“Markov's theorem

[Stephen P. King]

Hi Bruno and Russell,

��� This is one of the reasons I am skeptical of Bruno's immaterialism:

http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=471&option_lang=eng


Markov's theorem and algorithmically non-recognizable combinatorial manifolds

M.�A.�Shtan'ko


Abstract: We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial

-dimensional manifold for every . We construct for the first time a�concrete manifold which is algorithmically non-recognizable. A�strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all . We use Borisov's group�[8] with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem.

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

[meekerdb]

Did you read the paper?� Can you provide a translation?

Brent

[Bruno Marchal]

Stephen,

I presented an argument. Whatever you read, if it casts a doubt on the validity of the argument, you have to use what you read to find the invalid step.

If not, you act like so many papers pretending that cannabis is a dangerous, but which are only speculation on plausible danger, not proof.

A proof, both in math and in applied math in some theoretical framework does not depend on any further research, by construction. If you doubt about immaterialism, by reading on Markow (say), then you might find a way to use Markov against computationalism, or you must make precise which step in the reasoning you are doubting and why, and this without doing interpretation or using philosophy.

If not, you confuse science and philosophy, which is easy when the scientific method tackle a problem easily randed in philosophy, or at the intersection of philosophy and science. 

Now, I don't see why the work you mention has anything to do with the immaterialism derived from comp. You might elaborate a lot.

Bruno

On 19 May 2012, at 07:19, Stephen P. King wrote:

Hi Bruno and Russell,

    This is one of the reasons I am skeptical of Bruno's immaterialism:

http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=471&option_lang=eng


Markov's theorem and algorithmically non-recognizable combinatorial manifolds

M. A. Shtan'ko

Abstract: We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial

<006E.png>-dimensional manifold for every <006E.png><2265.png><0034.png>. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all <006E.png><2265.png><0034.png>. We use Borisov's group [8] with insoluble word problem. It has two generators and twelve relations.

The use of this group forms the base for proving the strengthened form of Markov's theorem.

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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

[Stephen P. King]

--

My apologies. The full English version is behind a pay-wall. I have read of Markov's theorem on this previously but I cannot find my reference for it atm.

[Stephen P. King]

An accessible paper in postscript format that discusses the theorem is found here:

www.math.toronto.edu/nabutovsky/gravity2005.ps

��� I will write up more on this in my reply to Bruno.

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Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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[Stephen P. King]

On 5/19/2012 4:06 AM, Bruno Marchal wrote:

Stephen,

I presented an argument. Whatever you read, if it casts a doubt on the validity of the argument, you have to use what you read to find the invalid step.

If not, you act like so many papers pretending that cannabis is a dangerous, but which are only speculation on plausible danger, not proof.

A proof, both in math and in applied math in some theoretical framework does not depend on any further research, by construction. If you doubt about immaterialism, by reading on Markow (say), then you might find a way to use Markov against computationalism, or you must make precise which step in the reasoning you are doubting and why, and this without doing interpretation or using philosophy.

If not, you confuse science and philosophy, which is easy when the scientific method tackle a problem easily randed in philosophy, or at the intersection of philosophy and science.�

Now, I don't see why the work you mention has anything to do with the immaterialism derived from comp. You might elaborate a lot.

Bruno

�Dear Bruno,

��� I finally found a good and accessible paper that discusses my bone of contention. To quote from it:

"A� theorem� proved by Markov� on� the� non-classifiability� of� the� 4-manifolds� implies
that, given� some comprehensive specification� for� the� topology� of� a manifold� (such� as
its triangulation,� a� la� Regge� calculus,� or� instructions� for� constructing� it� via� cutting
and� gluing� simpler� spaces)� there� exists� no� general� algorithm� to� decide� whether� the
manifold is homeomorphic to some other manifold� [l].� The impossibility of� classifying
the� 4-manifolds is� a well-known� topological result,� the proof of which,� however,� may
not� be� well known� in� the� physics� community.� It� is� potentially� a� result� of� profound
physical� implications,� as� the� universe� certainly� appears� to be� a manifold� of� at� least
four� dimensions."

��� The reference to the proof by Markov is:

Markov A. A.� 1960 Proceedings of� the International� Congress of Mathematicians, Edinburgh� 1958
(edited by� J. Todd Cambridge University Press, Cambridge) p 300

��� The point of this is that if the relation between a pair of 4-manifolds is not related by a general algorithm, how then is it coherent to say that our observed physical universe is the result of general algorithms?

[Bruno Marchal]

On 19 May 2012, at 19:17, Stephen P. King wrote:

On 5/19/2012 4:06 AM, Bruno Marchal wrote:

Stephen,

I presented an argument. Whatever you read, if it casts a doubt on the validity of the argument, you have to use what you read to find the invalid step.

If not, you act like so many papers pretending that cannabis is a dangerous, but which are only speculation on plausible danger, not proof.

A proof, both in math and in applied math in some theoretical framework does not depend on any further research, by construction. If you doubt about immaterialism, by reading on Markow (say), then you might find a way to use Markov against computationalism, or you must make precise which step in the reasoning you are doubting and why, and this without doing interpretation or using philosophy.

If not, you confuse science and philosophy, which is easy when the scientific method tackle a problem easily randed in philosophy, or at the intersection of philosophy and science. 

Now, I don't see why the work you mention has anything to do with the immaterialism derived from comp. You might elaborate a lot.

Bruno

 Dear Bruno,

    I finally found a good and accessible paper that discusses my bone of contention. To quote from it:

"A  theorem  proved by Markov  on  the  non-classifiability  of  the  4-manifolds  implies
that, given  some comprehensive specification  for  the  topology  of  a manifold  (such  as
its triangulation,  a  la  Regge  calculus,  or  instructions  for  constructing  it  via  cutting
and  gluing  simpler  spaces)  there  exists  no  general  algorithm  to  decide  whether  the
manifold is homeomorphic to some other manifold  [l].  The impossibility of  classifying
the  4-manifolds is  a well-known  topological result,  the proof of which,  however,  may
not  be  well known  in  the  physics  community.  It  is  potentially  a  result  of  profound
physical  implications,  as  the  universe  certainly  appears  to be  a manifold  of  at  least
four  dimensions."

    The reference to the proof by Markov is:

Markov A. A.  1960 Proceedings of  the International  Congress of Mathematicians, Edinburgh  1958
(edited by  J. Todd Cambridge University Press, Cambridge) p 300

    The point of this is that if the relation between a pair of 4-manifolds is not related by a general algorithm, how then is it coherent to say that our observed physical universe is the result of general algorithms?

But comp explained why it has to be like that. The observable universe cannot be the result of general algorithm, given that it results from  a first person plural indeterminacy on infinite set of possible computations.

By "computation" I mean a set of states together with an universal number relating them.

The only thing proved by Markov here is that the homeomorphism relation is not Turing decidable. It suggests that 4-manifold + homeomorphism is Turing universal (as proved for braids). Any intensional identity, for any Turing complete system is as well not Turing decidable. There is no general algorithm saying that two programs compute the same functions, or even run the "same" computation.

It is a well known result for logicians. 

You don't give a clue what it has to do with immateriality. To be franc, I doubt that there is any. 

Bruno

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

[Stephen P. King]

On 5/19/2012 2:11 PM, Bruno Marchal wrote:

On 19 May 2012, at 19:17, Stephen P. King wrote:

On 5/19/2012 4:06 AM, Bruno Marchal wrote:

Stephen,

I presented an argument. Whatever you read, if it casts a doubt on the validity of the argument, you have to use what you read to find the invalid step.

If not, you act like so many papers pretending that cannabis is a dangerous, but which are only speculation on plausible danger, not proof.

A proof, both in math and in applied math in some theoretical framework does not depend on any further research, by construction. If you doubt about immaterialism, by reading on Markow (say), then you might find a way to use Markov against computationalism, or you must make precise which step in the reasoning you are doubting and why, and this without doing interpretation or using philosophy.

If not, you confuse science and philosophy, which is easy when the scientific method tackle a problem easily randed in philosophy, or at the intersection of philosophy and science.�

Now, I don't see why the work you mention has anything to do with the immaterialism derived from comp. You might elaborate a lot.

Bruno

�Dear Bruno,

��� I finally found a good and accessible paper that discusses my bone of contention. To quote from it:

"A� theorem� proved by Markov� on� the� non-classifiability� of� the� 4-manifolds� implies
that, given� some comprehensive specification� for� the� topology� of� a manifold� (such� as
its triangulation,� a� la� Regge� calculus,� or� instructions� for� constructing� it� via� cutting
and� gluing� simpler� spaces)� there� exists� no� general� algorithm� to� decide� whether� the
manifold is homeomorphic to some other manifold� [l].� The impossibility of� classifying
the� 4-manifolds is� a well-known� topological result,� the proof of which,� however,� may
not� be� well known� in� the� physics� community.� It� is� potentially� a� result� of� profound
physical� implications,� as� the� universe� certainly� appears� to be� a manifold� of� at� least
four� dimensions."

��� The reference to the proof by Markov is:

Markov A. A.� 1960 Proceedings of� the International� Congress of Mathematicians, Edinburgh� 1958

(edited by� J. Todd Cambridge University Press, Cambridge) p 300

��� The point of this is that if the relation between a pair of 4-manifolds is not related by a general algorithm, how then is it coherent to say that our observed physical universe is the result of general algorithms?

But comp explained why it has to be like that. The observable universe cannot be the result of general algorithm, given that it results from �a first person plural indeterminacy on infinite set of possible computations.

�Hi Bruno,

��� Can you not see that I am claiming that your notion of "an infinite set of possible computations" is incoherent if "the immaterialism derived from comp" is such that computations have content and consequences in a way that is separate from the physical implementations of those computations.

By "computation" I mean a set of states together with an universal number relating them.

��� "States" of what? Is there a referent, an object, that is the referent of the word "states" here? How are the "states" distinguished from each other?

��� You claim that this "computation" has "immaterial existence" in the sense that is is separable and independent of the physical word(s). You claim that the physical world are not primitive ontologically. I agree with this claim, but I do not agree that the "universal numbers" have a primitive existence either. We cannot put numbers, or any other entity, at a lower ontological level than the physical world.

