 The Peano axioms for numbers makes it seem like numbers are not dependent
 on us humans to exist which entails that there are infinite sets by assuming
 an induction property held by (sets of) numbers.

 So while counting may not have been around forever, numbers have,
 independent of us humans.  The Peano axioms are totally free of human
 baggage and did not need Peano to utter them in order for numbers to exist.
 Consequently, I believe most if not all of math is discovered.

 The formalism for counting as describing a one-to-one correspondence to a
 (formally defined) finite set of numbers also exists independent of humans
 in the same way that the unit circle exists.  The formalism for counting is
 of course not how biological machines such as we count; the formalism is
 just meant to intuitively express what we actually do when we count.


 Brent Meeker wrote:

 On 7/29/2010 3:28 PM, Mark Buda wrote:

 Quantum mechanics suggests maybe not. If there were no conscious observers
 to collapse the wave function of the universe after the big bang, then what,
 pray tell, would constitute an atom that might be counted?

 This assumes that conscious observers are necessary to collapse the wave
 function, of course.
 --
 Mark Buda her...@acm.org
 I get my monkeys for nothing and my chimps for free.



 --
 On Jul 29, 2010 2:01 PM, Brian Tenneson 
 tenn...@gmail.comtenn...@gmail.comwrote:

 Numbers existed before people on this rock began to understand them.  If
 not number of atoms in the universe, then the number of cells in organisms
 one day prior to 10,000 years ago. or anything really, that had the
 potential to be counted, one day prior to 10,000 years ago.


 I don't think the existence of some number of distinct things is the same
 as the existence of numbers.  Numbers are defined by order and successor -
 neither of which are present or implicit in a mere collection of atoms or
 anything else.

 Brent
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Re: numbers?

[Brian Tenneson]

I quite agree that counting and the existence of numbers are different.

The Peano axioms for numbers makes it seem like numbers are not 
dependent on us humans to exist which entails that there are infinite 
sets by assuming an induction property held by (sets of) numbers.


So while counting may not have been around forever, numbers have, 
independent of us humans.  The Peano axioms are totally free of human 
baggage and did not need Peano to utter them in order for numbers to 
exist.  Consequently, I believe most if not all of math is discovered.


The formalism for counting as describing a one-to-one correspondence to 
a (formally defined) finite set of numbers also exists independent of 
humans in the same way that the unit circle exists.  The formalism for 
counting is of course not how biological machines such as we count; the 
formalism is just meant to intuitively express what we actually do when 
we count.


Brent Meeker wrote:

On 7/29/2010 3:28 PM, Mark Buda wrote:
Quantum mechanics suggests maybe not. If there were no conscious 
observers to collapse the wave function of the universe after the big 
bang, then what, pray tell, would constitute an atom that might be 
counted?


This assumes that conscious observers are necessary to collapse the 
wave function, of course.

--
Mark Buda her...@acm.org mailto:her...@acm.org
I get my monkeys for nothing and my chimps for free.



On Jul 29, 2010 2:01 PM, Brian Tenneson tenn...@gmail.com wrote:

Numbers existed before people on this rock began to understand them.  
If not number of atoms in the universe, then the number of cells in 
organisms one day prior to 10,000 years ago. or anything really, that 
had the potential to be counted, one day prior to 10,000 years ago.


I don't think the existence of some number of distinct things is the 
same as the existence of numbers.  Numbers are defined by order and 
successor - neither of which are present or implicit in a mere 
collection of atoms or anything else.


Brent
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Re: numbers?

[Brian Tenneson]

As a corollary to some of Tegmark's theory I believe it will be possible 
to prove that the level 4 multiverse is accounted for by a 
mathematical structure.. It's a project I've been working on which 
assumes that the reality hypothesis implies the mathematical universe 
hypothesis.



Bruno Marchal wrote:



... and if you believe that the universe can be accounted for by a 
some consistent mathematical structure. Which is an open problem. 
Assuming mechanism, physical universes have no real existence at all, 
except as first person sharable experience by machines (mathematical 
digital machines).






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Re: numbers?

[Brent Meeker]

On 8/1/2010 3:24 PM, Brian Tenneson wrote:

I quite agree that counting and the existence of numbers are different.

The Peano axioms for numbers makes it seem like numbers are not 
dependent on us humans to exist which entails that there are infinite 
sets by assuming an induction property held by (sets of) numbers.


So while counting may not have been around forever, numbers have, 
independent of us humans.  The Peano axioms are totally free of human 
baggage 


I don't think so.  Where's the natural instance of successor. This is 
a successor of that seems to me a human conceptualization based on the 
mental equivalent of moving pebbles into a group.  That it can be done 
indefinitely is merely a convenient assumption.


Brent

and did not need Peano to utter them in order for numbers to exist.  
Consequently, I believe most if not all of math is discovered.


The formalism for counting as describing a one-to-one correspondence 
to a (formally defined) finite set of numbers also exists independent 
of humans in the same way that the unit circle exists.  The formalism 
for counting is of course not how biological machines such as we 
count; the formalism is just meant to intuitively express what we 
actually do when we count.


Brent Meeker wrote:

On 7/29/2010 3:28 PM, Mark Buda wrote:
Quantum mechanics suggests maybe not. If there were no conscious 
observers to collapse the wave function of the universe after the 
big bang, then what, pray tell, would constitute an atom that might 
be counted?


This assumes that conscious observers are necessary to collapse the 
wave function, of course.

--
Mark Buda her...@acm.org mailto:her...@acm.org
I get my monkeys for nothing and my chimps for free.



On Jul 29, 2010 2:01 PM, Brian Tenneson tenn...@gmail.com wrote:

Numbers existed before people on this rock began to understand 
them.  If not number of atoms in the universe, then the number of 
cells in organisms one day prior to 10,000 years ago. or anything 
really, that had the potential to be counted, one day prior to 
10,000 years ago.


I don't think the existence of some number of distinct things is the 
same as the existence of numbers.  Numbers are defined by order and 
successor - neither of which are present or implicit in a mere 
collection of atoms or anything else.


Brent
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Re: numbers?

[Quentin Anciaux]

2010/8/2 Brent Meeker meeke...@dslextreme.com

  On 8/1/2010 3:24 PM, Brian Tenneson wrote:

 I quite agree that counting and the existence of numbers are different.

 The Peano axioms for numbers makes it seem like numbers are not dependent
 on us humans to exist which entails that there are infinite sets by assuming
 an induction property held by (sets of) numbers.

 So while counting may not have been around forever, numbers have,
 independent of us humans.  The Peano axioms are totally free of human
 baggage


 I don't think so.  Where's the natural instance of successor. This is a
 successor of that seems to me a human conceptualization based on the mental
 equivalent of moving pebbles into a group.  That it can be done indefinitely
 is merely a convenient assumption.

 Brent


The only problem is if numbers were a human invention... other humans could
come with a prime number that is even and not 2... There would exists a
biggest number, 1+1=2 could be false somewhere sometime (even by following
the rules that makes 1+1=2 true always)...

Mathematical truth are independent of humans, life and the universe and the
rest, it's nonsense if it's otherwise.

Quentin




 and did not need Peano to utter them in order for numbers to exist.
 Consequently, I believe most if not all of math is discovered.

 The formalism for counting as describing a one-to-one correspondence to a
 (formally defined) finite set of numbers also exists independent of humans
 in the same way that the unit circle exists.  The formalism for counting is
 of course not how biological machines such as we count; the formalism is
 just meant to intuitively express what we actually do when we count.

 Brent Meeker wrote:

 On 7/29/2010 3:28 PM, Mark Buda wrote:

 Quantum mechanics suggests maybe not. If there were no conscious observers
 to collapse the wave function of the universe after the big bang, then what,
 pray tell, would constitute an atom that might be counted?

 This assumes that conscious observers are necessary to collapse the wave
 function, of course.
  --
 Mark Buda her...@acm.org
 I get my monkeys for nothing and my chimps for free.


  --
 On Jul 29, 2010 2:01 PM, Brian Tenneson 
 tenn...@gmail.comtenn...@gmail.comwrote:

 Numbers existed before people on this rock began to understand them.  If
 not number of atoms in the universe, then the number of cells in organisms
 one day prior to 10,000 years ago. or anything really, that had the
 potential to be counted, one day prior to 10,000 years ago.


 I don't think the existence of some number of distinct things is the same
 as the existence of numbers.  Numbers are defined by order and successor -
 neither of which are present or implicit in a mere collection of atoms or
 anything else.

 Brent
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Re: numbers?

[Brent Meeker]

On 8/1/2010 3:42 PM, Quentin Anciaux wrote:



2010/8/2 Brent Meeker meeke...@dslextreme.com 
mailto:meeke...@dslextreme.com


On 8/1/2010 3:24 PM, Brian Tenneson wrote:

I quite agree that counting and the existence of numbers are
different.

The Peano axioms for numbers makes it seem like numbers are not
dependent on us humans to exist which entails that there are
infinite sets by assuming an induction property held by (sets of)
numbers.

So while counting may not have been around forever, numbers have,
independent of us humans.  The Peano axioms are totally free of
human baggage 


I don't think so.  Where's the natural instance of successor.
This is a successor of that seems to me a human
conceptualization based on the mental equivalent of moving pebbles
into a group.  That it can be done indefinitely is merely a
convenient assumption.

Brent


The only problem is if numbers were a human invention... other humans 
could come with a prime number that is even and not 2... There would 
exists a biggest number, 1+1=2 could be false somewhere sometime (even 
by following the rules that makes 1+1=2 true always)...


They can and do.  In modulo two arithmetic 1+1=0.  You can invent all 
kinds of number systems or other logics and axiomatic systems.




Mathematical truth are independent of humans, life and the universe 
and the rest, it's nonsense if it's otherwise.


What's it's in the above sentence?

Brent



Quentin



and did not need Peano to utter them in order for numbers to
exist.  Consequently, I believe most if not all of math is
discovered.

The formalism for counting as describing a one-to-one
correspondence to a (formally defined) finite set of numbers also
exists independent of humans in the same way that the unit circle
exists.  The formalism for counting is of course not how
biological machines such as we count; the formalism is just meant
to intuitively express what we actually do when we count.

Brent Meeker wrote:

On 7/29/2010 3:28 PM, Mark Buda wrote:

Quantum mechanics suggests maybe not. If there were no
conscious observers to collapse the wave function of the
universe after the big bang, then what, pray tell, would
constitute an atom that might be counted?

This assumes that conscious observers are necessary to collapse
the wave function, of course.
-- 
Mark Buda her...@acm.org mailto:her...@acm.org

I get my monkeys for nothing and my chimps for free.



On Jul 29, 2010 2:01 PM, Brian Tenneson tenn...@gmail.com
mailto:tenn...@gmail.com wrote:

Numbers existed before people on this rock began to understand
them.  If not number of atoms in the universe, then the number
of cells in organisms one day prior to 10,000 years ago. or
anything really, that had the potential to be counted, one day
prior to 10,000 years ago.


I don't think the existence of some number of distinct things is
the same as the existence of numbers.  Numbers are defined by
order and successor - neither of which are present or implicit
in a mere collection of atoms or anything else.

Brent
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Re: numbers?

[Bruno Marchal]

On 31 Jul 2010, at 00:49, David Nyman wrote:


On 30 July 2010 17:35, Bruno Marchal marc...@ulb.ac.be wrote:

... and if you believe that the universe can be accounted for by a  
some

consistent mathematical structure. Which is an open problem. Assuming
mechanism, physical universes have no real existence at all, except  
as first
person sharable experience by machines (mathematical digital  
machines).


Bruno, consideration of the particular way you expressed this above
led to the following thoughts.  Let us leave aside for the moment the
question of whether the universe can be accounted for by some
consistent mathematical structure.  I am aware, of course, of your
detailed disproof per absurdum of the logical possibility of a
physical basis for the computational theory of mind (CTM).  It is
noteworthy, nonetheless, that even in its physicalist version, CTM
seeks to explain first person sharable experience as a virtual
mechanism, albeit here assumed to be capable of justification in
terms of the relations of fundamentally physical tokens of some
sort.  Leaving aside for the moment whether this is ultimately a
correct account or not, my point here is that it is already implicit,
per such a physicalist version of CTM, that the physical universe -
above whatever lowest level is taken to be fundamental - is
essentially a set of virtual levels. That is all entities, above the
ultimate level of analysis, are conceived as supervening entirely on -
and consequently as strictly superfluous to the independent operation
of - the basic events supposed to account for both physical and mental
processes.

Consequently it is already implicit that, even in a physicalist
version of CTM, to paraphrase what you say above:physical universes
(with the qualification - at any level above ultimate physical
events) have no real existence at all, except as first person
sharable experience by digital machines.


Above or below? I am not sure to understand your point.





However, given that IMO the
arguments you advance do convince that CTM based on physically real
tokens does indeed lead to absurd conclusions, this would remove the
qualification at any level above ultimate physical events.  This
leads directly to the unqualified claim, as you say, that assuming
mechanism, physical universes have no real existence at all, except as
first person sharable experience by machines (mathematical digital
machines).


I may agree. But computer science enters at this stage, and gives the  
way to extract physics, and physical features from it, so that it  
makes the CTM theory testable. Also we get simultaneously a theory of  
qualia and quanta. If we postulate a basic physical universe, we can  
infer quanta, and have to attach in some ad hoc and unsatisfiable way  
consciousness to some precise computation in terms of those primitive  
quanta (be it a multi-computation like with a quantum computer).


All right?

Bruno





David



On 30 Jul 2010, at 17:03, Jason Resch wrote:


On Fri, Jul 30, 2010 at 1:24 AM, Brent Meeker meeke...@dslextreme.com 


wrote:


On 7/29/2010 10:25 PM, Jason Resch wrote:

On Thu, Jul 29, 2010 at 10:55 PM, Mark Buda her...@acm.org wrote:


Numbers exist not in any physical sense but in the same sense  
that any

idea exists - they exist in the sense that minds exist that believe
logical propositions about them. They exist because minds believe
logical propositions about them. They are defined and  
distinguished by

the logical propositions that minds believe about them.

There are three worlds: the physical world of elementary  
particles, the

mental world of minds, and the imaginary world of ideas. They are
linked, somehow, by logical relationships, and the apparent flow  
of time
in the mental world causes/is caused by changes in these  
relationships.


I wouldn't be surprised if the laws of physics are changing,  
slowly,
incrementally, right under our noses. In fact, I would be  
delighted,

because it would explain many things.



The existence of numbers can explain the existence of the physical
universe but the converse is not true, the existence of the  
physical world

can't explain the existence of numbers.

William S. Cooper wrote a book to show the contrary.  Why should I
credence your bald assertion?


I should have elaborated more.  The existence of mathematical  
objects (not
just numbers, but all self-consistent structures in math) would  
imply the
existence of the universe (if you believe the universe is not in  
itself a

contradiction).

... and if you believe that the universe can be accounted for by a  
some

consistent mathematical structure. Which is an open problem. Assuming
mechanism, physical universes have no real existence at all, except  
as first
person sharable experience by machines (mathematical digital  
machines).



It would also clearly lead to Bruno's universal dovetailer, as all  
possible

Turing machines would exist.

... together with their executions.

Re: numbers?

[John Mikes]

Bruno and David:

there are concepts in your extremely interesting and informative discussion
- 'beyond me':

First the real existence (beyond Bruno's 1st person sharable experience by
machines).
I call 'existence' everything that emerges in (any) 'mind' without calling
it *real*, or *unreal*. Who has the means to distinguish the *reality of
an existence*? we can think only in our human  mini-solipsism (cf. Colin
Hales) ABOUT some 'reality' what we MAY assume.

Physical existence is IMO a figment by our explanatory skills (aided by
math/physics etc.) of the gradually disclosed items in phenomena - poorly
understood - over the millennia of human development. (Cf: the conventional
sciences).

Then again: CTM *testable?* by what rules? by the conventional
(reductionist) science figments? Who can identify the MIND to test it? *
Computational* also depends on the Comp applied unless we use(?) the Loebian
omniscient super machine, as I deducted from Brunos words lately (for being
'computer-emulable').

I fear: if we position CTM above the physical sciences, we cannot judge it
by physicality (the physically based scientific testability).

I apologize for my *agnostic position* based on an unlimited complexity and
its relations *of which we know only a fragment by a gradual epistemic
enrichment still going on*. It reduces CTM in both its C (ordinary
computer-applications) to the data-base and capabilities of the machine in
question and the M to the figment represented in the
reductionistic philosophy (including neurosciences, psychology, even
religious beliefs).

I am all for the *First Person Sharable Experience. *That's all we got and
that's all we can use. Even pertaining to communicated (3rd pers.?)
information, which first gets - adjusted to our personal indiviual mindset -
OUR 1st pers. experience.

John Mikes


On 7/31/10, Bruno Marchal marc...@ulb.ac.be wrote:


 On 31 Jul 2010, at 00:49, David Nyman wrote:

 On 30 July 2010 17:35, Bruno Marchal marc...@ulb.ac.be wrote:

 ... and if you believe that the universe can be accounted for by a some
 consistent mathematical structure. Which is an open problem. Assuming
 mechanism, physical universes have no real existence at all, except as
 first
 person sharable experience by machines (mathematical digital machines).


 Bruno, consideration of the particular way you expressed this above
 led to the following thoughts.  Let us leave aside for the moment the
 question of whether the universe can be accounted for by some
 consistent mathematical structure.  I am aware, of course, of your
 detailed disproof per absurdum of the logical possibility of a
 physical basis for the computational theory of mind (CTM).  It is
 noteworthy, nonetheless, that even in its physicalist version, CTM
 seeks to explain first person sharable experience as a virtual
 mechanism, albeit here assumed to be capable of justification in
 terms of the relations of fundamentally physical tokens of some
 sort.  Leaving aside for the moment whether this is ultimately a
 correct account or not, my point here is that it is already implicit,
 per such a physicalist version of CTM, that the physical universe -
 above whatever lowest level is taken to be fundamental - is
 essentially a set of virtual levels. That is all entities, above the
 ultimate level of analysis, are conceived as supervening entirely on -
 and consequently as strictly superfluous to the independent operation
 of - the basic events supposed to account for both physical and mental
 processes.

 Consequently it is already implicit that, even in a physicalist
 version of CTM, to paraphrase what you say above:physical universes
 (with the qualification - at any level above ultimate physical
 events) have no real existence at all, except as first person
 sharable experience by digital machines.


 Above or below? I am not sure to understand your point.




 However, given that IMO the
 arguments you advance do convince that CTM based on physically real
 tokens does indeed lead to absurd conclusions, this would remove the
 qualification at any level above ultimate physical events.  This
 leads directly to the unqualified claim, as you say, that assuming
 mechanism, physical universes have no real existence at all, except as
 first person sharable experience by machines (mathematical digital
 machines).


 I may agree. But computer science enters at this stage, and gives the way
 to extract physics, and physical features from it, so that it makes the CTM
 theory testable. Also we get simultaneously a theory of qualia and quanta.
 If we postulate a basic physical universe, we can infer quanta, and have to
 attach in some ad hoc and unsatisfiable way consciousness to some precise
 computation in terms of those primitive quanta (be it a multi-computation
 like with a quantum computer).

 All right?

 Bruno





 David


 On 30 Jul 2010, at 17:03, Jason Resch wrote:


 On Fri, Jul 30, 2010 at 1:24 AM, Brent Meeker meeke...@dslextreme.com
 

Re: numbers?

[Brent Meeker]

On 7/29/2010 10:25 PM, Jason Resch wrote:



On Thu, Jul 29, 2010 at 10:55 PM, Mark Buda her...@acm.org 
mailto:her...@acm.org wrote:



Numbers exist not in any physical sense but in the same sense that any
idea exists - they exist in the sense that minds exist that believe
logical propositions about them. They exist because minds believe
logical propositions about them. They are defined and distinguished by
the logical propositions that minds believe about them.

There are three worlds: the physical world of elementary
particles, the
mental world of minds, and the imaginary world of ideas. They are
linked, somehow, by logical relationships, and the apparent flow
of time
in the mental world causes/is caused by changes in these
relationships.

I wouldn't be surprised if the laws of physics are changing, slowly,
incrementally, right under our noses. In fact, I would be delighted,
because it would explain many things.


The existence of numbers can explain the existence of the physical 
universe but the converse is not true, the existence of the physical 
world can't explain the existence of numbers.


William S. Cooper wrote a book to show the contrary.  Why should I 
credence your bald assertion?


Belief in the existence of numbers also helps explain the unreasonable 
effectiveness of math, and the fine tuning of the universe to support 
life.


If numbers are derived from biology and physics that also explains their 
effectiveness.  Whether the universe if fine-tuned is very doubtful (see 
Vic Stengers new book on the subject) but even if it is I don't see how 
the existence of numbers explains it.


I think it is a smaller leap to believe properties of mathematical 
objects exist than to believe this large and complex universe exists 
(when the former implies the latter).


Even small numbers are bigger than our physical universe.  There are 
an infinite number of statements one could make about the number 3,


Actually not on any nomological reading of could.

some true and some false, but more statements exist than could ever be 
enumerated by any machine or mind in this universe.  Each of these 
properties of 3 shapes its essence, but if some of them are not 
accessible or knowable to us in this universe it implies if 3 must 
exist outside and beyond this universe.  Can 3 really be considered a 
human invention or idea when it has never been fully comprehended by 
any person?


On the contrary, I'd say numbers and other logical constructs can be 
more (but not completely) comprehended than the elements of physical 
models.  That's why explaining other things in terms of numbers is 
attractive.


Brent

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Re: numbers?

[Mark Buda]

Jason Resch jasonre...@gmail.com writes:

 On Thu, Jul 29, 2010 at 10:55 PM, Mark Buda her...@acm.org wrote:


 Numbers exist not in any physical sense but in the same sense that any
 idea exists - they exist in the sense that minds exist that believe
 logical propositions about them. They exist because minds believe
 logical propositions about them. They are defined and distinguished by
 the logical propositions that minds believe about them.

 There are three worlds: the physical world of elementary particles, the
 mental world of minds, and the imaginary world of ideas. They are
 linked, somehow, by logical relationships, and the apparent flow of time
 in the mental world causes/is caused by changes in these relationships.

 I wouldn't be surprised if the laws of physics are changing, slowly,
 incrementally, right under our noses. In fact, I would be delighted,
 because it would explain many things.



 The existence of numbers can explain the existence of the physical
 universe but the converse is not true, the existence of the physical
 world can't explain the existence of numbers.

Physical universe has brains, brains cause minds. Mental world has
minds, minds cause ideas (numbers). Ideal world has ideas, ideas cause
matter and energy - in some way we haven't figure out yet, which is why
the word cause seems to not fit.

It's like the impossible triangle. There are three worlds and three
parts to the explanation of reality, and taken individually they make
sense, but taken as a whole they are a paradox. That's why it's so damn
hard to figure out. I'm certain of it. I just need help working out the
details.

 Belief in the existence of numbers also helps explain the unreasonable
 effectiveness of math, and the fine tuning of the universe to support
 life. I think it is a smaller leap to believe properties of
 mathematical objects exist than to believe this large and complex
 universe exists (when the former implies the latter).

What has always disturbed me about the phrase unreasonable
effectiveness of mathematics is that it seems to me utterly reasonable
that mathematics be effective in explaining the universe, and I now know
why. The unreasonable effectiveness of mathematics in explaining the
universe is due to the fact that *I am in it*. For me, subjectively, it
needs no explanation for deeply personal reasons that are difficult to
explain succinctly. So take it this way: if you need an explanation for
the unreasonable effectiveness of mathematics, then assume I am God and
I created the universe, and then assume I'm one of Bruno's Löbian
machines and interview me for the laws of physics, because I can assure
you that if you took the time to talk to me in person I could provide
you with the evidence to make that assumption make enough sense to
explain the unreasonable effectiveness of mathematics.

I believe I understand the paradox. I believe the historical Jesus
understood the paradox as well, and the reason Christianity talks about
God's Word made flesh is that the paradox, the Logos, needs to be
understood by a mind to be explained. It doesn't fit in a book. If you
write it all down, you can't make any sense. It has to be explained
interactively, or it's too difficult to explain, because the
explanation, the Logos, is different for each person, because each
person is different. And each person has to discover the Logos on their
own, in their own way, in their own personal branch of the multiverse.

Or not. I could easily be wrong. But I can't figure out for the life of
me where I'm wrong.

 ... Can 3 really be considered a human invention or idea when it has never
 been fully comprehended by any person?

Sure. What's to comprehend? Why do I need to understand the inifinite
statements about 3 when I understand the rules by which they can be
made? That's enough for me. I have better things to do. Once I
understand the rules, I don't need to actually worry about the rest.

Analogously, once God created the universe, and then realized that He
created the universe, He worked furiously to understand it because He
was worried about his unwitting creations and loved them and wanted to
be happy. And once He figured out what exactly He had done, even though
He wasn't sure how He did it, He understood it enough to know that He
didn't need to worry about it, that it would take care of itself and He
could relax and have some fun.

That's *my* version of Genesis.
-- 
Mark Buda her...@acm.org
I get my monkeys for nothing and my chimps for free.

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Re: numbers?

[Jason Resch]

On Fri, Jul 30, 2010 at 1:24 AM, Brent Meeker meeke...@dslextreme.comwrote:

  On 7/29/2010 10:25 PM, Jason Resch wrote:



 On Thu, Jul 29, 2010 at 10:55 PM, Mark Buda her...@acm.org wrote:


  Numbers exist not in any physical sense but in the same sense that any
 idea exists - they exist in the sense that minds exist that believe
 logical propositions about them. They exist because minds believe
 logical propositions about them. They are defined and distinguished by
 the logical propositions that minds believe about them.

 There are three worlds: the physical world of elementary particles, the
 mental world of minds, and the imaginary world of ideas. They are
 linked, somehow, by logical relationships, and the apparent flow of time
 in the mental world causes/is caused by changes in these relationships.

 I wouldn't be surprised if the laws of physics are changing, slowly,
 incrementally, right under our noses. In fact, I would be delighted,
 because it would explain many things.


  The existence of numbers can explain the existence of the physical
 universe but the converse is not true, the existence of the physical world
 can't explain the existence of numbers.


 William S. Cooper wrote a book to show the contrary.  Why should I credence
 your bald assertion?


I should have elaborated more.  The existence of mathematical objects (not
just numbers, but all self-consistent structures in math) would imply the
existence of the universe (if you believe the universe is not in itself a
contradiction).  It would also clearly lead to Bruno's universal dovetailer,
as all possible Turing machines would exist.

Regarding the book you mentioned, I found a few books by William S. Cooper
on amazon.  What is the title of the book you are referring to?  Does it
show that math doesn't imply the existence of the physical universe, or that
the physical universe is what makes math real?  Most mathematicians believe
math is something explored and discovered than something invented, if true,
and both math and the physical universe have objective existence, it is a
better theory, by Ockham's razor, that math exists and the physical universe
is a consequence.  I do understand that the existence of the physical
universe leads to minds, and the minds lead to the existence of ideas of
math, but consider that both are objectively real, how does the universe's
existence lead to the objective existence of math, when math is infinite and
the physical universe is finite? (at least the observable universe).