The only thing proved by Markov here is that the homeomorphism relation is not Turing decidable. It suggests that 4-manifold +�homeomorphism is Turing universal (as proved for braids). Any intensional identity, for any Turing complete system is as well not Turing decidable. There is no general algorithm saying that two programs compute the same functions, or even run the "same" computation.

��� Therefore we know that there does not exist a means to generate a "Pre-established Harmony" nor can we imagine coherently that the universe we observe is just some kind of pre-existing structure that our mind is somehow running in. This implies to me that we have to think of the universe we observer to be something like the result of an ongoing and maybe even eternal process.

It is a well known result for logicians.�

You don't give a clue what it has to do with immateriality. To be franc, I doubt that there is any.

��� Immateriality, just as in Ideal monism, is a bankrupt ontology. It is incoherent to claim that something that is the result of a process exists prior to the actual implementation of the process.

[Russell Standish]

On Sat, May 19, 2012 at 01:17:18PM -0400, Stephen P. King wrote:
>
> Dear Bruno,
>
> I finally found a good and accessible paper <http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&sqi=2&ved=0CEoQFjAA&url=http%3A%2F%2Fntrs.nasa.gov%2Farchive%2Fnasa%2Fcasi.ntrs.nasa.gov%2F20050243612_2005246604.pdf&ei=8NO3T9LmFu-d6AHAq_3uCg&usg=AFQjCNHMBmwAi1K7yJY3oRBnJrYRC2H9RA&sig2=yb-YNcKWR6LNPSVy8bQquA>

> that discusses my bone of contention. To quote from it:
>

> "A theorem proved by Markov on the non-classifiability of the
> 4-manifolds implies
> that, given some comprehensive specification for the topology
> of a manifold (such as
> its triangulation, a la Regge calculus, or instructions for
> constructing it via cutting

> and gluing simpler spaces) _there exists no general algorithm
> to decide whether the
> manifold is homeomorphic to some other manifold _ [l]. The

> impossibility of classifying
> the 4-manifolds is a well-known topological result, the proof of
> which, however, may
> not be well known in the physics community. It is
> potentially a result of profound
> physical implications, as the universe certainly appears to
> be a manifold of at least
> four dimensions."

Funnily enough, I remember from the dim-distant undergraduate days,
that the classifiability of 3 and 4-manifolds were open problems. 1 &
2-manifolds had known classifications (2-manifolds are classified by
the number of "holes" (aka genus), for instance). Manifolds of
dimension higher than 4 are known to be unclassifiable. So a result
that 4-manifolds are unclassifiable would be a significant topological
result. What's suspicious is the claim that this was proved in
1960. Also suspicious in light of the Wikipedia entry claiming the
problem is still open: http://en.wikipedia.org/wiki/4-manifold

Conversely, as for the 3-manifold problem, this looks it might have been
solved by Perelman's work that also solved the more famous Poincare
conjecture in 2003. If there's anybody about that more knowledgeable on these
matters, please comment.

I remember there was something peculiar about 4-dimensional space that
wasn't true of any other dimension - unfortunately, the sands of time
have erased the details from my memory. But I remember people were
speculating that it was a possible reason for why we lived in 4D
space-time.


--

----------------------------------------------------------------------------
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Principal, High Performance Coders
Visiting Professor of Mathematics hpc...@hpcoders.com.au
University of New South Wales http://www.hpcoders.com.au
----------------------------------------------------------------------------

[Stephen P. King]

Hi Russell,

Could you be a bit more exact? The paper that I linked and quoted
was considering classification in terms of general algorithms. This is a
rather narrow case, no? I am not discussing the Poincare conjecture...

> Conversely, as for the 3-manifold problem, this looks it might have been
> solved by Perelman's work that also solved the more famous Poincare
> conjecture in 2003. If there's anybody about that more knowledgeable on these
> matters, please comment.

Perelman solved the 3-d case of the Poincare conjecture AFAIK. I am
pointing out something different, a bit more subtle.

> I remember there was something peculiar about 4-dimensional space that
> wasn't true of any other dimension - unfortunately, the sands of time
> have erased the details from my memory. But I remember people were
> speculating that it was a possible reason for why we lived in 4D
> space-time.
>

Yes, the possibility that dovetailing via general algorithm is not
possible for 4-manifolds. This is important because if our perceived
physical world has a structure that cannot be defined by a general
algorithm then some other explanation is necessary. Bruno is trying to
convince us that our experiences of a physical world is nothing more
than the shared dreams of numbers. I believe that this is false, numbers
cannot form a primitive ontological basis from which our experiences of
our universe and its physics obtains.

It is my opinion that we "live" in a 4D space-time because of this
non-computable feature. It cannot be specified in advance, thus we
actually have to go through the process of computing finite
approximations to the general problem of 4-manifold classification. This
problem and the one of QM (of finding boolean Satisfiable lattices of
Abelian von Neuman subalgebras or equivalent) are both places where
physics is not reducible to a pre-existing string of numbers.
My discussion of Leibniz' Monadology and its flawed idea of
pre-established harmony was an attempt to show how this problem has
shown up in philosophy many years ago and we are only now finding
solutions to it.

[Quentin Anciaux]

2012/5/20 Stephen P. King <step...@charter.net>

In Bruno's theory, the physical world is not computed by an algorithm, the physical world is the limit of all computations going throught your current state... what is computable is your current state, an infinity of computations goes through it. So I don't see the problem here, the UD is not an algorithm which computes the physical world 4D or whatever.

Quentin
 

   It is my opinion that we "live" in a 4D space-time because of this non-computable feature. It cannot be specified in advance, thus we actually have to go through the process of computing finite approximations to the general problem of 4-manifold classification. This problem and the one of QM (of finding boolean Satisfiable lattices of Abelian von Neuman subalgebras or equivalent) are both places where physics is not reducible to a pre-existing string of numbers.
   My discussion of Leibniz' Monadology and its flawed idea of  pre-established harmony was an attempt to show how this problem has shown up in philosophy many years ago and we are only now finding solutions to it.

--
Onward!

Stephen

"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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All those moments will be lost in time, like tears in rain.

[Evgenii Rudnyi]

Stephen,

I have a more general question. I am not a mathematician and I do not
quite understand the relationship between mathematics and the world that
surround me.

It seems to me that your writing implies that there is the intimate
connections between mathematics and the Universe. Could you please
express your viewpoint in more detail on why findings in mathematics
could influence our understanding of the world? From a viewpoint of a
not-mathematician this looks a bit like a numerology.

Evgenii

[Stephen P. King]

On 5/20/2012 6:06 AM, Quentin Anciaux wrote:

In Bruno's theory, the physical world is not computed by an algorithm, the physical world is the limit of all computations going throught your current state... what is computable is your current state, an infinity of computations goes through it. So I don't see the problem here, the UD is not an algorithm which computes the physical world 4D or whatever.

Quentin

Hi Quentin,

��� Maybe you can answer some questions. These might be badly composed so feel free to "fix" them. ;-)

1) If my "current state" is equivalent to a 4-manifold and the "next" state is also, what is connecting the two? Markov's proof tells us that it is not a algorithm. So what is it?

2) Is there another equivalent set of words for "the physical world is the limit of all computations going through your current state"?

3) Is there at least one physical system running the computations? Is the "physical universe" a purely subjective appearance/experience for each conscious entity? What is it that shifts from one state to the next?

4) What is the cardinality of "all computations"?

5) Is the totality of what exists static and timeless and are all of the subsets of that totality static and timeless as well?

6) Does all "succession of events" emerge only from the well ordering of Natural numbers?

[Stephen P. King]

On 5/20/2012 9:39 AM, Evgenii Rudnyi wrote:
> Stephen,
>
> I have a more general question. I am not a mathematician and I do not
> quite understand the relationship between mathematics and the world
> that surround me.

Dear Evgenii,

I am just a person with insatiable curiosity and the strange
ability/curse of dyslexia. I consider myself a student of philosophy. I
think of mathematics as a more precise form of language and that it is,
like all other languages, a representation of experience in the
collective sense. Some people believe that there is a one-to-one and
onto relationship between mathematics and the totality of what exists. I
do not have sufficient information for form an opinion yet.

>
> It seems to me that your writing implies that there is the intimate
> connections between mathematics and the Universe.

Well, our ability to understand representations, mathematical or
purely linguistic, argues strongly for some kind of intimate
relationship between representations and the Universe (which is to me a
word representing the totality of what exists).

> Could you please express your viewpoint in more detail on why findings
> in mathematics could influence our understanding of the world? From a
> viewpoint of a not-mathematician this looks a bit like a numerology.

We use mathematics to reason and argue about the world because that
is all we have. We cannot communicate with each other without the
ability to represent. These are good questions!

>
> Evgenii

[Quentin Anciaux]

2012/5/20 Stephen P. King <step...@charter.net>

On 5/20/2012 6:06 AM, Quentin Anciaux wrote:

In Bruno's theory, the physical world is not computed by an algorithm, the physical world is the limit of all computations going throught your current state... what is computable is your current state, an infinity of computations goes through it. So I don't see the problem here, the UD is not an algorithm which computes the physical world 4D or whatever.

Quentin

Hi Quentin,

    Maybe you can answer some questions. These might be badly composed so feel free to "fix" them. ;-)

1) If my "current state" is equivalent to a 4-manifold and the "next" state is also, what is connecting the two? Markov's proof tells us that it is not a algorithm. So what is it?

Any computations going through your current state has a next state. You don't have *a* next state but many next state, any state is always computed by an infinity of computation.

2) Is there another equivalent set of words for "the physical world is the limit of all computations going through your current state"?

The physical world is the thing that is stable in the majority of computations that compute your current conscious moment, if computationalism is true (if consciousness is turing emulable).

3) Is there at least one physical system running the computations?

No, if the UDA is correct... well technically there still could be a primitive physical universe, but you could not use it to correctly predict your next moment, nor what you see, and you would not be able to know what it is (because all of what is accessible to you is in the computations that support you, still if computationalism is true).
 