  Belief in the existence of numbers also helps explain the unreasonable
 effectiveness of math, and the fine tuning of the universe to support life.



 If numbers are derived from biology and physics that also explains their
 effectiveness.  Whether the universe if fine-tuned is very doubtful (see Vic
 Stengers new book on the subject) but even if it is I don't see how the
 existence of numbers explains it.


Vic Stenger's argument is that fine-tuning is flawed because it assumes life
such as ours.  But even assuming a much more general definition of life,
which requires minimally reproduction, competition over finite resources,
and a relatively stable environment for many billions of generations what
percentage of universes would support this?  Does Stenger show that life is
common across the set of possible mathematical structures?

The existence of all mathematical structures + the anthropic principal
implies observers finding themselves in an apparently fine-tuned universe.
Whereas if one only believes in the physical universe it is a mystery, best
answered by the idea that all possible universes exist, and going that far,
you might simply say you believe in the objective reality of math (the
science of all possible structures).



  I think it is a smaller leap to believe properties of mathematical
 objects exist than to believe this large and complex universe exists (when
 the former implies the latter).

  Even small numbers are bigger than our physical universe.  There are an
 infinite number of statements one could make about the number 3,


 Actually not on any nomological reading of could.


If 3 exists, but we don't know everything about it, how can 3 be a human
idea?  There are things left to be discovered about that number and things
no mind in this physical universe will ever know about it, do you think our
knowledge or lack of knowledge about it somehow affects 3's identity?  What
if in a different branch of the multiverse a different set of facts about 3
is learned, would you say there are different types of 3's which exist in
different branches?  I think this would lead to the idea that there is a
different 3 in every persons mind, which changes constantly, and only exists
when a person is thinking about it.  However the fact that different minds,
or different civilizations can come to know the same things about it implies
otherwise.



   some true and some false, but more statements exist than could 

Re: numbers?

[Mark Buda]

Jason Resch jasonre...@gmail.com writes:

 On Fri, Jul 30, 2010 at 1:24 AM, Brent Meeker meeke...@dslextreme.com wrote:

 On 7/29/2010 10:25 PM, Jason Resch wrote:



 On Thu, Jul 29, 2010 at 10:55 PM, Mark Buda her...@acm.org wrote:

 ... I do understand that the existence of the physical universe leads
 to minds, and the minds lead to the existence of ideas of math, but consider
 that both are objectively real, how does the universe's existence lead to the
 objective existence of math, when math is infinite and the physical universe 
 is
 finite? (at least the observable universe).

Your physical observable universe is finite in space, but not
necessarily in time. Besides, the observable universe is an
ill-defined concept. An observer a million light-years away from you
sees a different observable universe - where does it end? For that
matter - if your body were a million light-years across, wouldn't that
make the boundary of your observable universe a little unclear?

Put another way, suppose the universe is X seconds old. That would make
your observable universe a sphere X light-seconds in radius, right?
Where, exactly, would you locate the center of that sphere? Probably
somewhere in your body... but where, exactly? And assuming you come up
with a point in space, why did you choose that point over any other?

 ... I am interested in how the approach that numbers/math are only
 ideas handles such questions.

It fails, because there are other ideas than numbers. Love, for
instance. God, for another. If you believe God does not exist, or that
there is insufficient evidence, then I would suggest that you have the
wrong idea of what the symbol God means, and have insufficiently
considered the possibility that you are God.

I'm not sure how love or God would be represented mathemaatically, but I
have some ideas about that.
-- 
Mark Buda her...@acm.org
I get my monkeys for nothing and my chimps for free.

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Re: numbers?

[Bruno Marchal]

On 30 Jul 2010, at 17:03, Jason Resch wrote:




On Fri, Jul 30, 2010 at 1:24 AM, Brent Meeker  
meeke...@dslextreme.com wrote:

On 7/29/2010 10:25 PM, Jason Resch wrote:




On Thu, Jul 29, 2010 at 10:55 PM, Mark Buda her...@acm.org wrote:

Numbers exist not in any physical sense but in the same sense that  
any

idea exists - they exist in the sense that minds exist that believe
logical propositions about them. They exist because minds believe
logical propositions about them. They are defined and distinguished  
by

the logical propositions that minds believe about them.

There are three worlds: the physical world of elementary particles,  
the

mental world of minds, and the imaginary world of ideas. They are
linked, somehow, by logical relationships, and the apparent flow of  
time
in the mental world causes/is caused by changes in these  
relationships.


I wouldn't be surprised if the laws of physics are changing,  
slowly,

incrementally, right under our noses. In fact, I would be delighted,
because it would explain many things.


The existence of numbers can explain the existence of the physical  
universe but the converse is not true, the existence of the  
physical world can't explain the existence of numbers.


William S. Cooper wrote a book to show the contrary.  Why should I  
credence your bald assertion?



I should have elaborated more.  The existence of mathematical  
objects (not just numbers, but all self-consistent structures in  
math) would imply the existence of the universe (if you believe the  
universe is not in itself a contradiction).



... and if you believe that the universe can be accounted for by a  
some consistent mathematical structure. Which is an open problem.  
Assuming mechanism, physical universes have no real existence at all,  
except as first person sharable experience by machines (mathematical  
digital machines).




It would also clearly lead to Bruno's universal dovetailer, as all  
possible Turing machines would exist.


... together with their executions.




Regarding the book you mentioned, I found a few books by William S.  
Cooper on amazon.  What is the title of the book you are referring  
to?  Does it show that math doesn't imply the existence of the  
physical universe, or that the physical universe is what makes math  
real?  Most mathematicians believe math is something explored and  
discovered than something invented, if true, and both math and the  
physical universe have objective existence, it is a better theory,  
by Ockham's razor, that math exists and the physical universe is a  
consequence.  I do understand that the existence of the physical  
universe leads to minds, and the minds lead to the existence of  
ideas of math, but consider that both are objectively real, how does  
the universe's existence lead to the objective existence of math,  
when math is infinite and the physical universe is finite? (at least  
the observable universe).



Also, Cooper's book just address the question of the origin of man's  
beliefs in numbers. I don't think Cooper tries to understand the  
origin of natural numbers.
Actually, we can explain that numbers cannot be justified by anything  
simpler than numbers. That is why it is a good starting point.
I doubt your statement that a physical universes can explain mind.  
Unless you take physical in a very large sense. The kind of mind a  
physical universe can explain cannot locate himself in a physical  
universe. This comes from the fact that the identity thesis (mind- 
brain, or mind/piece-of-matter) breaks down once we assume we can  
survive a 'physical' digital brain substitution.
We can ascribe a mind (first person) to a body (third person), but if  
that body is turing emulable, then a mind cannot ascribe a body to  
itself. It can ascribe an infinity of bodies only, weighted by  
diverging computational histories generating the relevant states of  
that body, below the substitution level. This can be said confirmed by  
quantum mechanics, where our bodies are given by all the Heisenberg- 
uncertainty variant of it.


I agree roughly with the rest of your remarks (and so don't comment  
them).


Bruno







Belief in the existence of numbers also helps explain the  
unreasonable effectiveness of math, and the fine tuning of the  
universe to support life.


If numbers are derived from biology and physics that also explains  
their effectiveness.  Whether the universe if fine-tuned is very  
doubtful (see Vic Stengers new book on the subject) but even if it  
is I don't see how the existence of numbers explains it.



Vic Stenger's argument is that fine-tuning is flawed because it  
assumes life such as ours.  But even assuming a much more general  
definition of life, which requires minimally reproduction,  
competition over finite resources, and a relatively stable  
environment for many billions of generations what percentage of  
universes would support this?  Does Stenger show that life 

Re: numbers?

[David Nyman]

On 30 July 2010 17:35, Bruno Marchal marc...@ulb.ac.be wrote:

 ... and if you believe that the universe can be accounted for by a some
 consistent mathematical structure. Which is an open problem. Assuming
 mechanism, physical universes have no real existence at all, except as first
 person sharable experience by machines (mathematical digital machines).

Bruno, consideration of the particular way you expressed this above
led to the following thoughts.  Let us leave aside for the moment the
question of whether the universe can be accounted for by some
consistent mathematical structure.  I am aware, of course, of your
detailed disproof per absurdum of the logical possibility of a
physical basis for the computational theory of mind (CTM).  It is
noteworthy, nonetheless, that even in its physicalist version, CTM
seeks to explain first person sharable experience as a virtual
mechanism, albeit here assumed to be capable of justification in
terms of the relations of fundamentally physical tokens of some
sort.  Leaving aside for the moment whether this is ultimately a
correct account or not, my point here is that it is already implicit,
per such a physicalist version of CTM, that the physical universe -
above whatever lowest level is taken to be fundamental - is
essentially a set of virtual levels. That is all entities, above the
ultimate level of analysis, are conceived as supervening entirely on -
and consequently as strictly superfluous to the independent operation
of - the basic events supposed to account for both physical and mental
processes.

Consequently it is already implicit that, even in a physicalist
version of CTM, to paraphrase what you say above:physical universes
(with the qualification - at any level above ultimate physical
events) have no real existence at all, except as first person
sharable experience by digital machines.  However, given that IMO the
arguments you advance do convince that CTM based on physically real
tokens does indeed lead to absurd conclusions, this would remove the
qualification at any level above ultimate physical events.  This
leads directly to the unqualified claim, as you say, that assuming
mechanism, physical universes have no real existence at all, except as
first person sharable experience by machines (mathematical digital
machines).

David


 On 30 Jul 2010, at 17:03, Jason Resch wrote:


 On Fri, Jul 30, 2010 at 1:24 AM, Brent Meeker meeke...@dslextreme.com
 wrote:

 On 7/29/2010 10:25 PM, Jason Resch wrote:

 On Thu, Jul 29, 2010 at 10:55 PM, Mark Buda her...@acm.org wrote:

 Numbers exist not in any physical sense but in the same sense that any
 idea exists - they exist in the sense that minds exist that believe
 logical propositions about them. They exist because minds believe
 logical propositions about them. They are defined and distinguished by
 the logical propositions that minds believe about them.

 There are three worlds: the physical world of elementary particles, the
 mental world of minds, and the imaginary world of ideas. They are
 linked, somehow, by logical relationships, and the apparent flow of time
 in the mental world causes/is caused by changes in these relationships.

 I wouldn't be surprised if the laws of physics are changing, slowly,
 incrementally, right under our noses. In fact, I would be delighted,
 because it would explain many things.


 The existence of numbers can explain the existence of the physical
 universe but the converse is not true, the existence of the physical world
 can't explain the existence of numbers.

 William S. Cooper wrote a book to show the contrary.  Why should I
 credence your bald assertion?

 I should have elaborated more.  The existence of mathematical objects (not
 just numbers, but all self-consistent structures in math) would imply the
 existence of the universe (if you believe the universe is not in itself a
 contradiction).

 ... and if you believe that the universe can be accounted for by a some
 consistent mathematical structure. Which is an open problem. Assuming
 mechanism, physical universes have no real existence at all, except as first
 person sharable experience by machines (mathematical digital machines).


 It would also clearly lead to Bruno's universal dovetailer, as all possible
 Turing machines would exist.

 ... together with their executions.


 Regarding the book you mentioned, I found a few books by William S. Cooper
 on amazon.  What is the title of the book you are referring to?  Does it
 show that math doesn't imply the existence of the physical universe, or that
 the physical universe is what makes math real?  Most mathematicians believe
 math is something explored and discovered than something invented, if true,
 and both math and the physical universe have objective existence, it is a
 better theory, by Ockham's razor, that math exists and the physical universe
 is a consequence.  I do understand that the existence of the physical
 universe leads to minds, and the minds lead to 

Re: numbers?

[Brian Tenneson]

Numbers existed before people on this rock began to understand them.  If not
number of atoms in the universe, then the number of cells in organisms one
day prior to 10,000 years ago. or anything really, that had the potential to
be counted, one day prior to 10,000 years ago.

If all numbers are invented, then there is a largest number ever conceived
by a human, which we're a long way from but will be there still.

I know this isn't a proof, but there being a largest number strikes me as
wrong.  If my assumption that there is no largest number is correct, then
numbers are not invented.

Brent Meeker:
But there weren't an infinite number of atoms (or anything else).

The existence of infinite sets certainly is an assumption.
If you were to form a list of numbers relevant to this discussion, that list
either has the potential to stop one day, or the list will never be
complete.  The first case is equivalent to numbers being invented; the
second case is equivalent to numbers being not invented (ie, discovered).

My assumption is that there is no largest number.  That entails that numbers
are not invented as argued above.  Thus, the list will never be complete and
so my assumption implies that infinite sets exist, if only infinite set of
numbers.

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Re: numbers?

[Brent Meeker]

On 7/29/2010 3:28 PM, Mark Buda wrote:
Quantum mechanics suggests maybe not. If there were no conscious 
observers to collapse the wave function of the universe after the big 
bang, then what, pray tell, would constitute an atom that might be 
counted?


This assumes that conscious observers are necessary to collapse the 
wave function, of course.

--
Mark Buda her...@acm.org mailto:her...@acm.org
I get my monkeys for nothing and my chimps for free.



On Jul 29, 2010 2:01 PM, Brian Tenneson tenn...@gmail.com wrote:

Numbers existed before people on this rock began to understand them.  
If not number of atoms in the universe, then the number of cells in 
organisms one day prior to 10,000 years ago. or anything really, that 
had the potential to be counted, one day prior to 10,000 years ago.


I don't think the existence of some number of distinct things is the 
same as the existence of numbers.  Numbers are defined by order and 
successor - neither of which are present or implicit in a mere 
collection of atoms or anything else.


Brent

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Re: numbers?

[Mark Buda]

Agreed, but I would point out that the answer to the question of the existence 
of numbers is the truth value of a logical proposition about the ideas we call 
number and existence. And if you bring a definition of number in terms of 
other ideas such as successor, then you are simply restating the logical 
propositions in terms of other ideas.

Most logical propositions about what we usually call reality are meaningless. 
Those that are meaningful are those that have to do, ultimately, with your 
present perceptions and set of beliefs about the universe. As such, their truth 
value depends on who you are and what you choose to do.
--nbsp;
Mark Buda lt;her...@acm.orggt;
I get my monkeys for nothing and my chimps for free.


On Jul 29, 2010 6:36 PM, Brent Meeker lt;meeke...@dslextreme.comgt; 
wrote:nbsp;

I don't think the existence of some number of distinct things is the
same as the existence of numbers.nbsp; Numbers are defined by order and
successor - neither of which are present or implicit in a mere
collection of atoms or anything else.



Brent




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Re: numbers?

[Brent Meeker]

On 7/29/2010 4:03 PM, Mark Buda wrote:
Agreed, but I would point out that the answer to the question of the 
existence of numbers is the truth value of a logical proposition about 
the ideas we call number and existence. 


What logical proposition would that be?  A proposition like Every 
number has a successor or 2+2=4 don't say tell us anything about 
whether numbers exist.  Truth values in logic are just arbitrary 
assignments of T to some propositions (axioms) and F to others 
(contradictions).  The are not evidence of existence.


And if you bring a definition of number in terms of other ideas such 
as successor, then you are simply restating the logical propositions 
in terms of other ideas.


Most logical propositions about what we usually call reality are 
meaningless. Those that are meaningful are those that have to do, 
ultimately, with your present perceptions and set of beliefs about the 
universe. 


But those aren't specifically *logical* propositions.  The kind of truth 
value that attaches to them is epistemological.  In fact you'll notice 
that if you ask a scientist whether some statement about the world is 
true he's likely to give you a litany of evidence with qualifications, 
rather than a 'yes' or 'no'.


As such, their truth value depends on who you are and what you choose 
to do.


I don't know what you mean by that, but I would agree that knowledge and 
meaning propositions is ultimately grounded in actions or at least 
potential actions.


Brent


--
Mark Buda her...@acm.org mailto:her...@acm.org
I get my monkeys for nothing and my chimps for free.



On Jul 29, 2010 6:36 PM, Brent Meeker meeke...@dslextreme.com wrote:
I don't think the existence of some number of distinct things is the 
same as the existence of numbers.  Numbers are defined by order and 
successor - neither of which are present or implicit in a mere 
collection of atoms or anything else.


Brent
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Re: numbers?

[Mark Buda]

Brent Meeker meeke...@dslextreme.com writes:

 On 7/29/2010 4:03 PM, Mark Buda wrote:

 Agreed, but I would point out that the answer to the question of the
 existence of numbers is the truth value of a logical proposition about the
 ideas we call number and existence.


 What logical proposition would that be?

Pardon my Unicode, but that would be

∃x: x ∈ ℕ

 A proposition like Every number has a successor or 2+2=4 don't say
 tell us anything about whether numbers exist.  Truth values in logic
 are just arbitrary assignments of T to some propositions (axioms) and
 F to others (contradictions).  The are not evidence of existence.

Numbers exist not in any physical sense but in the same sense that any
idea exists - they exist in the sense that minds exist that believe
logical propositions about them. They exist because minds believe
logical propositions about them. They are defined and distinguished by
the logical propositions that minds believe about them.

There are three worlds: the physical world of elementary particles, the
mental world of minds, and the imaginary world of ideas. They are
linked, somehow, by logical relationships, and the apparent flow of time
in the mental world causes/is caused by changes in these relationships.

I wouldn't be surprised if the laws of physics are changing, slowly,
incrementally, right under our noses. In fact, I would be delighted,
because it would explain many things.

 ...their truth value depends on who you are and what you choose to
 do.

 I don't know what you mean by that...

I meant that reality is subjective. Right down to the laws of
physics. Which I believe I have figured out how to change. A testable,
falsifiable, silly, hypothesis!
-- 
Mark Buda her...@acm.org
I get my monkeys for nothing and my chimps for free.

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Re: numbers?

[Jason Resch]

On Thu, Jul 29, 2010 at 10:55 PM, Mark Buda her...@acm.org wrote:


 Numbers exist not in any physical sense but in the same sense that any
 idea exists - they exist in the sense that minds exist that believe
 logical propositions about them. They exist because minds believe
 logical propositions about them. They are defined and distinguished by
 the logical propositions that minds believe about them.

 There are three worlds: the physical world of elementary particles, the
 mental world of minds, and the imaginary world of ideas. They are
 linked, somehow, by logical relationships, and the apparent flow of time
 in the mental world causes/is caused by changes in these relationships.

 I wouldn't be surprised if the laws of physics are changing, slowly,
 incrementally, right under our noses. In fact, I would be delighted,
 because it would explain many things.


The existence of numbers can explain the existence of the physical universe
but the converse is not true, the existence of the physical world can't
explain the existence of numbers.  Belief in the existence of numbers also
helps explain the unreasonable effectiveness of math, and the fine tuning of
the universe to support life.  I think it is a smaller leap to believe
properties of mathematical objects exist than to believe this large and
complex universe exists (when the former implies the latter).

Even small numbers are bigger than our physical universe.  There are an
infinite number of statements one could make about the number 3, some true
and some false, but more statements exist than could ever be enumerated by
any machine or mind in this universe.  Each of these properties of 3 shapes
its essence, but if some of them are not accessible or knowable to us in
this universe it implies if 3 must exist outside and beyond this universe.
 Can 3 really be considered a human invention or idea when it has never been
fully comprehended by any person?

Jason

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Re: numbers?

[John Mikes]

Bruno wrote:

   * ( - ...are true independently of you, matter, universe, bibles, etc.
*- )
*   No theorem of math, even of intuitionist math makes any sense,
without such belief*...
*
*WHO'S BELIEF?* or rather: *WHATS BELIEF*? does a snail believe  that
2+13=15, or a rock?
I bet for the answer it is:  *h u m a n s .  -  or - maybe: super-human
intelligence. *
So it is US, humans, (at least) who ought to believe the numbers. Most of us
do. It's OK.

John



On 7/26/10, Bruno Marchal marc...@ulb.ac.be wrote:


 On 26 Jul 2010, at 18:22, Brent Meeker wrote:

 On 7/26/2010 6:24 AM, Brian Tenneson wrote:


 Does this mean that sets of numbers are inventions or just particular
 numbers are inventions?
 If the latter, then there must be a largest number which is, to me,
 counterintuitive.

 Numbers existed before 10,000 years ago when they were first understood
 by humans to some extent.  There was a specific number of atoms in the
 universe one day before any numbers were understood by humans, for example.


 But there weren't an infinite number of atoms (or anything else).



 But arithmetical realism does not ask for an infinite number. All finite
 numbers is quite enough. You need only to believe that statement like

 s(s(0)) + s(s(s(s(s(s(s(s(s(s(s(s(0) =
 s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))  (commonly written 2 + 13 =
 15)

 are true independently of you, matter, universe, bibles, etc.

 No theorem of math, even of intuitionist math makes any sense, without such
 belief. You can threw Pythagorus theorem in the trash.

 Only ultrafinitists are not arithmetical realist. But it is impossible for
 them to say so, because the cognitive abilities you need to say that you do
 NOT believe in arithmetical realism needs arithmetical realism.

 Bruno

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



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Re: numbers?

[Brian Tenneson]

Does this mean that sets of numbers are inventions or just particular 
numbers are inventions?
If the latter, then there must be a largest number which is, to me, 
counterintuitive.


Numbers existed before 10,000 years ago when they were first understood 
by humans to some extent.  There was a specific number of atoms in the 
universe one day before any numbers were understood by humans, for example.




John Mikes wrote:

Dear Bruno,
on diverse lists I bounce into the 'numbers' idea - in different 
variations. I wonder if your position states that the world (whatever) 
has been 'erected' (wrong word) based on integer numbers and their 
additive multiplicity, or it can be 'explained' by such?
It makes a big difference in my agnostic views (I dunno) because to 
explain is human logic (never mind which kind) while to erect means 
ontological bind - what I cannot condone in its entire meaning.
Consciousness came up as being primary or not: I hope thought of in my 
version, as _response to information_ - with /response/ in ANY way 
and /information/ as our acquired knowledge of relations among 
components of the totality (unlimited wholeness).
Numbers, however, as I referred to earlier - quoting David Bohm, are 
_'human inventions'_ - unidentified further. Now I got additional news 
from /*_Keith Devlin_*/ (Stanford U., /The Math Gene: How 
Matheamtical Thinking Evolved/ and /Why Numbers Are Like Gos/sip 
- plus other ~2 dozen books) who stated that:


/Numbers are so ubiquitous and seem so concrete, it is easy to
forget they are /
/a human invention and a recent one at that, dating back only
10,000 years. /
/Though the things we count are often in the world, the numbers we
use to count /
/them are figments of our imagination. For that reason we should
not be surprised /
/(though we usually are) to discover they are usually influenced
by the way our /
/brains work. ...  When we try to attach numbers to things in
the world , as /
/William Poundstone describes, we find psychology gets into the mix. /
/Numbers may be - I think they are - among the most concrete and
precise ways /
/to describe our world, but they are still a human creation, and
as such they reflect /
/us as much as the things in our environment./

~2,500 years ago 'math' with the then recently acquired 
'numbers-knowledge' had but a little domain to overcome and our awe 
for the wisdom of the old Greeks accepted the numbers as 'GOD. I have 
no problem to use numbers for *explaining *most of the world (the only 
exceptions I carried earlier were the 'non-quantizable' concepts - 
earlier, I said, because lately I condone in my agnosticism that there 
may be ways (beyond our knowledge of yesterday) to find quantitative 
characteristics in those, as well) but in our 'yesterday's views' I 
don't want to give up to find something more /general and underlying/ 
upon which even the numbers can be used and applied for the world, of 
which our human mind is a part - that invented the numbers.
 
Anoither question arose in my mind about the discussion with Rex 
Allen: the postulate that the world is Turing Emulable - as per your 
not too thoroughly detailed response to me some time ago - would refer 
to 'more than just the binary contraptions we presently use as Turing 
Machines - but - maybe - a /Universal Machine (Computer/) that covers 
all. This position would make the thing volatile: meaning that the 
world is emulable by some construct that makes it - well, emulable. 
(We know precious little about the (technical) workings of the so 
called  Universal Machine). In that case I would write the name of 
Turing at least in lower case as a /_type_/: *'turing'* to eliminate 
the reference to the very invention of *Alan Turing. *
** 
*Respectfully*
** 
John M
** 
 
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Re: numbers?

[John Mikes]

Brian:
it is not so simple. Not that some chap sat down 10,000 years ago and said
I just invented the numbers let's say: from 1 to 1 zillion, - the process
is a long development parallel with brain, bodily and life-style evolution.
The date - I think - refers to numbering amounts with a gradual path from
2 (TWO as a basic, looking at the hands, eyes and feet) and 1 as half of
this. That might have been some million years before the 10,000 mark. And I
am not so sure whether the 'atoms' are not a figment of calculative
explanation upon poorly observed phenomena. Numbered or not. Furthermore:
are numbers understood indeed? (without referring to quantity I mean). Bruno
substituted '2' by II and '4' by  - what is exactly the QUANTITY of
lines in the representation of a sign - otherwise meaningless; what also
shows in the Roman numerals.
('V' is a composition of 5 lines (too much individually) and X is 2 V-s (XX:
4Vs) pasted together).
The 'late' invention of the zero points exactly to such slowly developing
complex series.
As human complexity got more and more intrigued (and that in a very short
time-frame) the understanding of 'numbers' evolved in parallel, with ideas
what to do with them (math-thinking).
The abstraction 3 from e.g. 3 blind mice is - I believe - still a
mystery, unless someone pretends to be 'smarter'.
Assumptions - presumptions and their consequences up to an n^mth level give
us - what I call - our conventional sciences. In an ongoing steady growth of
our epistemic enrichment of human cognitive inventory and its application in
technology. Math (m-logic) is a supporter of such figments, allowing
matching equations as evidence for the inclusion of the so far learned and
insufficient (incomplete) items omitting the modifying power of the still
unknown. History is full of such modifications when 'science' changed
course. And it will go on in the future as well.

John M


On 7/26/10, Brian Tenneson tenn...@gmail.com wrote:

 Does this mean that sets of numbers are inventions or just particular
 numbers are inventions?
 If the latter, then there must be a largest number which is, to me,
 counterintuitive.

 Numbers existed before 10,000 years ago when they were first understood by
 humans to some extent.  There was a specific number of atoms in the universe
 one day before any numbers were understood by humans, for example.