Is the "physical universe" a purely subjective appearance/experience for each conscious entity?

It is subjective in the sense that it can be only known subjectively. It is objective as the thing that each conscious entity can observe.
 

What is it that shifts from one state to the next?

The computations.

4) What is the cardinality of "all computations"?

N0 ? and if we take that to contains oracle program, even the continuum.

 

5) Is the totality of what exists static and timeless and are all of the subsets of that totality static and timeless as well?

Time is an internal thing of existence, time is related to an observer.

6) Does all "succession of events" emerge only from the well ordering of Natural numbers?

Succession of events emerge from the succession of states, of what is needed to compute you, it does not have to be related to the ordering of natural numbers.

Quentin

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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[Bruno Marchal]

On 20 May 2012, at 19:03, Stephen P. King wrote:

> On 5/20/2012 9:39 AM, Evgenii Rudnyi wrote:
>> Stephen,
>>
>> I have a more general question. I am not a mathematician and I do
>> not quite understand the relationship between mathematics and the
>> world that surround me.
>
> Dear Evgenii,
>
> I am just a person with insatiable curiosity and the strange
> ability/curse of dyslexia. I consider myself a student of
> philosophy. I think of mathematics as a more precise form of
> language and that it is, like all other languages, a representation
> of experience in the collective sense. Some people believe that
> there is a one-to-one and onto relationship between mathematics and
> the totality of what exists. I do not have sufficient information
> for form an opinion yet.

Nor me. But with comp, we know that there are no such correspondence.

Now, using axiomatic, or semi-axiomatic, like mathematicians, in any
field, makes possible to progress, even when disagreeing on the
interpretations on the terms.

>
>>
>> It seems to me that your writing implies that there is the intimate
>> connections between mathematics and the Universe.
>
> Well, our ability to understand representations, mathematical or
> purely linguistic, argues strongly for some kind of intimate
> relationship between representations and the Universe (which is to
> me a word representing the totality of what exists).

OK.

>
>> Could you please express your viewpoint in more detail on why
>> findings in mathematics could influence our understanding of the
>> world? From a viewpoint of a not-mathematician this looks a bit
>> like a numerology.
>
> We use mathematics to reason and argue about the world because
> that is all we have. We cannot communicate with each other without
> the ability to represent.

And the ability to point, too.

Bruno

> These are good questions!
>
>>
>> Evgenii
>>
>
>
> --
> Onward!
>
> Stephen
>
> "Nature, to be commanded, must be obeyed."
> ~ Francis Bacon
>
>

[meekerdb]

On 5/20/2012 9:27 AM, Stephen P. King wrote:

On 5/20/2012 6:06 AM, Quentin Anciaux wrote:

In Bruno's theory, the physical world is not computed by an algorithm, the physical world is the limit of all computations going throught your current state... what is computable is your current state, an infinity of computations goes through it. So I don't see the problem here, the UD is not an algorithm which computes the physical world 4D or whatever.

Quentin

Hi Quentin,

    Maybe you can answer some questions. These might be badly composed so feel free to "fix" them. ;-)

1) If my "current state" is equivalent to a 4-manifold and the "next" state is also, what is connecting the two? Markov's proof tells us that it is not a algorithm. So what is it?

I don't think Markov's theorem tells you that.  It says there can be no algorithm that will determine the homomorphy of any two arbitrary compact 4-manifolds.  But there is nothing that says the next state can be any arbitrary 4-manifold.  In most theories it is an evolution of the Cauchy data on the present manifold, where 'present' is defined by some time slice.

2) Is there another equivalent set of words for "the physical world is the limit of all computations going through your current state"?

3) Is there at least one physical system running the computations? Is the "physical universe" a purely subjective appearance/experience for each conscious entity? What is it that shifts from one state to the next?

Well that's a crucial question.  Bruno assumes that truth implies existence.  So if 1+1=2 is true that implies that 1, +, =, and 2 exist.  I think this is a doubtful proposition; particularly when talking about infinities.  Even if every number has a successor is true, what existence is implied?  Just the non-existence of a number with no successor.

4) What is the cardinality of "all computations"?

Aleph1.

5) Is the totality of what exists static and timeless and are all of the subsets of that totality static and timeless as well?

6) Does all "succession of events" emerge only from the well ordering of Natural numbers?

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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[meekerdb]

On 5/20/2012 10:03 AM, Quentin Anciaux wrote:

3) Is there at least one physical system running the computations?

No, if the UDA is correct... well technically there still could be a primitive physical universe, but you could not use it to correctly predict your next moment, nor what you see, and you would not be able to know what it is (because all of what is accessible to you is in the computations that support you, still if computationalism is true).

If there is a primitive physical universe, and it's Turing emulable, then you could in principle know it's program.

Brent

[Stephen P. King]

On 5/20/2012 1:03 PM, Quentin Anciaux wrote:

2012/5/20 Stephen P. King <step...@charter.net>

On 5/20/2012 6:06 AM, Quentin Anciaux wrote:

In Bruno's theory, the physical world is not computed by an algorithm, the physical world is the limit of all computations going throught your current state... what is computable is your current state, an infinity of computations goes through it. So I don't see the problem here, the UD is not an algorithm which computes the physical world 4D or whatever.

Quentin

Hi Quentin,

    Maybe you can answer some questions. These might be badly composed so feel free to "fix" them. ;-)

1) If my "current state" is equivalent to a 4-manifold and the "next" state is also, what is connecting the two? Markov's proof tells us that it is not a algorithm. So what is it?

Any computations going through your current state has a next state. You don't have *a* next state but many next state, any state is always computed by an infinity of computation.

Dear Quentin,

    OK, but what exactly is it that operates the transition from one state to the next? What is the connecting function(s)? This is what theories of time try to explain.

2) Is there another equivalent set of words for "the physical world is the limit of all computations going through your current state"?

The physical world is the thing that is stable in the majority of computations that compute your current conscious moment, if computationalism is true (if consciousness is turing emulable).

    Sure, it is a form of invariant or fixed point on a collection of transformations. But I invite you to look into exactly what is known about how these invariants exist and what are their requirements. For example, in the Brouwer fixed point theorem there is the requirement that there exist a closed, convex and compact set of points, a function transforming them and a means to evaluate the functions. If the conditions are met then the theorem predicts that a function f(x)=x exists.
    When we say that "physical world is the thing that is stable in the majority of computations that compute your current conscious moment", we are effectively saying that the physical world is much like that x such that f(x) = x. The computations are the functions transforming the states. They are actions, not entities. Additionally we have to account for all possible versions of "your current conscious moment" since whoever "your" is referring to is not a set of only one member, thus we have to have an explanation that applies to all possible observers (aka entities with the capacity of having a "current conscious moment").

3) Is there at least one physical system running the computations?

No, if the UDA is correct... well technically there still could be a primitive physical universe, but you could not use it to correctly predict your next moment, nor what you see, and you would not be able to know what it is (because all of what is accessible to you is in the computations that support you, still if computationalism is true).

    What purpose would the "primitive physical universe" serve? Here I agree 100% with Bruno. His result proves that there cannot be "a primitive physical universe". My argument with Bruno is over the ontological status of numbers. He claims that they are ontologically primitive and I claim that they cannot be.

 

Is the "physical universe" a purely subjective appearance/experience for each conscious entity?

It is subjective in the sense that it can be only known subjectively. It is objective as the thing that each conscious entity can observe.

    We can define "objective" to be that which is invariant with respect to transformations on the collection of content of all possible conscious entities can observe *and* communicate to each other. In other words, the "objective universe" is what which we can all agree upon as existing. We do not need to think that it is somehow "independent of us". It is sufficient to say that it is dependent on all of us and not dependent on any one of us. This way of thinking applies to computational universality as well: a computation is universal iff can be run on any functionally equivalent physical system such that it does not depend on any one physical configuration.

 

What is it that shifts from one state to the next?

The computations.

    And what defines the computations? Do definitions just appear by fiat?

4) What is the cardinality of "all computations"?

N0 ? and if we take that to contains oracle program, even the continuum.

    How many paths exist in the continuum that you are considering here? Each path would be equivalent to a computation in your thinking, no? Are the paths capable of being smoothly transformed into each other? If so, then the continuum has a certain topological property known as "simply connected". There are situations that involve computations that show that this topological condition cannot be satisfied. The concurrency problem is one of these situations.

 

5) Is the totality of what exists static and timeless and are all of the subsets of that totality static and timeless as well?

Time is an internal thing of existence, time is related to an observer.

    I agree, but this does not make time any less "real".

6) Does all "succession of events" emerge only from the well ordering of Natural numbers?

Succession of events emerge from the succession of states, of what is needed to compute you, it does not have to be related to the ordering of natural numbers.

Quentin

    We are OK with a circular reasoning? Succesion of states => succession of events => succession of states => ...

    I am OK with circularity if and only if one is consistent with the set theory and logic that is required. This is a well studied area in mathematics...

[Stephen P. King]

On 5/20/2012 3:06 PM, meekerdb wrote:

On 5/20/2012 9:27 AM, Stephen P. King wrote:

On 5/20/2012 6:06 AM, Quentin Anciaux wrote:

In Bruno's theory, the physical world is not computed by an algorithm, the physical world is the limit of all computations going throught your current state... what is computable is your current state, an infinity of computations goes through it. So I don't see the problem here, the UD is not an algorithm which computes the physical world 4D or whatever.

Quentin

Hi Quentin,

    Maybe you can answer some questions. These might be badly composed so feel free to "fix" them. ;-)

1) If my "current state" is equivalent to a 4-manifold and the "next" state is also, what is connecting the two? Markov's proof tells us that it is not a algorithm. So what is it?

I don't think Markov's theorem tells you that.  It says there can be no algorithm that will determine the homomorphy of any two arbitrary compact 4-manifolds.  But there is nothing that says the next state can be any arbitrary 4-manifold.  In most theories it is an evolution of the Cauchy data on the present manifold, where 'present' is defined by some time slice.