 John Mikes wrote:

  Dear Bruno,
 on diverse lists I bounce into the 'numbers' idea - in different
 variations. I wonder if your position states that the world (whatever) has
 been 'erected' (wrong word) based on integer numbers and their additive
 multiplicity, or it can be 'explained' by such?
 It makes a big difference in my agnostic views (I dunno) because to explain
 is human logic (never mind which kind) while to erect means ontological bind
 - what I cannot condone in its entire meaning.
 Consciousness came up as being primary or not: I hope thought of in my
 version, as *response to information* - with *response* in ANY way and *
 information* as our acquired knowledge of relations among components of
 the totality (unlimited wholeness).
 Numbers, however, as I referred to earlier - quoting David Bohm, are *'human
 inventions'* - unidentified further. Now I got additional news from *Keith
 Devlin* (Stanford U., *The Math Gene: How Matheamtical Thinking Evolved* 
 and
 *Why Numbers Are Like Gos*sip - plus other ~2 dozen books) who stated
 that:

 *Numbers are so ubiquitous and seem so concrete, it is easy to forget
 they are *
 *a human invention and a recent one at that, dating back only 10,000
 years. *
 *Though the things we count are often in the world, the numbers we use to
 count *
 *them are figments of our imagination. For that reason we should not be
 surprised *
 *(though we usually are) to discover they are usually influenced by the
 way our *
 *brains work. ...  When we try to attach numbers to things in the world
 , as *
 *William Poundstone describes, we find psychology gets into the mix. *
 *Numbers may be - I think they are - among the most concrete and
 precise ways *
 *to describe our world, but they are still a human creation, and as such
 they reflect *
 *us as much as the things in our environment.*

 ~2,500 years ago 'math' with the then recently acquired 'numbers-knowledge'
 had but a little domain to overcome and our awe for the wisdom of the old
 Greeks accepted the numbers as 'GOD. I have no problem to use numbers for
 *explaining *most of the world (the only exceptions I carried earlier were
 the 'non-quantizable' concepts - earlier, I said, because lately I condone
 in my agnosticism that there may be ways (beyond our knowledge of yesterday)
 to find quantitative characteristics in those, as well) but in our
 'yesterday's views' I don't want to give up to find something more *general
 and underlying* upon which even the numbers can be used and applied for
 the world, of which our human mind is a part - that invented the numbers.

 

Re: numbers?

[Brent Meeker]

On 7/26/2010 6:24 AM, Brian Tenneson wrote:
Does this mean that sets of numbers are inventions or just particular 
numbers are inventions?
If the latter, then there must be a largest number which is, to me, 
counterintuitive.


Numbers existed before 10,000 years ago when they were first 
understood by humans to some extent.  There was a specific number of 
atoms in the universe one day before any numbers were understood by 
humans, for example.


But there weren't an infinite number of atoms (or anything else).

Brent

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Re: numbers?

[Bruno Marchal]

On 26 Jul 2010, at 18:22, Brent Meeker wrote:


On 7/26/2010 6:24 AM, Brian Tenneson wrote:


Does this mean that sets of numbers are inventions or just  
particular numbers are inventions?
If the latter, then there must be a largest number which is, to me,  
counterintuitive.


Numbers existed before 10,000 years ago when they were first  
understood by humans to some extent.  There was a specific number  
of atoms in the universe one day before any numbers were understood  
by humans, for example.


But there weren't an infinite number of atoms (or anything else).



But arithmetical realism does not ask for an infinite number. All  
finite numbers is quite enough. You need only to believe that  
statement like


s(s(0)) + s(s(s(s(s(s(s(s(s(s(s(s(0) =  
s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))  (commonly written 2  
+ 13 = 15)


are true independently of you, matter, universe, bibles, etc.

No theorem of math, even of intuitionist math makes any sense, without  
such belief. You can threw Pythagorus theorem in the trash.


Only ultrafinitists are not arithmetical realist. But it is impossible  
for them to say so, because the cognitive abilities you need to say  
that you do NOT believe in arithmetical realism needs arithmetical  
realism.


Bruno

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



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Re: numbers?

[Bruno Marchal]

Dear John,


On 21 Jul 2010, at 22:03, John Mikes wrote:


Dear Bruno,
on diverse lists I bounce into the 'numbers' idea - in different  
variations. I wonder if your position states that the world  
(whatever) has been 'erected' (wrong word) based on integer numbers  
and their additive multiplicity, or it can be 'explained' by such?


The answer is it can be explained by such. The world is not  
computable. It is not a number, nor is it made of numbers.
It is not so much a mosition of mine (which I keep for myself) than a  
point, or proof, or argument. All what I say is that if we are Turing  
emulable, then the phsyical lwas are no more fundamental, and are a  
consequence of the way the numbers are related with each other. But  
the comp non locality, and the comp indeterminacy entails that matter  
is in principle a highly non computational stuff.
The fact that the world seems partially computable g-has to be  
explained. We can no more (assuming the comp hyp) take the existence  
of laws for granted.
Instead of number, we have the choice of taking any terms from any  
Turing-complete theory. I would take the combinators or the lambda  
terms if people were not so freaked out by new mathematical symbols.  
At least numbers are taught in school.



It makes a big difference in my agnostic views (I dunno) because to  
explain is human logic (never mind which kind)


All right. Sure.


while to erect means ontological bind - what I cannot condone in its  
entire meaning.
Consciousness came up as being primary or not: I hope thought of in  
my version, as response to information - with response in ANY way  
and information as our acquired knowledge of relations among  
components of the totality (unlimited wholeness).


OK.


Numbers, however, as I referred to earlier - quoting David Bohm, are  
'human inventions' - unidentified further.


I think it is a human discovery. I find a bit pretentious the idea  
that we have made them. You may say so, but assuming comp, you would  
have to say that galaxies and dinosaurs are human inventions too. That  
would be confusing, to say the least. I put in the hypothesis of comp  
(if only to making sense) that I take some truth like 1+2=3 as being  
a non local, atemporal, and aspatial statement. It does not depend of  
the apparition of humans. Of course the symbol 1, and 2 are human  
invention, but they should not be confused with the abstract objects  
they are pointing too. I could have written the same assertion in  
english with a sentence like  the successor of zero added to the  
successor of the successor of 0 gives the successor of the successor  
of the successor of zero.
When we do theories, we have to start from something. If you agree  
that 1+2=3, we can proceed.






Now I got additional news from Keith Devlin (Stanford U., The Math  
Gene: How Matheamtical Thinking Evolved and Why Numbers Are Like  
Gossip - plus other ~2 dozen books)


I read with interest his book on information.



who stated that:
Numbers are so ubiquitous and seem so concrete, it is easy to  
forget they are
a human invention and a recent one at that, dating back only 10,000  
years.
Though the things we count are often in the world, the numbers we  
use to count
them are figments of our imagination. For that reason we should not  
be surprised
(though we usually are) to discover they are usually influenced by  
the way our
brains work. ...  When we try to attach numbers to things in the  
world , as

William Poundstone describes, we find psychology gets into the mix.
Numbers may be - I think they are - among the most concrete and  
precise ways
to describe our world, but they are still a human creation, and as  
such they reflect

us as much as the things in our environment.
~2,500 years ago 'math' with the then recently acquired 'numbers- 
knowledge' had but a little domain to overcome and our awe for the  
wisdom of the old Greeks accepted the numbers as 'GOD. I have no  
problem to use numbers for explaining most of the world (the only  
exceptions I carried earlier were the 'non-quantizable' concepts -  
earlier, I said, because lately I condone in my agnosticism that  
there may be ways (beyond our knowledge of yesterday) to find  
quantitative characteristics in those, as well)


Both are true. Some qualitative things can have quantitative features.  
And numbers themselves have a lot of qualitative features, some of  
them having no quantitative features at all. After Gödel's  
incompleteness result, humans assuming comp can say: already about the  
numbers we can only scratch the surface. Comp kills reductive thinking  
at his root. Digital mechanism is the most modest and humble  
hypothesis in the field.





but in our 'yesterday's views' I don't want to give up to find  
something more general and underlying upon which even the numbers  
can be used and applied for the world, of which our human mind is a  
part - that invented the numbers.


That is the idea. 

Re: Numbers, Machine and Father Ted

[dan9el]

Tom Caylor wrote:
 Brent Meeker wrote:
  Stathis Papaioannou wrote:
  
   Brent Meeker writes:
  
   This cannot be explained away by
   faith in the sense that one can have faith in the gravity god or a
   deist god (because no empirical finding counts for or against such
   beliefs): rather, it comes down to a matter of simultaneously
   believing x and not-x.
  
   Seems like faith to me - belief without or contrary to evidence.  What 
   is the x you refer to?
  
   There is a subtle difference. It is possible to have faith in something 
   stupid
   and still be consistent. For example, I could say that I have faith that 
   God
   will answer my prayers regardless of whether he has ever answered any
   prayers before in the history of the world. However, I think most 
   religious
   people would say that they have faith that God will answer their prayers
   because that it what God does and has done in the past. In so saying, they
   are making an empirically verifiable claim, at least in theory. They can 
   be invited
   to come up with a test to support their belief, which can be as stringent 
   as they
   like; for example, they might allow only historical analysis because God 
   would
   not comply with any experiment designed to test him. I suspect that no 
   such
   test would have any impact on their beliefs because at bottom they are 
   just
   based on blind faith, but given that they do not volunteer this to begin 
   with, it
   shows them up as inconsistent and hypocritical.
  
   Stathis Papaioannou
 
  OK.  But I'd say that in fact almost no one believes something without any 
  evidence, i.e. on *blind* faith.  Religious faith is usually belief based 
  on *selected* evidence; it is faith because it is contrary to the total 
  evidence.  Bruno seems to use faith somewhat differently: to mean what I 
  would call a working hypothesis.
 
  Brent Meeker

 This gets us to the question that has been pondered here before, a
 question that is more appropriate to the general
 metaphysical/epistemological thoughts of this List: What does it mean
 to believe something?  I'd say that you can't really know if you or
 someone else really believes something unless you/they act on it.  An
 act could simply be investing some of our precious limited time to look
 at its consequences.  I'd say that for that non-trivial period of time
 in your life, you had at least somewhat of a belief in it.  It is not a
 trivial thing to use up some of your life doing something (at least in
 my worldview).  I think this shows how Bruno's belief can be brought
 equal in essence (if not necessarily the quantity of investment) to any
 other belief.  Evidence is relative, and I think is important in
 practical terms, but it is not essential to the definition of belief.
 
 Tom


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Re: Numbers, Machine and Father Ted

[Brent Meeker]

dan9el wrote:
 
 Tom Caylor wrote:
 Brent Meeker wrote:
 Stathis Papaioannou wrote:
 Brent Meeker writes:
 
 This cannot be explained away by faith in the sense that
 one can have faith in the gravity god or a deist god
 (because no empirical finding counts for or against such 
 beliefs): rather, it comes down to a matter of
 simultaneously believing x and not-x.
 
 Seems like faith to me - belief without or contrary to
 evidence.  What is the x you refer to?
 There is a subtle difference. It is possible to have faith in
 something stupid and still be consistent. For example, I could
 say that I have faith that God will answer my prayers
 regardless of whether he has ever answered any prayers before
 in the history of the world. However, I think most religious 
 people would say that they have faith that God will answer
 their prayers because that it what God does and has done in the
 past. In so saying, they are making an empirically verifiable
 claim, at least in theory. They can be invited to come up with
 a test to support their belief, which can be as stringent as
 they like; for example, they might allow only historical
 analysis because God would not comply with any experiment
 designed to test him. I suspect that no such test would have
 any impact on their beliefs because at bottom they are just 
 based on blind faith, but given that they do not volunteer this
 to begin with, it shows them up as inconsistent and
 hypocritical.
 
 Stathis Papaioannou
 OK.  But I'd say that in fact almost no one believes something
 without any evidence, i.e. on *blind* faith.  Religious faith is
 usually belief based on *selected* evidence; it is faith
 because it is contrary to the total evidence.  Bruno seems to use
 faith somewhat differently: to mean what I would call a working
 hypothesis.
 
 Brent Meeker
 This gets us to the question that has been pondered here before, a 
 question that is more appropriate to the general 
 metaphysical/epistemological thoughts of this List: What does it
 mean to believe something?  I'd say that you can't really know if
 you or someone else really believes something unless you/they act
 on it.  An act could simply be investing some of our precious
 limited time to look at its consequences.  I'd say that for that
 non-trivial period of time in your life, you had at least somewhat
 of a belief in it.  It is not a trivial thing to use up some of
 your life doing something (at least in my worldview).  I think this
 shows how Bruno's belief can be brought equal in essence (if not
 necessarily the quantity of investment) to any other belief.
 Evidence is relative, and I think is important in practical terms,
 but it is not essential to the definition of belief.
 
 Tom

I agree that action is the measure of belief (recognizing that speech is also a 
form of action).  I didn't say that evidence was of the essence of belief.  I 
just observed that belief without any evidence at all is very rare.  Even 
people who hold completely crazy beliefs, like their toaster gives them orders 
they must obey, can usually give reasons for their belief.  It's just a matter 
of scope and relevance of evidence.

Brent Meeker


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Re: Numbers, Machine and Father Ted

[Bruno Marchal]

Le 11-nov.-06, à 19:07, 1Z a écrit :



 Bruno Marchal wrote:
 Le 11-nov.-06, à 01:09, 1Z a écrit :

 No, because there are no possible worlds where (2^32582657)-1
 is not  a prime number.

 This is for me a typical arithmetical realist statement.

 Most philosophers who use the possible
 worlds terminology do nothing PW's actually
 exist.

 Of course it is AR in the sense of appealing to
 mind-independent truth. And of course it
 remains unclear whether your AR is a claim
 about truth, or about existence.


It depends on the sense of the term existence. But frankly such 
discussion is premature. It is probably a 1004 fallacy, like those who 
were condemning the old quantum mechanics, after its birth, because it 
is philosophically unclear. I think you should study the comp-theory 
before arguing about its interpretation. You are introducing nuances, 
like the difference between 2 exists is true and '2 exists' which, 
although not uninteresting per se, are too much involved considering 
the existence of a precise (refutable) new theory of mind/matter.




 You still want it both ways: keeping comp and primary material 
 reality,
 but I have already argued in detail that this cannot work in any
 reasonable way.

 No you haven't. You argument requires an assumption of Platonism
 as well as computationalism. Computationalism
 alone is compatible with materialism.


I need only A or ~A. You can call it classical computationalism. I 
prefer to call it comp, because the reasoning goes through even with 
weaken form of classical logic (that is I can use the intuitionist 
excluded middle principle for arithmetic instead: ~~(A v ~A)).

I do believe the formalist philosophy has been shown dead wrong after 
Godel, but in case you have trouble with what I call platonism or even 
plotinism you could for all practical purpose adopt formalism 
temporarily. In that case I will say that an ideal lobian machine (in 
her chatty mode) is an arithmetical platonist if she asserts A v ~A 
for any arithmetical proposition A. This could help to proceed, and 
then we can come back on discussing on the interpretation problem of 
the formalism.

Bruno



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


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RE: Numbers, Machine and Father Ted

[Stathis Papaioannou]

Tom Caylor writes:

 Brent Meeker wrote:

  OK.  But I'd say that in fact almost no one believes something without any 
  evidence, i.e. on *blind* faith.  Religious faith is usually belief based 
  on *selected* evidence; it is faith because it is contrary to the total 
  evidence.  Bruno seems to use faith somewhat differently: to mean what I 
  would call a working hypothesis.
 
  Brent Meeker
 
 This gets us to the question that has been pondered here before, a
 question that is more appropriate to the general
 metaphysical/epistemological thoughts of this List: What does it mean
 to believe something?  I'd say that you can't really know if you or
 someone else really believes something unless you/they act on it.  An
 act could simply be investing some of our precious limited time to look
 at its consequences.  I'd say that for that non-trivial period of time
 in your life, you had at least somewhat of a belief in it.  It is not a
 trivial thing to use up some of your life doing something (at least in
 my worldview).  I think this shows how Bruno's belief can be brought
 equal in essence (if not necessarily the quantity of investment) to any
 other belief.  Evidence is relative, and I think is important in
 practical terms, but it is not essential to the definition of belief.

Belief could probably be entirely described in social, behavioural and 
psychological terms. 
But problems arise when you consider *only* this aspect of belief, ignoring the 
question 
of whether there is a basis for saying some beliefs are true and others false. 
This does not 
just apply to religious beliefs but is at the basis of the theories espoused by 
the sort of 
secular academics shown up in recent years by the Sokal hoax. 

Stathis Papaioannou
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Re: Numbers, Machine and Father Ted

[Bruno Marchal]

Le 11-nov.-06, à 01:09, 1Z a écrit :

 No, because there are no possible worlds where (2^32582657)-1
 is not  a prime number.

This is for me a typical arithmetical realist statement.


 Causality , as opposed
 to material implication, requires contingency.

Yes. And grosso modo there will be as many notion of causality that 
there are possible modal logic. Causality, like matter, 
consciousness, etc. are higher order notions. Causality is as different 
from material implication that B(p - q) is different from p - q, 
for many possible logical systems.

You still want it both ways: keeping comp and primary material reality, 
but I have already argued in detail that this cannot work in any 
reasonable way. Postulating matter cannot explain appearance of 
matter (cf UDA, but we are in a loop, I think).

Bruno

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


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Re: Numbers, Machine and Father Ted

[1Z]

Bruno Marchal wrote:
 Le 11-nov.-06, à 01:09, 1Z a écrit :

  No, because there are no possible worlds where (2^32582657)-1
  is not  a prime number.

 This is for me a typical arithmetical realist statement.

Most philosophers who use the possible
worlds terminology do nothing PW's actually
exist.

Of course it is AR in the sense of appealing to
mind-independent truth. And of course it
remains unclear whether your AR is a claim
about truth, or about existence.

 You still want it both ways: keeping comp and primary material reality,
 but I have already argued in detail that this cannot work in any
 reasonable way.

No you haven't. You argument requires an assumption of Platonism
as well as computationalism. Computationalism
alone is compatible with materialism.


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RE: Numbers, Machine and Father Ted

[Stathis Papaioannou]

Brent Meeker writes:

 This cannot be explained away by
  faith in the sense that one can have faith in the gravity god or a
  deist god (because no empirical finding counts for or against such
  beliefs): rather, it comes down to a matter of simultaneously
  believing x and not-x.
 
 Seems like faith to me - belief without or contrary to evidence.  What is 
 the x you refer to?

There is a subtle difference. It is possible to have faith in something stupid 
and still be consistent. For example, I could say that I have faith that God 
will answer my prayers regardless of whether he has ever answered any 
prayers before in the history of the world. However, I think most religious 
people would say that they have faith that God will answer their prayers 
because that it what God does and has done in the past. In so saying, they 
are making an empirically verifiable claim, at least in theory. They can be 
invited 
to come up with a test to support their belief, which can be as stringent as 
they 
like; for example, they might allow only historical analysis because God would 
not comply with any experiment designed to test him. I suspect that no such 
test would have any impact on their beliefs because at bottom they are just 
based on blind faith, but given that they do not volunteer this to begin with, 
it 
shows them up as inconsistent and hypocritical.

Stathis Papaioannou
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RE: Numbers, Machine and Father Ted

[Stathis Papaioannou]

Johnathan Corgan writes:

  That's because for hundreds, if not thousands, of years their theologians 
  have had to explain why their God is invisible, unnoticable, 
  incompehensible, and undetectable.  So a null experimental outcome, 
  like the recent studies of the efficacy of healing prayer, is ho-hum.
 
 For a rather lengthy, straight-faced treatment of intercessory prayer
 and victims of amputation:
 
 http://whywontgodhealamputees.com/god5.htm

Great article! I initially thought that it was written by some poor, honest 
Christian 
genuinely struggling with the logical consequences of his beliefs. But then 
such a 
person would quickly either fall back on blind faith or reject his beliefs as 
false, so 
there can't be many around. 

On the other hand, I once spoke to someone who claimed he saw God miraculously 
fill a cavity in a tooth with amalgam while the faithful were invited to 
observe with 
little flashlights, so I guess someone will say that God *does* heal amputees.

Stathis Papaioannou

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RE: Numbers, Machine and Father Ted

[Johnathan Corgan]

On Sat, 2006-11-11 at 00:30 +1100, Stathis Papaioannou wrote:

  http://whywontgodhealamputees.com/god5.htm
 
 Great article! I initially thought that it was written by some poor, honest 
 Christian 
 genuinely struggling with the logical consequences of his beliefs. But then 
 such a 
 person would quickly either fall back on blind faith or reject his beliefs as 
 false, so 
 there can't be many around. 

One thing that stands out about this author is his even-handed,
non-strident walk through of his argument, taking claims regarding
prayer and statements in the Christian bible at face value.  There is no
politicizing, sarcasm, or innuendo.  It's almost as if he very strongly
wants these claims to be true but is forced to conclude they are not
through irrefutable logic.  

We certainly could use more people this eloquent in their presentation!

-Johnathan


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Re: Numbers, Machine and Father Ted

[1Z]

Bruno Marchal wrote:
 Le 09-nov.-06, à 14:07, 1Z a écrit :

  Bruno Marchal wrote:
  Le 31-oct.-06, à 19:37, 1Z a écrit :
 
  Well, I think numbers don't exist AT ALL
 
  I have not the slightest idea what you mean by that.
 
  If you don't understand anti-Platonism, that would certainly explain
  why you don't argue against it.


 I still don't understand what you mean by numbers does not exist at
 all.
 If that is antiplatonism, it would help me if you could explain
 what is antiplatonism, or better what could it mean that the numbers
 don't exist. We already agree they don't exist physically, but saying
 they does not exist at all ???

It means they don't non-physically exist either.

Mathematical claims about existence can be true
of false, but so can fictional claims like Harry Potter exists
in Middle Earth

  Even Licorne exists in some sense,
 without referent in the physical world, but with referent (meaning)
 in some fantasy worlds?

Fantasy worlds don't exist -- that's why they are called fantasy
worlds, --
Licornes don't exist, and Licornes' don't exist in fantasy worlds.

Meaning is *not* the same thing as reference (Bedeutung). That is the
box the anti-Platonist has climbed out of. Some terms have
referents (non-linguistic items they denote), others have only
sense (Sinn). Sense and reference are two dimensions
aspects of meaning, but not every term has both.
Sense is internal to langauge, it  a relationship between a
word/concept
and others. It is like a dictionary definition, whereas reference is
like
defining a word by pointing and saying it is one of those.
But no-one has ever defined a Licorne that way, since
there is no Licorne to be pointed to. Mathematical concepts
are defined in terms of other mathematical concepts.
Mathematical reference is impossible and unnecessary.

 Why could numbers not exist in some similar
 sense, except that the number fantasy kiks back (as Tom has recalled
 recently).

Saying that Licornes exist in a fantasy world
is a cumbersome way of saying they don't
literally exist. Well, numbers don't literally
kick back. They don't interact causally
with my reality.

 I am just trying to understand what you say.
 
 Bruno
 
 
 http://iridia.ulb.ac.be/~marchal/


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Re: Numbers, Machine and Father Ted

[Tom Caylor]

Brent Meeker wrote:
 Stathis Papaioannou wrote:
 
  Brent Meeker writes:
 
  This cannot be explained away by
  faith in the sense that one can have faith in the gravity god or a
  deist god (because no empirical finding counts for or against such
  beliefs): rather, it comes down to a matter of simultaneously
  believing x and not-x.
 
  Seems like faith to me - belief without or contrary to evidence.  What 
  is the x you refer to?
 
  There is a subtle difference. It is possible to have faith in something 
  stupid
  and still be consistent. For example, I could say that I have faith that God
  will answer my prayers regardless of whether he has ever answered any
  prayers before in the history of the world. However, I think most religious
  people would say that they have faith that God will answer their prayers
  because that it what God does and has done in the past. In so saying, they
  are making an empirically verifiable claim, at least in theory. They can be 
  invited
  to come up with a test to support their belief, which can be as stringent 
  as they
  like; for example, they might allow only historical analysis because God 
  would
  not comply with any experiment designed to test him. I suspect that no such
  test would have any impact on their beliefs because at bottom they are just
  based on blind faith, but given that they do not volunteer this to begin 
  with, it
  shows them up as inconsistent and hypocritical.
 
  Stathis Papaioannou

 OK.  But I'd say that in fact almost no one believes something without any 
 evidence, i.e. on *blind* faith.  Religious faith is usually belief based on 
 *selected* evidence; it is faith because it is contrary to the total 
 evidence.  Bruno seems to use faith somewhat differently: to mean what I 
 would call a working hypothesis.

 Brent Meeker

This gets us to the question that has been pondered here before, a
question that is more appropriate to the general
metaphysical/epistemological thoughts of this List: What does it mean
to believe something?  I'd say that you can't really know if you or
someone else really believes something unless you/they act on it.  An
act could simply be investing some of our precious limited time to look
at its consequences.  I'd say that for that non-trivial period of time
in your life, you had at least somewhat of a belief in it.  It is not a
trivial thing to use up some of your life doing something (at least in
my worldview).  I think this shows how Bruno's belief can be brought
equal in essence (if not necessarily the quantity of investment) to any
other belief.  Evidence is relative, and I think is important in
practical terms, but it is not essential to the definition of belief.

Tom


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Re: Numbers, Machine and Father Ted

[Brent Meeker]

Tom Caylor wrote:
 1Z wrote:
 Bruno Marchal wrote:
 Le 09-nov.-06, à 14:07, 1Z a écrit :

 Bruno Marchal wrote:
 Le 31-oct.-06, à 19:37, 1Z a écrit :

 Well, I think numbers don't exist AT ALL
 I have not the slightest idea what you mean by that.
 If you don't understand anti-Platonism, that would certainly explain
 why you don't argue against it.

 I still don't understand what you mean by numbers does not exist at
 all.
 If that is antiplatonism, it would help me if you could explain
 what is antiplatonism, or better what could it mean that the numbers
 don't exist. We already agree they don't exist physically, but saying
 they does not exist at all ???
 It means they don't non-physically exist either.

 Mathematical claims about existence can be true
 of false, but so can fictional claims like Harry Potter exists
 in Middle Earth

  Even Licorne exists in some sense,
 without referent in the physical world, but with referent (meaning)
 in some fantasy worlds?
 Fantasy worlds don't exist -- that's why they are called fantasy
 worlds, --
 Licornes don't exist, and Licornes' don't exist in fantasy worlds.

 Meaning is *not* the same thing as reference (Bedeutung). That is the
 box the anti-Platonist has climbed out of. Some terms have
 referents (non-linguistic items they denote), others have only
 sense (Sinn). Sense and reference are two dimensions
 aspects of meaning, but not every term has both.
 Sense is internal to langauge, it  a relationship between a
 word/concept
 and others. It is like a dictionary definition, whereas reference is
 like
 defining a word by pointing and saying it is one of those.
 But no-one has ever defined a Licorne that way, since
 there is no Licorne to be pointed to. Mathematical concepts
 are defined in terms of other mathematical concepts.
 Mathematical reference is impossible and unnecessary.

 Why could numbers not exist in some similar
 sense, except that the number fantasy kiks back (as Tom has recalled
 recently).
 Saying that Licornes exist in a fantasy world
 is a cumbersome way of saying they don't
 literally exist. Well, numbers don't literally
 kick back. They don't interact causally
 with my reality.
 