 Dear Quentin,

    "there can be no algorithm that will determine the homomorphy of any two arbitrary compact 4-manifolds" Exactly. The physical theories that are used today and accepted as fact define our objective universe as a "compact 3,1-manifold"(up to isomorphisms), this includes "time" as a dimension. There is only a technical difference between a 3,1-manifold and a 4-manifold.

    My point is that for there to exist an a priori given string of numbers that is equivalent our universe there must exist a computation of the homomorphies between all possible 4-manifolds. Markov theorem tells us that no such homomorphy exists, therefore our universe cannot be considered to be the result of a computation in the Turing universal sense. It is well known that the act of defining an exact "time slice" is a computationally intractable problem, the Cauchy surface problem. Physicists use approximations and cheats to get around this intractability.

2) Is there another equivalent set of words for "the physical world is the limit of all computations going through your current state"?

3) Is there at least one physical system running the computations? Is the "physical universe" a purely subjective appearance/experience for each conscious entity? What is it that shifts from one state to the next?

Well that's a crucial question.  Bruno assumes that truth implies existence.

    I agree with that claim. An entity must exist for there to be a true representation of it.

  So if 1+1=2 is true that implies that 1, +, =, and 2 exist.

    No, existence does not determine or define properties, it is the mere necessary possibility of such. Just because some unstated sentence may be true and its referents might exist does nothing to the determination of the properties of said sentence or its referents. Properties are determined by physical acts of measurement and by nothing else, therefore the meaning of the sentence "1+1=2" is indefinite in the absence of a physical means to evaluate the sentence.

  I think this is a doubtful proposition; particularly when talking about infinities.  Even if every number has a successor is true, what existence is implied?  Just the non-existence of a number with no successor.

4) What is the cardinality of "all computations"?

Aleph1.

    Is the content of Alph_1 sufficient to represent all knowledge?

5) Is the totality of what exists static and timeless and are all of the subsets of that totality static and timeless as well?

6) Does all "succession of events" emerge only from the well ordering of Natural numbers?

    Do you understand these questions?

[meekerdb]

On 5/20/2012 1:31 PM, Stephen P. King wrote:

    My point is that for there to exist an a priori given string of numbers that is equivalent our universe there must exist a computation of the homomorphies between all possible 4-manifolds.

Why? 

Markov theorem tells us that no such homomorphy exists,

No, it tells there is no algorithm for deciding such homomorphy *that works for all possible 4-manifolds*.  If our universe-now has a particular topology and our universe-next has a particular topology, there in nothing in Markov's theorem that says that an algorithm can't determine that.  It just says that same algorithm can't work for *every pair*.

therefore our universe cannot be considered to be the result of a computation in the Turing universal sense.

Sure it can.  Even if your interpretation of Markov's theorem were correct our universe could, for example, always have the same topology, or it could evolve only through topologies that were computable from one another?  Where does it say our universe must have all possible topologies?

Brent

[Stephen P. King]

On 5/20/2012 4:39 PM, meekerdb wrote:

On 5/20/2012 1:31 PM, Stephen P. King wrote:

    My point is that for there to exist an a priori given string of numbers that is equivalent our universe there must exist a computation of the homomorphies between all possible 4-manifolds.

Why? 

Hi Brent,

    Because otherwise the amazing precision of the mathematical models based on the assumption of, among other things, that physical systems exist in space-time that is equivalent to a 4-manifold. The mathematical reasoning involved is much like a huge Jenga tower; pull the wrong piece out and it collapses.

Markov theorem tells us that no such homomorphy exists,

No, it tells there is no algorithm for deciding such homomorphy *that works for all possible 4-manifolds*.  If our universe-now has a particular topology and our universe-next has a particular topology, there in nothing in Markov's theorem that says that an algorithm can't determine that.  It just says that same algorithm can't work for *every pair*.

    I agree with your point that Markov's theorem does not disallow the existence of some particular algorithm that can compute the relation between some particular pair of 4-manifolds. Please understand that this moves us out of considering universal algorithms and into specific algorithms. This difference is very important. It is the difference between the class of universal algorithms and a particular algorithm that is the computation of some particular function. The non-existence of the general algorithm implies the non-existence of an a priori structure of relations between the possible 4-manifolds.
    I am making an ontological argument against the idea that there exists an a priori given structure that *is* the computation of the Universe. This is my argument against Platonism.

therefore our universe cannot be considered to be the result of a computation in the Turing universal sense.

Sure it can.  Even if your interpretation of Markov's theorem were correct our universe could, for example, always have the same topology,

    No, it cannot. If there does not exist a general algorithm that can compute the homomorphy relations between all 4-manifolds then what is the result of such cannot exit either. We cannot talk coherently within computational methods about "a topology" when such cannot be specified in advance. Algorithms are recursively enumerable functions. That means that you must specify their code in advance, otherwise your are not really talking about computations; you are talking about some imaginary things created by imaginary entities in imaginary places that do imaginary acts; hence my previous references to Pink Unicorns.

    Let me put this in other words. If you cannot build the equipment needed to mix, bake and decorate the cake then you cannot eat it. We cannot have a coherent ontological theory that assumes something that can only exist as the result of some process and that same ontological theory prohibits the process from occurring.

or it could evolve only through topologies that were computable from one another?  Where does it say our universe must have all possible topologies?

   

    The alternative is to consider that the computation of the homomorphies is an ongoing process, not one that is "already existing in Platonia as a string of numbers" or anything equivalent. I would even say that time is the computation of the homomorphies. Time exists because everything cannot happen simultaneously.

    We must say that the universe has all possible topologies unless we can specify reasons why it does not. That is what goes into defining meaningfulness. When you define that X is Y, you are also defining all not-X to equal not-Y, no? When you start talking about a collection then you have to define what are its members. Absent the specification or ability to specify the members of a collection, what can you say of the collection?

    What is the a priori constraint on the Universe? Why this one and not some other? Is the limit of all computations not a computation? How did this happen?

[Stephen P. King]

On 5/20/2012 7:13 PM, Stephen P. King wrote:

On 5/20/2012 4:39 PM, meekerdb wrote:

On 5/20/2012 1:31 PM, Stephen P. King wrote:

    My point is that for there to exist an a priori given string of numbers that is equivalent our universe there must exist a computation of the homomorphies between all possible 4-manifolds.

Why? 

Hi Brent,

    Because otherwise the amazing precision of the mathematical models based on the assumption of, among other things, that physical systems exist in space-time that is equivalent to a 4-manifold. The mathematical reasoning involved is much like a huge Jenga tower; pull the wrong piece out and it collapses.

    I need to add a remark here. We cannot just assume one particular 4-manifold as the one we exist on/in. We have to consider the entire ensemble of them to even ask coherent questions about the one we are in. Why do you think cosmologists are so busy looking at such things as the spectral distribution of the CMB and so forth? It is because those are clues as to the specific type of 4-manifold that we are on/in. Additionally, when we try to model the cosmology setting of many observers and their observations we have to consider that each observer has a ensemble of possible of 4-manifolds that represent the universe that they observe.

[meekerdb]

On 5/20/2012 4:13 PM, Stephen P. King wrote:

On 5/20/2012 4:39 PM, meekerdb wrote:

On 5/20/2012 1:31 PM, Stephen P. King wrote:

    My point is that for there to exist an a priori given string of numbers that is equivalent our universe there must exist a computation of the homomorphies between all possible 4-manifolds.

Why? 

Hi Brent,

    Because otherwise the amazing precision of the mathematical models based on the assumption of, among other things, that physical systems exist in space-time that is equivalent to a 4-manifold. The mathematical reasoning involved is much like a huge Jenga tower; pull the wrong piece out and it collapses.

Markov theorem tells us that no such homomorphy exists,

No, it tells there is no algorithm for deciding such homomorphy *that works for all possible 4-manifolds*.  If our universe-now has a particular topology and our universe-next has a particular topology, there in nothing in Markov's theorem that says that an algorithm can't determine that.  It just says that same algorithm can't work for *every pair*.

    I agree with your point that Markov's theorem does not disallow the existence of some particular algorithm that can compute the relation between some particular pair of 4-manifolds. Please understand that this moves us out of considering universal algorithms and into specific algorithms. This difference is very important. It is the difference between the class of universal algorithms and a particular algorithm that is the computation of some particular function. The non-existence of the general algorithm implies the non-existence of an a priori structure of relations between the possible 4-manifolds.
    I am making an ontological argument against the idea that there exists an a priori given structure that *is* the computation of the Universe. This is my argument against Platonism.

therefore our universe cannot be considered to be the result of a computation in the Turing universal sense.

Sure it can.  Even if your interpretation of Markov's theorem were correct our universe could, for example, always have the same topology,

    No, it cannot. If there does not exist a general algorithm that can compute the homomorphy relations between all 4-manifolds then what is the result of such cannot exit either.

The result is an exhaustive classification of compact 4-mainifolds.  The absence of such a classification neither prevents nor entails the existence of the manifolds. 

We cannot talk coherently within computational methods about "a topology" when such cannot be specified in advance. Algorithms are recursively enumerable functions. That means that you must specify their code in advance, otherwise your are not really talking about computations; you are talking about some imaginary things created by imaginary entities in imaginary places that do imaginary acts; hence my previous references to Pink Unicorns.

    Let me put this in other words. If you cannot build the equipment needed to mix, bake and decorate the cake then you cannot eat it.

You can have the equipment mix, bake, decorate and eat a cake without having the equipment to mix, bake, decorate, and eat all possible cakes.

We cannot have a coherent ontological theory that assumes something that can only exist as the result of some process and that same ontological theory prohibits the process from occurring.

or it could evolve only through topologies that were computable from one another?  Where does it say our universe must have all possible topologies?

   
    The alternative is to consider that the computation of the homomorphies is an ongoing process, not one that is "already existing in Platonia as a string of numbers" or anything equivalent. I would even say that time is the computation of the homomorphies. Time exists because everything cannot happen simultaneously.

    We must say that the universe has all possible topologies unless we can specify reasons why it does not.

I don't fee any compulsion to say that.  In any case, this universe does not have all possible topologies.  If you want to hypothesize a multiverse that includes universes with all possible topologies then there will be no *single* algorithm that can classify all of them.  But this is just the same as there is no algorithm which can tell you which of the UD programs will halt.