 What about:
 If (2^32582657)-1 is a prime number, I will not eat my hat.
 In all possible worlds where I always keep my promises, I will not eat
 my hat.
 This is causally a result of the fact that (2^32582657)-1 is a prime
 number.
 
 Tom

I think a clue is in the fact that you picked (2^32582657 -1) instead of 7.

Brent Meeker

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Re: Numbers, Machine and Father Ted

[Tom Caylor]

Brent Meeker wrote:
 Tom Caylor wrote:
  1Z wrote:
  Bruno Marchal wrote:
  Le 09-nov.-06, à 14:07, 1Z a écrit :
 
  Bruno Marchal wrote:
  Le 31-oct.-06, à 19:37, 1Z a écrit :
 
  Well, I think numbers don't exist AT ALL
  I have not the slightest idea what you mean by that.
  If you don't understand anti-Platonism, that would certainly explain
  why you don't argue against it.
 
  I still don't understand what you mean by numbers does not exist at
  all.
  If that is antiplatonism, it would help me if you could explain
  what is antiplatonism, or better what could it mean that the numbers
  don't exist. We already agree they don't exist physically, but saying
  they does not exist at all ???
  It means they don't non-physically exist either.
 
  Mathematical claims about existence can be true
  of false, but so can fictional claims like Harry Potter exists
  in Middle Earth
 
   Even Licorne exists in some sense,
  without referent in the physical world, but with referent (meaning)
  in some fantasy worlds?
  Fantasy worlds don't exist -- that's why they are called fantasy
  worlds, --
  Licornes don't exist, and Licornes' don't exist in fantasy worlds.
 
  Meaning is *not* the same thing as reference (Bedeutung). That is the
  box the anti-Platonist has climbed out of. Some terms have
  referents (non-linguistic items they denote), others have only
  sense (Sinn). Sense and reference are two dimensions
  aspects of meaning, but not every term has both.
  Sense is internal to langauge, it  a relationship between a
  word/concept
  and others. It is like a dictionary definition, whereas reference is
  like
  defining a word by pointing and saying it is one of those.
  But no-one has ever defined a Licorne that way, since
  there is no Licorne to be pointed to. Mathematical concepts
  are defined in terms of other mathematical concepts.
  Mathematical reference is impossible and unnecessary.
 
  Why could numbers not exist in some similar
  sense, except that the number fantasy kiks back (as Tom has recalled
  recently).
  Saying that Licornes exist in a fantasy world
  is a cumbersome way of saying they don't
  literally exist. Well, numbers don't literally
  kick back. They don't interact causally
  with my reality.
 
  What about:
  If (2^32582657)-1 is a prime number, I will not eat my hat.
  In all possible worlds where I always keep my promises, I will not eat
  my hat.
  This is causally a result of the fact that (2^32582657)-1 is a prime
  number.
 
  Tom

 I think a clue is in the fact that you picked (2^32582657 -1) instead of 7.

 Brent Meeker

OK.  I'll go with 7.  Compare

If 7 is a prime number, I will not eat my hat.

vs.

If this table holds up my coffee cup, I will not eat my hat.

Signed,
Tom


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RE: Numbers, Machine and Father Ted

[Stathis Papaioannou]

Peter Jones writes:

   Most people would not say yes doctor to a process that recorded
   their
   brain on a tape a left it in a filing cabinet. Yet, that is all you
   can
   get out of the timeless world of Plato's heaven (programme vs
   process).
 
 
  Why? Plato's heaven is full of mathematical process, which looks non
  dynamical from outside, like a block universe, but can be dynamical
  from inside.
 
 If you can show that subjective experience exists in Platonia,
 you can use that to show that some things will seem dynamical.
 
 If you can show that there a dynamic processes in Platonia,
 you can use that to show there are running computations
 and therefore minds, and therefore experiences.
 
 But can you do both without circularity?

That subjective experience exists in Platonia is shown by Maudlin-type 
arguments, although admittedly there are several other ways around this 
such as rejecting computationalism. 

That dynamic processes can occur in the absence of traditional linear time is 
less problematic. You haven't come up with a test that would tell me whether 
I am living in a properly implemented block universe or a linear universe, and 
I 
think it is impossible in principle to come up with such a test. That does not 
mean 
we are living in a block universe, but it does mean we would not know it if we 
were. 

Stathis Papaioannou
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Re: Numbers, Machine and Father Ted

[Tom Caylor]

1Z wrote:
 Tom Caylor wrote:
  1Z wrote:
   Bruno Marchal wrote:
Le 09-nov.-06, à 14:07, 1Z a écrit :
   
 Bruno Marchal wrote:
 Le 31-oct.-06, à 19:37, 1Z a écrit :

 Well, I think numbers don't exist AT ALL

 I have not the slightest idea what you mean by that.

 If you don't understand anti-Platonism, that would certainly explain
 why you don't argue against it.
   
   
I still don't understand what you mean by numbers does not exist at
all.
If that is antiplatonism, it would help me if you could explain
what is antiplatonism, or better what could it mean that the numbers
don't exist. We already agree they don't exist physically, but saying
they does not exist at all ???
  
   It means they don't non-physically exist either.
  
   Mathematical claims about existence can be true
   of false, but so can fictional claims like Harry Potter exists
   in Middle Earth
  
 Even Licorne exists in some sense,
without referent in the physical world, but with referent (meaning)
in some fantasy worlds?
  
   Fantasy worlds don't exist -- that's why they are called fantasy
   worlds, --
   Licornes don't exist, and Licornes' don't exist in fantasy worlds.
  
   Meaning is *not* the same thing as reference (Bedeutung). That is the
   box the anti-Platonist has climbed out of. Some terms have
   referents (non-linguistic items they denote), others have only
   sense (Sinn). Sense and reference are two dimensions
   aspects of meaning, but not every term has both.
   Sense is internal to langauge, it  a relationship between a
   word/concept
   and others. It is like a dictionary definition, whereas reference is
   like
   defining a word by pointing and saying it is one of those.
   But no-one has ever defined a Licorne that way, since
   there is no Licorne to be pointed to. Mathematical concepts
   are defined in terms of other mathematical concepts.
   Mathematical reference is impossible and unnecessary.
  
Why could numbers not exist in some similar
sense, except that the number fantasy kiks back (as Tom has recalled
recently).
  
   Saying that Licornes exist in a fantasy world
   is a cumbersome way of saying they don't
   literally exist. Well, numbers don't literally
   kick back. They don't interact causally
   with my reality.
 
  What about:
  If (2^32582657)-1 is a prime number, I will not eat my hat.
  In all possible worlds where I always keep my promises, I will not eat
  my hat.
  This is causally a result of the fact that (2^32582657)-1 is a prime
  number.


 No, because there are no possible worlds where (2^32582657)-1
 is not  a prime number. Causality , as opposed
 to material implication, requires contingency.


So reality requires contingency.  This is getting circular.



  Tom
 
  
I am just trying to understand what you say.
   
Bruno


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


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Re: Numbers, Machine and Father Ted

[1Z]

Tom Caylor wrote:
 Brent Meeker wrote:
  Tom Caylor wrote:
   1Z wrote:
   Bruno Marchal wrote:
   Le 09-nov.-06, à 14:07, 1Z a écrit :
  
   Bruno Marchal wrote:
   Le 31-oct.-06, à 19:37, 1Z a écrit :
  
   Well, I think numbers don't exist AT ALL
   I have not the slightest idea what you mean by that.
   If you don't understand anti-Platonism, that would certainly explain
   why you don't argue against it.
  
   I still don't understand what you mean by numbers does not exist at
   all.
   If that is antiplatonism, it would help me if you could explain
   what is antiplatonism, or better what could it mean that the numbers
   don't exist. We already agree they don't exist physically, but saying
   they does not exist at all ???
   It means they don't non-physically exist either.
  
   Mathematical claims about existence can be true
   of false, but so can fictional claims like Harry Potter exists
   in Middle Earth
  
Even Licorne exists in some sense,
   without referent in the physical world, but with referent (meaning)
   in some fantasy worlds?
   Fantasy worlds don't exist -- that's why they are called fantasy
   worlds, --
   Licornes don't exist, and Licornes' don't exist in fantasy worlds.
  
   Meaning is *not* the same thing as reference (Bedeutung). That is the
   box the anti-Platonist has climbed out of. Some terms have
   referents (non-linguistic items they denote), others have only
   sense (Sinn). Sense and reference are two dimensions
   aspects of meaning, but not every term has both.
   Sense is internal to langauge, it  a relationship between a
   word/concept
   and others. It is like a dictionary definition, whereas reference is
   like
   defining a word by pointing and saying it is one of those.
   But no-one has ever defined a Licorne that way, since
   there is no Licorne to be pointed to. Mathematical concepts
   are defined in terms of other mathematical concepts.
   Mathematical reference is impossible and unnecessary.
  
   Why could numbers not exist in some similar
   sense, except that the number fantasy kiks back (as Tom has recalled
   recently).
   Saying that Licornes exist in a fantasy world
   is a cumbersome way of saying they don't
   literally exist. Well, numbers don't literally
   kick back. They don't interact causally
   with my reality.
  
   What about:
   If (2^32582657)-1 is a prime number, I will not eat my hat.
   In all possible worlds where I always keep my promises, I will not eat
   my hat.
   This is causally a result of the fact that (2^32582657)-1 is a prime
   number.
  
   Tom
 
  I think a clue is in the fact that you picked (2^32582657 -1) instead of 7.
 
  Brent Meeker

 OK.  I'll go with 7.  Compare

 If 7 is a prime number, I will not eat my hat.


http://www.earlham.edu/~peters/courses/log/mat-imp.htm

http://plato.stanford.edu/entries/logic-relevance/


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Re: Numbers, Machine and Father Ted

[Bruno Marchal]

Peter Jones (1Z) a écrit :

 Most people would not say yes doctor to a process that recorded 
 their
 brain on a tape a left it in a filing cabinet. Yet, that is all you 
 can
 get out of the timeless world of Plato's heaven (programme vs 
 process).


Why? Plato's heaven is full of mathematical process, which looks non 
dynamical from outside, like a block universe, but can be dynamical 
from inside.

Bruno


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


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Re: Numbers, Machine and Father Ted

[Bruno Marchal]

Le 31-oct.-06, à 19:37, 1Z a écrit :

 Well, I think numbers don't exist AT ALL

I have not the slightest idea what you mean by that. Your longer 
metaphysics post begs many of the questions addressed in this list.
Personally: I have no theory, just an argument showing that if we take 
the yes doctor seriously enough then there is no primitive physical 
objects AT ALL(**), and then I show how to recover constructively the 
stable appearances of physical objects, and this in a precise 
empirically verifiable way(*).
(And to be sure, I have always expected to get a refutation, but 
instead the theory has been confirmed until now. Of course QM, loop 
gravity and string theories are still in advance for the physical stuff 
but (a)comp is in advance for the explanation of the quanta-qualia 
relations, (and more generally the relation between all point of views 
(n-persons, hypostases) I would say).

Bruno

(*) This makes me an empirist, but I do not subscribe to math is 
physics form of empiry. It belongs more on the type physics is 
mathematics as seen from some internal observer-universal machine.
(**) More precisely: such a notion of primitive physical objects can no 
more be invoked for justifying the appearances of physical laws.
BTW (a minor detail) rational numbers are also dense, but are 
constructive objects. Cf your long post.

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


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Re: Numbers, Machine and Father Ted

[1Z]

Bruno Marchal wrote:
 Peter Jones (1Z) a écrit :

  Most people would not say yes doctor to a process that recorded
  their
  brain on a tape a left it in a filing cabinet. Yet, that is all you
  can
  get out of the timeless world of Plato's heaven (programme vs
  process).


 Why? Plato's heaven is full of mathematical process, which looks non
 dynamical from outside, like a block universe, but can be dynamical
 from inside.

If you can show that subjective experience exists in Platonia,
you can use that to show that some things will seem dynamical.

If you can show that there a dynamic processes in Platonia,
you can use that to show there are running computations
and therefore minds, and therefore experiences.

But can you do both without circularity?

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


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Re: Numbers, Machine and Father Ted

[1Z]

Bruno Marchal wrote:
 Le 31-oct.-06, à 19:37, 1Z a écrit :

  Well, I think numbers don't exist AT ALL

 I have not the slightest idea what you mean by that.

If you don't understand anti-Platonism, that would certainly explain
why you don't argue against it.

 Your longer
 metaphysics post begs many of the questions addressed in this list.
 Personally: I have no theory, just an argument showing that if we take
 the yes doctor seriously enough then there is no primitive physical
 objects AT ALL(**), and then I show how to recover constructively the
 stable appearances of physical objects, and this in a precise
 empirically verifiable way(*).
 (And to be sure, I have always expected to get a refutation, but
 instead the theory has been confirmed until now. Of course QM, loop
 gravity and string theories are still in advance for the physical stuff
 but (a)comp is in advance for the explanation of the quanta-qualia
 relations, (and more generally the relation between all point of views
 (n-persons, hypostases) I would say).

 Bruno

 (*) This makes me an empirist, but I do not subscribe to math is
 physics form of empiry. It belongs more on the type physics is
 mathematics as seen from some internal observer-universal machine.
 (**) More precisely: such a notion of primitive physical objects can no
 more be invoked for justifying the appearances of physical laws.

Just as I have an argument that Platonically existing mathematical
objects are not needed to explain mathematics or anything else.