That is what goes into defining meaningfulness. When you define that X is Y, you are also defining all not-X to equal not-Y, no?

No. Unless your simply defining X to be identical with Y, a mere semantic renaming, then a definition is something like X:=Y|Zx.  And it is not the case that ~X=~Y.

When you start talking about a collection then you have to define what are its members. Absent the specification or ability to specify the members of a collection, what can you say of the collection?

This universe is defined ostensively.

Brent

    What is the a priori constraint on the Universe? Why this one and not some other? Is the limit of all computations not a computation? How did this happen?

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

--

[meekerdb]

On 5/20/2012 4:25 PM, Stephen P. King wrote:
> I need to add a remark here. We cannot just assume one particular 4-manifold as the
> one we exist on/in. We have to consider the entire ensemble of them to even ask coherent
> questions about the one we are in.

But we don't have to assume the ensemble has a single algorithm that will exhaustively
classify them. That would be like saying we can't investigate what programs exist without
first solving the halting problem - which we know to insoluble.

> Why do you think cosmologists are so busy looking at such things as the spectral
> distribution of the CMB and so forth? It is because those are clues as to the specific
> type of 4-manifold that we are on/in.

If we are in one specific one. So what?

> Additionally, when we try to model the cosmology setting of many observers and their
> observations we have to consider that each observer has a ensemble of possible of
> 4-manifolds that represent the universe that they observe.

So what? We don't have to suppose they classifiable by a single algorithm.

Brent

[Stephen P. King]

On 5/20/2012 8:08 PM, meekerdb wrote:

On 5/20/2012 4:13 PM, Stephen P. King wrote:

On 5/20/2012 4:39 PM, meekerdb wrote:

On 5/20/2012 1:31 PM, Stephen P. King wrote:

    My point is that for there to exist an a priori given string of numbers that is equivalent our universe there must exist a computation of the homomorphies between all possible 4-manifolds.

Why? 

Hi Brent,

    Because otherwise the amazing precision of the mathematical models based on the assumption of, among other things, that physical systems exist in space-time that is equivalent to a 4-manifold. The mathematical reasoning involved is much like a huge Jenga tower; pull the wrong piece out and it collapses.

Markov theorem tells us that no such homomorphy exists,

No, it tells there is no algorithm for deciding such homomorphy *that works for all possible 4-manifolds*.  If our universe-now has a particular topology and our universe-next has a particular topology, there in nothing in Markov's theorem that says that an algorithm can't determine that.  It just says that same algorithm can't work for *every pair*.

    I agree with your point that Markov's theorem does not disallow the existence of some particular algorithm that can compute the relation between some particular pair of 4-manifolds. Please understand that this moves us out of considering universal algorithms and into specific algorithms. This difference is very important. It is the difference between the class of universal algorithms and a particular algorithm that is the computation of some particular function. The non-existence of the general algorithm implies the non-existence of an a priori structure of relations between the possible 4-manifolds.
    I am making an ontological argument against the idea that there exists an a priori given structure that *is* the computation of the Universe. This is my argument against Platonism.

therefore our universe cannot be considered to be the result of a computation in the Turing universal sense.

Sure it can.  Even if your interpretation of Markov's theorem were correct our universe could, for example, always have the same topology,

    No, it cannot. If there does not exist a general algorithm that can compute the homomorphy relations between all 4-manifolds then what is the result of such cannot exit either.

The result is an exhaustive classification of compact 4-mainifolds.  The absence of such a classification neither prevents nor entails the existence of the manifolds. 

 But you fail to see that without the means to define the manifolds, there is nothing to distinguish a manifold from a fruitloop from a pink unicorn from a ..... Absent the means to distinguish properties there is no such thing as definite properties.

We cannot talk coherently within computational methods about "a topology" when such cannot be specified in advance. Algorithms are recursively enumerable functions. That means that you must specify their code in advance, otherwise your are not really talking about computations; you are talking about some imaginary things created by imaginary entities in imaginary places that do imaginary acts; hence my previous references to Pink Unicorns.

    Let me put this in other words. If you cannot build the equipment needed to mix, bake and decorate the cake then you cannot eat it.

You can have the equipment mix, bake, decorate and eat a cake without having the equipment to mix, bake, decorate, and eat all possible cakes.

   My analogy failed to demonstrate its intended idea, it seems. Let me rephrase. Do cakes exist as cakes if it is impossible to mix, bake and decorate them? Do they just magically appear out of nothing? No. Neither does meaningfulness and the definiteness of properties.

We cannot have a coherent ontological theory that assumes something that can only exist as the result of some process and that same ontological theory prohibits the process from occurring.

or it could evolve only through topologies that were computable from one another?  Where does it say our universe must have all possible topologies?

   
    The alternative is to consider that the computation of the homomorphies is an ongoing process, not one that is "already existing in Platonia as a string of numbers" or anything equivalent. I would even say that time is the computation of the homomorphies. Time exists because everything cannot happen simultaneously.

    We must say that the universe has all possible topologies unless we can specify reasons why it does not.

I don't fee any compulsion to say that.  In any case, this universe does not have all possible topologies.

 Why do not see that as surprising? We experience one particular universe, having one particular set of properties. How does this happen? What picked it out of the hat?

If you want to hypothesize a multiverse that includes universes with all possible topologies then there will be no *single* algorithm that can classify all of them.  But this is just the same as there is no algorithm which can tell you which of the UD programs will halt.

    Indeed! It is exactly the same! The point is that since there is nothing that can computationally "pick the winner out of the hat" then how is it that we experience precisely that winner? Maybe the selection process is not a computation in the Platonic sense at all. Maybe it is a real computation running on all possible physical systems in all possible universes for all time.

    I am trying to get you to see the difference between structures that are assumed to exist by fiat and structures that are the result of ongoing processes. This is debate that has been going on since Democritus and Heraclitus stepped into the Academy. Can you guess what ontology I am championing?

That is what goes into defining meaningfulness. When you define that X is Y, you are also defining all not-X to equal not-Y, no?

No. Unless your simply defining X to be identical with Y, a mere semantic renaming, then a definition is something like X:=Y|Zx.  And it is not the case that ~X=~Y.

    OK.

When you start talking about a collection then you have to define what are its members. Absent the specification or ability to specify the members of a collection, what can you say of the collection?

This universe is defined ostensively.

    Interesting word: Ostensively.

    "Represented or appearing as such..." It implies a subject to whom the representations or appearances have meaningful content. Who plays that role in your thinking?

Brent

    What is the a priori constraint on the Universe? Why this one and not some other? Is the limit of all computations not a computation? How did this happen?

    No attempts to even comment on these?

[meekerdb]

On 5/20/2012 6:53 PM, Stephen P. King wrote:

On 5/20/2012 8:08 PM, meekerdb wrote:

On 5/20/2012 4:13 PM, Stephen P. King wrote:

On 5/20/2012 4:39 PM, meekerdb wrote:

On 5/20/2012 1:31 PM, Stephen P. King wrote:

    My point is that for there to exist an a priori given string of numbers that is equivalent our universe there must exist a computation of the homomorphies between all possible 4-manifolds.

Why? 

Hi Brent,

    Because otherwise the amazing precision of the mathematical models based on the assumption of, among other things, that physical systems exist in space-time that is equivalent to a 4-manifold. The mathematical reasoning involved is much like a huge Jenga tower; pull the wrong piece out and it collapses.

Markov theorem tells us that no such homomorphy exists,

No, it tells there is no algorithm for deciding such homomorphy *that works for all possible 4-manifolds*.  If our universe-now has a particular topology and our universe-next has a particular topology, there in nothing in Markov's theorem that says that an algorithm can't determine that.  It just says that same algorithm can't work for *every pair*.

    I agree with your point that Markov's theorem does not disallow the existence of some particular algorithm that can compute the relation between some particular pair of 4-manifolds. Please understand that this moves us out of considering universal algorithms and into specific algorithms. This difference is very important. It is the difference between the class of universal algorithms and a particular algorithm that is the computation of some particular function. The non-existence of the general algorithm implies the non-existence of an a priori structure of relations between the possible 4-manifolds.
    I am making an ontological argument against the idea that there exists an a priori given structure that *is* the computation of the Universe. This is my argument against Platonism.

therefore our universe cannot be considered to be the result of a computation in the Turing universal sense.

Sure it can.  Even if your interpretation of Markov's theorem were correct our universe could, for example, always have the same topology,

    No, it cannot. If there does not exist a general algorithm that can compute the homomorphy relations between all 4-manifolds then what is the result of such cannot exit either.

The result is an exhaustive classification of compact 4-mainifolds.  The absence of such a classification neither prevents nor entails the existence of the manifolds. 

 But you fail to see that without the means to define the manifolds, there is nothing to distinguish a manifold from a fruitloop from a pink unicorn from a ..... Absent the means to distinguish properties there is no such thing as definite properties.

We cannot talk coherently within computational methods about "a topology" when such cannot be specified in advance. Algorithms are recursively enumerable functions. That means that you must specify their code in advance, otherwise your are not really talking about computations; you are talking about some imaginary things created by imaginary entities in imaginary places that do imaginary acts; hence my previous references to Pink Unicorns.

    Let me put this in other words. If you cannot build the equipment needed to mix, bake and decorate the cake then you cannot eat it.

You can have the equipment mix, bake, decorate and eat a cake without having the equipment to mix, bake, decorate, and eat all possible cakes.

   My analogy failed to demonstrate its intended idea, it seems. Let me rephrase. Do cakes exist as cakes if it is impossible to mix, bake and decorate them? Do they just magically appear out of nothing? No. Neither does meaningfulness and the definiteness of properties.

Because I can bake a cake, does it follow that all possible cakes exist?

We cannot have a coherent ontological theory that assumes something that can only exist as the result of some process and that same ontological theory prohibits the process from occurring.

or it could evolve only through topologies that were computable from one another?  Where does it say our universe must have all possible topologies?

   
    The alternative is to consider that the computation of the homomorphies is an ongoing process, not one that is "already existing in Platonia as a string of numbers" or anything equivalent. I would even say that time is the computation of the homomorphies. Time exists because everything cannot happen simultaneously.

    We must say that the universe has all possible topologies unless we can specify reasons why it does not.

I don't fee any compulsion to say that.  In any case, this universe does not have all possible topologies.

 Why do not see that as surprising? We experience one particular universe, having one particular set of properties. How does this happen? What picked it out of the hat?

If you want to hypothesize a multiverse that includes universes with all possible topologies then there will be no *single* algorithm that can classify all of them.  But this is just the same as there is no algorithm which can tell you which of the UD programs will halt.

    Indeed! It is exactly the same! The point is that since there is nothing that can computationally "pick the winner out of the hat" then how is it that we experience precisely that winner? Maybe the selection process is not a computation in the Platonic sense at all. Maybe it is a real computation running on all possible physical systems in all possible universes for all time.

    I am trying to get you to see the difference between structures that are assumed to exist by fiat and structures that are the result of ongoing processes.

You mean like the integers, the multiverse, Turing machines,...?

This is debate that has been going on since Democritus and Heraclitus stepped into the Academy. Can you guess what ontology I am championing?

That is what goes into defining meaningfulness. When you define that X is Y, you are also defining all not-X to equal not-Y, no?

No. Unless your simply defining X to be identical with Y, a mere semantic renaming, then a definition is something like X:=Y|Zx.  And it is not the case that ~X=~Y.

    OK.

When you start talking about a collection then you have to define what are its members.

I'm not talking about a collection.  You're the one assuming that all 4-manifolds exist and that everything existing must be computed BY THE SAME ALGORITHM.  That's two more assumptions than I'm willing to make.

Absent the specification or ability to specify the members of a collection, what can you say of the collection?

This universe is defined ostensively.

    Interesting word: Ostensively.

    "Represented or appearing as such..." It implies a subject to whom the representations or appearances have meaningful content. Who plays that role in your thinking?

You do.  When I write "this" you know what I mean.

Brent

    What is the a priori constraint on the Universe? Why this one and not some other? Is the limit of all computations not a computation? How did this happen?

    No attempts to even comment on these?

As Mark Twain said, "I'm pleased to be able to answer all your questions directly.  I don't know."

Brent

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

--

[meekerdb]

On 5/20/2012 6:53 PM, Stephen P. King wrote:
>> The result is an exhaustive classification of compact 4-mainifolds. The absence of
>> such a classification neither prevents nor entails the existence of the manifolds.
>
> But you fail to see that without the means to define the manifolds, there is nothing to
> distinguish a manifold from a fruitloop from a pink unicorn from a ..... Absent the
> means to distinguish properties there is no such thing as definite properties.

But there are means to distinguish the properties and ways to define different 4-manifolds
and ways to determine whether two 4-manifolds are homeomorphic. If there weren't the
theorem would be uninteresting. What makes it interesting, just as it is interesting that
some programs compute a total function and some don't, it is interesting because there
exist enough different 4-manifolds so that it is impossible to have a single algorithm
classify them. You seem to be arguing that only a subset that can be calculated by some
single algorithm can exist?

Brent

[Stephen P. King]

On 5/20/2012 10:17 PM, meekerdb wrote:

On 5/20/2012 6:53 PM, Stephen P. King wrote:

On 5/20/2012 8:08 PM, meekerdb wrote:

On 5/20/2012 4:13 PM, Stephen P. King wrote:

On 5/20/2012 4:39 PM, meekerdb wrote:

On 5/20/2012 1:31 PM, Stephen P. King wrote:

    My point is that for there to exist an a priori given string of numbers that is equivalent our universe there must exist a computation of the homomorphies between all possible 4-manifolds.

Why? 

Hi Brent,

    Because otherwise the amazing precision of the mathematical models based on the assumption of, among other things, that physical systems exist in space-time that is equivalent to a 4-manifold. The mathematical reasoning involved is much like a huge Jenga tower; pull the wrong piece out and it collapses.

Markov theorem tells us that no such homomorphy exists,

No, it tells there is no algorithm for deciding such homomorphy *that works for all possible 4-manifolds*.  If our universe-now has a particular topology and our universe-next has a particular topology, there in nothing in Markov's theorem that says that an algorithm can't determine that.  It just says that same algorithm can't work for *every pair*.

    I agree with your point that Markov's theorem does not disallow the existence of some particular algorithm that can compute the relation between some particular pair of 4-manifolds. Please understand that this moves us out of considering universal algorithms and into specific algorithms. This difference is very important. It is the difference between the class of universal algorithms and a particular algorithm that is the computation of some particular function. The non-existence of the general algorithm implies the non-existence of an a priori structure of relations between the possible 4-manifolds.
    I am making an ontological argument against the idea that there exists an a priori given structure that *is* the computation of the Universe. This is my argument against Platonism.

therefore our universe cannot be considered to be the result of a computation in the Turing universal sense.

Sure it can.  Even if your interpretation of Markov's theorem were correct our universe could, for example, always have the same topology,

    No, it cannot. If there does not exist a general algorithm that can compute the homomorphy relations between all 4-manifolds then what is the result of such cannot exit either.

The result is an exhaustive classification of compact 4-mainifolds.  The absence of such a classification neither prevents nor entails the existence of the manifolds. 

 But you fail to see that without the means to define the manifolds, there is nothing to distinguish a manifold from a fruitloop from a pink unicorn from a ..... Absent the means to distinguish properties there is no such thing as definite properties.

We cannot talk coherently within computational methods about "a topology" when such cannot be specified in advance. Algorithms are recursively enumerable functions. That means that you must specify their code in advance, otherwise your are not really talking about computations; you are talking about some imaginary things created by imaginary entities in imaginary places that do imaginary acts; hence my previous references to Pink Unicorns.

    Let me put this in other words. If you cannot build the equipment needed to mix, bake and decorate the cake then you cannot eat it.

You can have the equipment mix, bake, decorate and eat a cake without having the equipment to mix, bake, decorate, and eat all possible cakes.

   My analogy failed to demonstrate its intended idea, it seems. Let me rephrase. Do cakes exist as cakes if it is impossible to mix, bake and decorate them? Do they just magically appear out of nothing? No. Neither does meaningfulness and the definiteness of properties.

Because I can bake a cake, does it follow that all possible cakes exist?

    Are you the only entity that exists? This is not about "you"per se, this is about the possibility and our discussion of ideas.

    The answer to your question is: Yes, because I can bake a cake, it follows that "all possible cakes" must exist. Why? Because if the statement "I can bake a cake" is true and I have not specified which cake I have baked, then it follows that I have possibly baked all possible cakes. Otherwise, one has to stipulate which of the many cakes one has baked to be able to claim that all possible cakes do not exist. You are treating the possibility of something the same as the actuality of something when they are not the same.

We cannot have a coherent ontological theory that assumes something that can only exist as the result of some process and that same ontological theory prohibits the process from occurring.

or it could evolve only through topologies that were computable from one another?  Where does it say our universe must have all possible topologies?

   
    The alternative is to consider that the computation of the homomorphies is an ongoing process, not one that is "already existing in Platonia as a string of numbers" or anything equivalent. I would even say that time is the computation of the homomorphies. Time exists because everything cannot happen simultaneously.

    We must say that the universe has all possible topologies unless we can specify reasons why it does not.

I don't fee any compulsion to say that.  In any case, this universe does not have all possible topologies.

 Why do not see that as surprising? We experience one particular universe, having one particular set of properties. How does this happen? What picked it out of the hat?

If you want to hypothesize a multiverse that includes universes with all possible topologies then there will be no *single* algorithm that can classify all of them.  But this is just the same as there is no algorithm which can tell you which of the UD programs will halt.

    Indeed! It is exactly the same! The point is that since there is nothing that can computationally "pick the winner out of the hat" then how is it that we experience precisely that winner? Maybe the selection process is not a computation in the Platonic sense at all. Maybe it is a real computation running on all possible physical systems in all possible universes for all time.

    I am trying to get you to see the difference between structures that are assumed to exist by fiat and structures that are the result of ongoing processes.

You mean like the integers, the multiverse, Turing machines,...?

    Yes. Are those entities that exist from the beginning (which is what ontological primitivity implies...) or are they aspects of the unfolding reality?

This is debate that has been going on since Democritus and Heraclitus stepped into the Academy. Can you guess what ontology I am championing?

That is what goes into defining meaningfulness. When you define that X is Y, you are also defining all not-X to equal not-Y, no?

No. Unless your simply defining X to be identical with Y, a mere semantic renaming, then a definition is something like X:=Y|Zx.  And it is not the case that ~X=~Y.

    OK.

When you start talking about a collection then you have to define what are its members.

I'm not talking about a collection.  You're the one assuming that all 4-manifolds exist and that everything existing must be computed BY THE SAME ALGORITHM.  That's two more assumptions than I'm willing to make.

    Is a universal algorithm capable of generating all possible outputs when feed all possible inputs? What exactly is an algorithm in your thinking?

Absent the specification or ability to specify the members of a collection, what can you say of the collection?

This universe is defined ostensively.

    Interesting word: Ostensively.

    "Represented or appearing as such..." It implies a subject to whom the representations or appearances have meaningful content. Who plays that role in your thinking?

You do.  When I write "this" you know what I mean.

    And are we alone in the universe? You seem to take for granted the existence of "others".

Brent

    What is the a priori constraint on the Universe? Why this one and not some other? Is the limit of all computations not a computation? How did this happen?

    No attempts to even comment on these?

As Mark Twain said, "I'm pleased to be able to answer all your questions directly.  I don't know."

Brent

    OK...

[Stephen P. King]

Sorry Brent,

You are not grasping what I am talking about.

[meekerdb]

I'm afraid you've caught the 'everything disease' - the inability to conceive anything but infinite, ill defined ensembles.

We cannot have a coherent ontological theory that assumes something that can only exist as the result of some process and that same ontological theory prohibits the process from occurring.

or it could evolve only through topologies that were computable from one another?  Where does it say our universe must have all possible topologies?