 BTW (a minor detail) rational numbers are also dense, but are
 constructive objects. Cf your long post.
 
 http://iridia.ulb.ac.be/~marchal/


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Re: Numbers, Machine and Father Ted

[Bruno Marchal]

Le 09-nov.-06, à 13:53, 1Z a écrit :


 If you can show that subjective experience exists in Platonia,
 you can use that to show that some things will seem dynamical.

 If you can show that there a dynamic processes in Platonia,
 you can use that to show there are running computations
 and therefore minds, and therefore experiences.

 But can you do both without circularity?



Yes. That circularity is worked out through a mathematical theory of 
self-reference. Of course that is not something I can explain in just 
one post.

I suggest you search in the archive, or you consult my papers, or you 
could wait some explanation I have promised to David (but he seems busy 
right now).

What can be explained in a few lines is that *discourses* about 
subjective experience and time appears naturally in the modal 
variant of self-reference.

I study what a ideally correct machine can prove about herself. Then 
I borrow one of Theaetetus' definition of the knower/first person: so 
that
to know p is defined by to ((I can justify p)  p). This makes 
sense thanks to the fact that no machine can prove that proving p 
entails necessarily p (and this is a consequence of incompleteness). 
Then math shows that the arithmetical knower so defined has a 
discourse similar to the Berson/Brouwer ... theory of the creative 
and temporal subject, + a lot of mathematical property making it closer 
to some intuitionistic view of math. This gives a subjective time 
theory, but also an arithmetical topos, etc.
In the same way we get a physics (according to the UDA) when we 
define I observe p, by I am measuring p with a 
probability/credibility of one. This means we can define observing p 
by I  can justify p and p is consistent. By Godel *completeness* 
theorem this is equivalent with p is true in all accessible world and p 
is true in at least one accessible world). Note that here I am using 
implicitly a lot of theorems in the math of self-reference---I just 
summarize, look into my papers for more). Here we should get some 
geometry, and we already get a quantum like probability logic, 
including a purely arithmetical interpretation of it.

Of course nobody can prove the existence of subjective experience in 
Platonia or anywhere. We know that exists because somehow we live 
them, but they cannot be communicated.
But once we grant that similarity of some possible discourses on 
subjective experience can be taken as evidence of the presence of 
subjective experience (what I have sometimes refer to as the 
politeness principle), then what I say above can help to figure out 
how subjective experiences and subjective times can appear as internal 
modality of any arithmetical realm. Put in another way, if this would 
not be true, it would entails the existence of many zombies in 
platonia. But of course this is a short way to present this and I ask 
you to not taking too much literally what I try to explain shortly.

To sum up: circularity is handled by the mathematical theory of 
self-reference (encapsulated by the modal logic G and G* at the 
propositional level). Psychological and physical things are either 
modelised or recovered by intensional variants of the self-reference 
logic G (for the provable) and G* (for the true but not necessarily 
provable).

Note that here I was talking on subjective time. The running UD in 
platonia defined implicitly another notion of time, which is just the 
number of steps the UD needs to access states. This can be well defined 
up to some constant thanks to machine independence theorem in computer 
science. But this as nothing to do with subjective time, or with the 
feeling or seeming of time flows.


Bruno



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


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Re: Numbers, Machine and Father Ted

[Bruno Marchal]

Le 09-nov.-06, à 14:07, 1Z a écrit :

 Bruno Marchal wrote:
 Le 31-oct.-06, à 19:37, 1Z a écrit :

 Well, I think numbers don't exist AT ALL

 I have not the slightest idea what you mean by that.

 If you don't understand anti-Platonism, that would certainly explain
 why you don't argue against it.


I still don't understand what you mean by numbers does not exist at 
all. If that is antiplatonism, it would help me if you could explain 
what is antiplatonism, or better what could it mean that the numbers 
don't exist. We already agree they don't exist physically, but saying 
they does not exist at all ??? Even Licorne exists in some sense, 
without referent in the physical world, but with referent (meaning) 
in some fantasy worlds? Why could numbers not exist in some similar 
sense, except that the number fantasy kiks back (as Tom has recalled 
recently).

I am just trying to understand what you say.

Bruno


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


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Re: Numbers, Machine and Father Ted

[Stephen Paul King]

Dear Stathis,

Is this not an extreme form of Occasionalism?

http://en.wikipedia.org/wiki/Occasionalism

Why does it seem that we humans perpetually imagine the possibility that 
the Universe we observe requires some form of hidden behind the curtains 
machinery to hold it up; I am remined of the image of Atlas standing on a 
Tortoise hold up the Earth.

Could it be that all of the machinery required is right in front of 
us?


Consider the question of the computational resources required to compute 
the dynamics of the Earth's ecosphere, as Stephen Wolfram wrote:

http://www.stephenwolfram.com/publications/articles/physics/85-undecidability/2/text.html

The behavior of a physical system may always be calculated by simulating 
explicitly each step in its evolution. Much of theoretical physics has, 
however, been concerned with devising shorter methods of calculation that 
reproduce the outcome without tracing each step. Such shortcuts can be made 
if the computations used in the calculation are more sophisticated than 
those that the physical system can itself perform. Any computations must, 
however, be carried out on a computer. But the computer is itself an example 
of a physical system. And it can determine the outcome of its own evolution 
only by explicitly following it through: No shortcut is possible. Such 
computational irreducibility occurs whenever a physical system can act as a 
computer. The behavior of the system can be found only by direct simulation 
or observation: No general predictive procedure is possible.

...

...their own evolution is effectively the most efficient procedure for 
determining their future.

The Universe's Computation of its future is its Evolution.


Onward!

Stephen

- Original Message - 
From: Stathis Papaioannou [EMAIL PROTECTED]
To: everything-list@googlegroups.com
Sent: Tuesday, November 07, 2006 11:11 PM
Subject: RE: Numbers, Machine and Father Ted




Brent Meeker writes:
snip
 A theist God (as opposed to a deist God) is one who intervenes in the 
 natural order, i.e. does miracles.  Stenger will readily admit that his 
 argument does not apply to a deist God.

It's also possible that God intervenes all the time in a perfectly 
consistent
manner to sustain natural laws, such that if he stopped doing so the whole
universe would instantly disintegrate. This would make it seem as if God 
either
does not exist or, if he does, he is a deist, whereas in fact he is a 
theist. The
problem with this idea, and for that matter with deism, is that it is empty 
of
explanatory value. Ironically perhaps, it is God-as-miracle-worker which 
comes
closest to a legitimate scientific theory, albeit one without any supporting 
evidence
in its favour.

Stathis Papaioannou 


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RE: Numbers, Machine and Father Ted

[Stathis Papaioannou]

Brent Meeker writes:

  It's also possible that God intervenes all the time in a perfectly 
  consistent 
  manner to sustain natural laws, such that if he stopped doing so the whole 
  universe would instantly disintegrate. 
 
 That's possible, but then he's a deist God.  He doesn't do miracles in 
 response to prayer.  It seems to me there's a contradiction between 
 intervenes and prefectly consistent.  There's no more reason to believe 
 that the universe needs sustaining than to believe there's a teapot 
 orbiting Jupiter.

A deist God does not intervene once the universe is set in motion. But one can 
imagine 
for example a gravity god, who pushes matter around in a perfectly consistent 
way so 
as to give the impression of natural laws. If he stopped doing his thing, stars 
would explode 
and the universe would fall apart. It's only because the gravity god is very 
conscientious in 
his work that we don't notice he is constantly performing miracles. Of course, 
there is no more 
reason to believe in the gravity god than there is to believe in any other kind 
of god, but at the 
same time it is not possible to be rigidly atheistic about the gravity god just 
as it is not possible to 
be rigidly atheistic about Zeus or Thor. 

 This would make it seem as if God either 
  does not exist or, if he does, he is a deist, whereas in fact he is a 
  theist. The 
  problem with this idea, and for that matter with deism, is that it is empty 
  of 
  explanatory value. Ironically perhaps, it is God-as-miracle-worker which 
  comes 
  closest to a legitimate scientific theory, albeit one without any 
  supporting evidence 
  in its favour.
 
 If it's lawlike it ain't a miracle.  Deism was a common position that come 
 out of the Enlightenment.  It comported perfectly with a Newtonian, clockwork 
 universe.  It avoided the problem of evil.  Franklin, Paine, and Jefferson 
 were deists.  But it fits well with scientific models because it does nothing.

Good old-fashioned miracles are not lawlike, which is what makes them subject 
to empirical verification. 
If God is a Protestant, then an examination of a list of lottery ticket winners 
or people with serious 
illnesses should show that Protestants are statistically more likely to have 
their prayers answered than 
Catholics, Muslims or atheists (who wish for things, even if they don't 
actually pray). If not, then either 
God is not a Protestant or there is no point in praying for anything even if 
you and he are both Protestants. 
And yet I doubt that there are any Protestants, Catholics or Muslims who be at 
all perturbed by the findings 
of such a study, or countless other possible studies or experiments. This 
cannot be explained away by faith 
in the sense that one can have faith in the gravity god or a deist god (because 
no empirical finding counts for 
or against such beliefs): rather, it comes down to a matter of simultaneously 
believing x and not-x. 

Stathis Papaioannou
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Re: Numbers, Machine and Father Ted

[Bruno Marchal]

Le 07-nov.-06, à 20:10, Tom Caylor a écrit :


 Brent Meeker wrote:
 Tom Caylor wrote:
 Brent Meeker wrote:
 Tom Caylor wrote:
 Bruno has tried to introduce us before to the concept of universes 
 or
 worlds made from logic, bottom up (a la constructing elephants).  
 These
 universes can be consistent or inconsistent.

 But approaching it from the empirical side (top down rather bottom 
 up),
 here is an example of a consistent structure:  I think you assume 
 that
 you as a person are a structure, or that you can assume that
 temporarily for the purpose of argument.  You as a person can be
 consistent in what you say, can you not?  Given certain assumptions
 (axioms) and inference rules you can be consistent or inconsistent 
 in
 what you say.
 Depending on your definition of consistent and inconsistent, there 
 need not be any axioms or inference rules at all.  If I say I'm 
 married and I'm not married. then I've said something inconsistent 
 - regardless of axioms or rules.  But *I'm* not inconsistent - just 
 what I've said is.

 I'm not saying the what you say is all there is to who
 you are.  Actually this illustrates what I was saying before about 
 the
 need for a reference frame to talk about consistency, e.g. what 
 you
 say, given your currently held axioms and rules.
 If you have axioms and rules and you can infer X and not-X then 
 the axioms+rules are inconsistent - but so what?  Nothing of import 
 about the universe follows.


 Yes, but if you see that one set of axioms/rules is inconsistent with
 another set of axioms/rules, then you can deduce something about the
 possible configurations of the universe, but only if you assume that
 the universe is consistent (which you apparently are calling a 
 category
 error).  A case in point is Euclid's fifth postulate in fact.  By
 observing that Euclidean geometry is inconsistent with non-Euclidean
 geometry (the word observe here is not a pun or even a metaphor!),
 you can conclude that the local geometry of the universe should 
 follow
 one or the other of these geometries.

 No, you are mistaken.  You can only conclude that, based on my 
 methods of measurement, a non-Euclidean model of the universe is 
 simpler and more convenient than an Euclidean one.

 This is exactly the reasoning
 they are using in analyzing the WIMP observations.

 The WIMP observations are consistent with a Euclidean 
 model...provided you change a lot of other physics.

 Time and again in
 history, math has been the guide for what to look for in the 
 universe.
 Not just provability (as Bruno pointed out) inside one set of
 axioms/rules (paradigm), but the most powerful tool is generating
 multiple consistent paradigms, and playing them against one another,
 and against the observed structure of the universe.

 Right.  As my mathematician friend Norm Levitt put it,The duty of 
 abstract mathematics, as I see it, is precisely to expand our 
 capacity for hypothesizing possible ontologies.


 This quote is basically what I've been trying to get at.  The possible
 ontologies are the multiple self-consistent paradigms that I was
 referring to.  When we keep finding that using abstract math to
 hypothesize actually works in guiding us correctly to what to look
 for, then we have to start believing that there's got to be some kind
 of truth to math that is greater than trivial self-consistent logical
 inference.  I think this is what Bruno is getting at with the border
 between G (provable truth) and G* (provable and unprovable truth).
 Math helps us find not just G, but we can also explore the border of G
 and G*.



Yes. Note that a lobian machine M1 can *deduce* the G and the G* 
corresponding to a simpler lobian machine M2, but can only infer or 
hope or fear ... about its own G*.

Remark: I recall for others that G is the modal logic which axiomatizes 
completely the self-referential provable discourse of sufficiently 
powerful classical proving machine, and G* formalize completely (at 
some level) the true discourse (the provable one and the inferable 
one).
It corresponds to the third person point of view (the second hypostase 
of Plotinus). G is the discursive, G* is the divine one (true).
The main axiom of G is B(Bp - p) - Bp and its arithmetical 
interpretation is lob theorem. Exercise: deduce from Godel's theorem  
it (I have already answer it but ask if you don't find the answer).

B represents here Godel's provability predicate: Godel's theorem = ~Bf 
- ~B(~Bf) (If the false is not provable, then that fact itself is not 
provable).



 Agreement would be great.  But the proof of scientific pudding is 
 predicting something suprising that is subsequently confirmed.

 Brent Meeker
Tom:
 I would like to hear Bruno's thoughts on comp with respect to
 prediction of global aspects such as geometry, as I brought up in the
 above paragraph from a previous post.

A sort of physical geometry should arise from the Bp  Dp ( p) povs.
Mathematical geometry can occur