   
    The alternative is to consider that the computation of the homomorphies is an ongoing process, not one that is "already existing in Platonia as a string of numbers" or anything equivalent. I would even say that time is the computation of the homomorphies. Time exists because everything cannot happen simultaneously.

    We must say that the universe has all possible topologies unless we can specify reasons why it does not.

I don't fee any compulsion to say that.  In any case, this universe does not have all possible topologies.

 Why do not see that as surprising? We experience one particular universe, having one particular set of properties. How does this happen? What picked it out of the hat?

If you want to hypothesize a multiverse that includes universes with all possible topologies then there will be no *single* algorithm that can classify all of them.  But this is just the same as there is no algorithm which can tell you which of the UD programs will halt.

    Indeed! It is exactly the same! The point is that since there is nothing that can computationally "pick the winner out of the hat" then how is it that we experience precisely that winner? Maybe the selection process is not a computation in the Platonic sense at all. Maybe it is a real computation running on all possible physical systems in all possible universes for all time.

    I am trying to get you to see the difference between structures that are assumed to exist by fiat and structures that are the result of ongoing processes.

You mean like the integers, the multiverse, Turing machines,...?

    Yes. Are those entities that exist from the beginning (which is what ontological primitivity implies...) or are they aspects of the unfolding reality?

I think they are concepts we made up.  But you're the one claiming the universe (actually I think you mean the multiverse) is not computable and you think this is contrary to Bruno.  But Bruno's UD isn't a Turing machine and what it produces is not computable, if I understand him correctly.

This is debate that has been going on since Democritus and Heraclitus stepped into the Academy. Can you guess what ontology I am championing?

That is what goes into defining meaningfulness. When you define that X is Y, you are also defining all not-X to equal not-Y, no?

No. Unless your simply defining X to be identical with Y, a mere semantic renaming, then a definition is something like X:=Y|Zx.  And it is not the case that ~X=~Y.

    OK.

When you start talking about a collection then you have to define what are its members.

I'm not talking about a collection.  You're the one assuming that all 4-manifolds exist and that everything existing must be computed BY THE SAME ALGORITHM.  That's two more assumptions than I'm willing to make.

    Is a universal algorithm capable of generating all possible outputs when feed all possible inputs?

I dunno what "a universal algorithm" is.  What you describe however is easy to write:

x<-input
print x.

What exactly is an algorithm in your thinking?

An explicit sequence of instructions.

Absent the specification or ability to specify the members of a collection, what can you say of the collection?

This universe is defined ostensively.

    Interesting word: Ostensively.

    "Represented or appearing as such..." It implies a subject to whom the representations or appearances have meaningful content. Who plays that role in your thinking?

You do.  When I write "this" you know what I mean.

    And are we alone in the universe? You seem to take for granted the existence of "others".

I wouldn't say taken for granted.  I have some evidence.

Brent

Brent

    What is the a priori constraint on the Universe? Why this one and not some other? Is the limit of all computations not a computation? How did this happen?

    No attempts to even comment on these?

As Mark Twain said, "I'm pleased to be able to answer all your questions directly.  I don't know."

Brent

    OK...

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

--

[Quentin Anciaux]

2012/5/21 Stephen P. King <step...@charter.net>

No it's not a computation, it arises because at every step, computations diverge into new sets of infinite computations, giving rise to the 1p indeterminacy.

Quentin

 

How did this happen?

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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[Bruno Marchal]

On 20 May 2012, at 18:27, Stephen P. King wrote:

> On 5/20/2012 6:06 AM, Quentin Anciaux wrote:
>>
>>
>> In Bruno's theory, the physical world is not computed by an
>> algorithm, the physical world is the limit of all computations
>> going throught your current state... what is computable is your
>> current state, an infinity of computations goes through it. So I
>> don't see the problem here, the UD is not an algorithm which
>> computes the physical world 4D or whatever.
>>
>> Quentin
>>
> Hi Quentin,
>

> Maybe you can answer some questions. These might be badly
> composed so feel free to "fix" them. ;-)
>
> 1) If my "current state" is equivalent to a 4-manifold and the
> "next" state is also, what is connecting the two? Markov's proof
> tells us that it is not a algorithm. So what is it?

Markov theorem says that giving two arbitrary "states", it is
undecidable to know if a "computation" will relate those states or not.
It does not say that some states are not algorithmically linked.


With computer it is not in general possible to know in advance if
states are related by computations. If they are, this can be usually
decided, but if there are not , well there are no algorithm for
deciding that in general.

>
> 2) Is there another equivalent set of words for "the physical world
> is the limit of all computations going through your current state"?
>
> 3) Is there at least one physical system running the computations?
> Is the "physical universe" a purely subjective appearance/experience
> for each conscious entity? What is it that shifts from one state to
> the next?
>
> 4) What is the cardinality of "all computations"?

Aleph_0, when see in the third person picture.
2^aleph_0, when seen in the first person picture (well, the 3-view on
the 1-views, because it is 1, from the 1_view on the 1_view). In that
case, arbitrary sequence of natural numbers play the role of oracle.

>
> 5) Is the totality of what exists static and timeless and are all of
> the subsets of that totality static and timeless as well?

Yes, for the basic ontological reality. No, for the epistemological
reality.

>
> 6) Does all "succession of events" emerge only from the well
> ordering of Natural numbers?

Not for the physical events. (epistemological, with comp).

Bruno


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

[Bruno Marchal]

On 21 May 2012, at 07:31, meekerdb wrote:

On 5/20/2012 8:15 PM, Stephen P. King wrote:

    Yes. Are those entities that exist from the beginning (which is what ontological primitivity implies...) or are they aspects of the unfolding reality?

I think they are concepts we made up.  But you're the one claiming the universe (actually I think you mean the multiverse) is not computable and you think this is contrary to Bruno.  But Bruno's UD isn't a Turing machine and what it produces is not computable, if I understand him correctly.

?

The UD is a Turing machine. I gave the algorithm in LISP (and from this you can compile it into a Turing machine).

What it does is computable, in the 3-views, but not in the 1-view (which 'contains' consciousness and matter).

A simple pseudo code is

begin

For i, j, k, non negative integers

Compute phi_i(j) up to k steps

end

The relation 'phi_i(j) = r' is purely arithmetical.

The UD is just a cousin of the universal machine, forced to generate all what it can do. It has to dovetail for not being stuck in some infinite computations (which we cannot prevent in advance).

The existence of UMs and UDs are theorem of elementary arithmetic.

The UD gives the only one known effective notion of "everything".

This is debate that has been going on since Democritus and Heraclitus stepped into the Academy. Can you guess what ontology I am championing?

That is what goes into defining meaningfulness. When you define that X is Y, you are also defining all not-X to equal not-Y, no?

No. Unless your simply defining X to be identical with Y, a mere semantic renaming, then a definition is something like X:=Y|Zx.  And it is not the case that ~X=~Y.

    OK.

When you start talking about a collection then you have to define what are its members.

I'm not talking about a collection.  You're the one assuming that all 4-manifolds exist and that everything existing must be computed BY THE SAME ALGORITHM.  That's two more assumptions than I'm willing to make.

    Is a universal algorithm capable of generating all possible outputs when feed all possible inputs?

I dunno what "a universal algorithm" is.  What you describe however is easy to write:

x<-input
print x.

I think a better answer is a Universal Turing Machine, or universal computable function code. It is a number u such that phi_u(x, y) = phi_x(y).

This exist provably for all known and very different powerful enough 'programming language' (systems, numbers, programs, ...), and it exists absolutely, with Church thesis.

Bruno

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

[Bruno Marchal]

On 20 May 2012, at 21:06, meekerdb wrote:

On 5/20/2012 9:27 AM, Stephen P. King wrote:

On 5/20/2012 6:06 AM, Quentin Anciaux wrote:

In Bruno's theory, the physical world is not computed by an algorithm, the physical world is the limit of all computations going throught your current state... what is computable is your current state, an infinity of computations goes through it. So I don't see the problem here, the UD is not an algorithm which computes the physical world 4D or whatever.

Quentin

Hi Quentin,

    Maybe you can answer some questions. These might be badly composed so feel free to "fix" them. ;-)

1) If my "current state" is equivalent to a 4-manifold and the "next" state is also, what is connecting the two? Markov's proof tells us that it is not a algorithm. So what is it?

I don't think Markov's theorem tells you that.  It says there can be no algorithm that will determine the homomorphy of any two arbitrary compact 4-manifolds.  But there is nothing that says the next state can be any arbitrary 4-manifold.  In most theories it is an evolution of the Cauchy data on the present manifold, where 'present' is defined by some time slice.

2) Is there another equivalent set of words for "the physical world is the limit of all computations going through your current state"?

3) Is there at least one physical system running the computations? Is the "physical universe" a purely subjective appearance/experience for each conscious entity? What is it that shifts from one state to the next?

Well that's a crucial question.  Bruno assumes that truth implies existence. 

That makes no sense. Only truth of existential statement entails existence. "s(s(s(0))) is prime' entails "Ex x is prime"

So if 1+1=2 is true that implies that 1, +, =, and 2 exist. 

This is because we assume logic, and P(n) ===> ExP(x) is an inference rule in first order logic. And this works for 1 and 2, not for "+" and "=", which might exist for different reason, as well defined subsets of the models or as relation at the meta-level or through their Gödel numbers.

I think this is a doubtful proposition; particularly when talking about infinities.  Even if every number has a successor is true, what existence is implied?  Just the non-existence of a number with no successor.

4) What is the cardinality of "all computations"?

Aleph1.

From the 1-views (or from the 3-view of the many 1-views).

Bruno

5) Is the totality of what exists static and timeless and are all of the subsets of that totality static and timeless as well?

6) Does all "succession of events" emerge only from the well ordering of Natural numbers?

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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

[Russell Standish]

On Sun, May 20, 2012 at 12:06:05PM -0700, meekerdb wrote:
> On 5/20/2012 9:27 AM, Stephen P. King wrote:
> >
> >4) What is the cardinality of "all computations"?
>
> Aleph1.
>

Actually, it is aleph_0. The set of all computations is
countable. OTOH, the set of all experiences (under COMP) is uncountable
(2^\aleph_0 in fact), which only equals \aleph_1 if the continuity
hypothesis holds.

This is the origin of Bruno's claim that COMP entails that physics is
not computable, a corrolory of which is that Digital Physics is
refuted (since DP=>COMP).

--

----------------------------------------------------------------------------
Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics hpc...@hpcoders.com.au
University of New South Wales http://www.hpcoders.com.au
----------------------------------------------------------------------------

[Stephen P. King]

On 5/21/2012 12:33 AM, Russell Standish wrote:
> On Sun, May 20, 2012 at 12:06:05PM -0700, meekerdb wrote:
>> On 5/20/2012 9:27 AM, Stephen P. King wrote:
>>> 4) What is the cardinality of "all computations"?
>> Aleph1.
>>
> Actually, it is aleph_0. The set of all computations is
> countable. OTOH, the set of all experiences (under COMP) is uncountable
> (2^\aleph_0 in fact), which only equals \aleph_1 if the continuity
> hypothesis holds.

Hi Russell,

Interesting. Do you have any thoughts on what would follow from not
holding the continuity (Cantor's continuum?) hypothesis?

>
> This is the origin of Bruno's claim that COMP entails that physics is
> not computable, a corrolory of which is that Digital Physics is
> refuted (since DP=>COMP).
>

Does the symbol "=>" mean "implies"? I get confused ...

[Stephen P. King]

On 5/21/2012 1:55 AM, Quentin Anciaux wrote:
> No it's not a computation, it arises because at every step,
> computations diverge into new sets of infinite computations, giving
> rise to the 1p indeterminacy.
>
> Quentin
>

Hi Quentin,

So could we agree that the idea that the universe is
defined/determined ab initio ("in the beginning") is refuted by this?

[Quentin Anciaux]

2012/5/21 Stephen P. King <step...@charter.net>

On 5/21/2012 1:55 AM, Quentin Anciaux wrote:

No it's not a computation, it arises because at every step, computations diverge into new sets of infinite computations, giving rise to the 1p indeterminacy.

Quentin

 Hi Quentin,

   So could we agree that the idea that the universe is defined/determined ab initio ("in the beginning") is refuted by this?

I don't know what you mean here... but in comp the universe per se does not exist, it emerges from computations and is not an object by itself (independent of computations).
 
Quentin

--
Onward!

Stephen

"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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[Stephen P. King]

On 5/21/2012 7:54 AM, Quentin Anciaux wrote:

2012/5/21 Stephen P. King <step...@charter.net>

On 5/21/2012 1:55 AM, Quentin Anciaux wrote:

No it's not a computation, it arises because at every step, computations diverge into new sets of infinite computations, giving rise to the 1p indeterminacy.

Quentin

 Hi Quentin,

   So could we agree that the idea that the universe is defined/determined ab initio ("in the beginning") is refuted by this?

I don't know what you mean here... but in comp the universe per se does not exist, it emerges from computations and is not an object by itself (independent of computations).
 
Quentin

Hi Quentin,

    OK, you are equating "universe" with "physical universe"? Are you considering "computations" to be ontologically primitive? It feels like I am starting to explain myself all over again. That's OK, but just a bit frustrating.

[meekerdb]

On 5/20/2012 9:33 PM, Russell Standish wrote:
> On Sun, May 20, 2012 at 12:06:05PM -0700, meekerdb wrote:
>> On 5/20/2012 9:27 AM, Stephen P. King wrote:
>>> 4) What is the cardinality of "all computations"?
>> Aleph1.
>>
> Actually, it is aleph_0.

I see that the set of all programs is countable.

> The set of all computations is
> countable. OTOH, the set of all experiences (under COMP) is uncountable
> (2^\aleph_0 in fact), which only equals \aleph_1 if the continuity
> hypothesis holds.

Ok, I was thinking that because the outputs of infinitely many programs were infinite
there would be 2^\aleph_0, but I see that's a mistake.

Brent

[Stephen P. King]

On 5/21/2012 7:54 AM, Quentin Anciaux wrote:

2012/5/21 Stephen P. King <step...@charter.net>

On 5/21/2012 1:55 AM, Quentin Anciaux wrote:

No it's not a computation, it arises because at every step, computations diverge into new sets of infinite computations, giving rise to the 1p indeterminacy.

Quentin

 Hi Quentin,

   So could we agree that the idea that the universe is defined/determined ab initio ("in the beginning") is refuted by this?

I don't know what you mean here... but in comp the universe per se does not exist, it emerges from computations and is not an object by itself (independent of computations).
 

Dear Quentin,

    My interest is philosophy so I am asking questions in an attempt to learn about peoples ideas. Now I am learning about yours. Your sentence here implies to me that only "objects" (considered as capable of being separate and isolated from all others) can "exist". Only "objects" exist and not, for example, processes. Is this correct?

[Quentin Anciaux]

2012/5/21 Stephen P. King <step...@charter.net>

On 5/21/2012 7:54 AM, Quentin Anciaux wrote:

2012/5/21 Stephen P. King <step...@charter.net>

On 5/21/2012 1:55 AM, Quentin Anciaux wrote:

No it's not a computation, it arises because at every step, computations diverge into new sets of infinite computations, giving rise to the 1p indeterminacy.

Quentin

 Hi Quentin,

   So could we agree that the idea that the universe is defined/determined ab initio ("in the beginning") is refuted by this?

I don't know what you mean here... but in comp the universe per se does not exist, it emerges from computations and is not an object by itself (independent of computations).
 

Dear Quentin,

    My interest is philosophy so I am asking questions in an attempt to learn about peoples ideas. Now I am learning about yours. Your sentence here implies to me that only "objects" (considered as capable of being separate and isolated from all others) can "exist". Only "objects" exist and not, for example, processes. Is this correct?

No, it depends what you mean by existing. When I say "in comp the universe per se does not exist", I mean it does not exist ontologically as it emerge from computations. Existence means different thing at different level.

Does a table exist ? It depends at which level you describe it.

I still don't understand what you mean by "the idea that the universe is defined/determined ab initio ("in the beginning") is refuted by this".

Regards,
Quentin
 

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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[meekerdb]

On 5/21/2012 12:51 AM, Bruno Marchal wrote:

On 21 May 2012, at 07:31, meekerdb wrote:

On 5/20/2012 8:15 PM, Stephen P. King wrote:

    Yes. Are those entities that exist from the beginning (which is what ontological primitivity implies...) or are they aspects of the unfolding reality?

I think they are concepts we made up.  But you're the one claiming the universe (actually I think you mean the multiverse) is not computable and you think this is contrary to Bruno.  But Bruno's UD isn't a Turing machine and what it produces is not computable, if I understand him correctly.

?

The UD is a Turing machine. I gave the algorithm in LISP (and from this you can compile it into a Turing machine).

What it does is computable, in the 3-views, but not in the 1-view (which 'contains' consciousness and matter).

A simple pseudo code is

begin

For i, j, k, non negative integers

Compute phi_i(j) up to k steps

end

The relation 'phi_i(j) = r' is purely arithmetical.

The UD is just a cousin of the universal machine, forced to generate all what it can do. It has to dovetail for not being stuck in some infinite computations (which we cannot prevent in advance).

The existence of UMs and UDs are theorem of elementary arithmetic.

The UD gives the only one known effective notion of "everything".

Ok, I stand corrected.

Then what is the relation to the problem Stephen poses.  Can the UD compute the topology of all possible 4-manifolds - it seems it can since they correspond to Turing machine computations.  So does Markov's theorem just correspond to the fact that there is no general algortihm to determine whether to Turing machines compute the same function?

Brent

[Russell Standish]

On Mon, May 21, 2012 at 07:42:01AM -0400, Stephen P. King wrote:
> On 5/21/2012 12:33 AM, Russell Standish wrote:
> >On Sun, May 20, 2012 at 12:06:05PM -0700, meekerdb wrote:
> >>On 5/20/2012 9:27 AM, Stephen P. King wrote:
> >>>4) What is the cardinality of "all computations"?
> >>Aleph1.
> >>
> >Actually, it is aleph_0. The set of all computations is
> >countable. OTOH, the set of all experiences (under COMP) is uncountable
> >(2^\aleph_0 in fact), which only equals \aleph_1 if the continuity
> >hypothesis holds.
>
> Hi Russell,
>
> Interesting. Do you have any thoughts on what would follow from
> not holding the continuity (Cantor's continuum?) hypothesis?
>

No - its not my field. My understanding is that the CH has bugger all
impact on quotidian mathematics - the stuff physicists use,
basically. But it has a profound effect on the properties of
transfinite sets. And nobody can decide whether CH should be true or
false (both possibilities produce consistent results).

Its one reason why Bruno would like to restrict ontology to machines,
or at most integers - echoing Kronecker's quotable "God made the
integers, all else is the work of man".

> >
> >This is the origin of Bruno's claim that COMP entails that physics is
> >not computable, a corrolory of which is that Digital Physics is
> >refuted (since DP=>COMP).
> >
> Does the symbol "=>" mean "implies"? I get confused ...
>

Yes, that is the usual meaning. It can also be written (DP or not COMP).

Of course in Fortran, it means something entirely different: it
renames a type, much like the typedef statement of C. Sorry, that was
a digression.

> --
> Onward!
>
> Stephen
>
> "Nature, to be commanded, must be obeyed."
> ~ Francis Bacon
>
>

> --
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> To post to this group, send email to everyth...@googlegroups.com.
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[Stephen P. King]

On 5/21/2012 3:49 PM, Quentin Anciaux wrote:

2012/5/21 Stephen P. King <step...@charter.net>

On 5/21/2012 7:54 AM, Quentin Anciaux wrote:

2012/5/21 Stephen P. King <step...@charter.net>

On 5/21/2012 1:55 AM, Quentin Anciaux wrote:

No it's not a computation, it arises because at every step, computations diverge into new sets of infinite computations, giving rise to the 1p indeterminacy.

Quentin

 Hi Quentin,

   So could we agree that the idea that the universe is defined/determined ab initio ("in the beginning") is refuted by this?

I don't know what you mean here... but in comp the universe per se does not exist, it emerges from computations and is not an object by itself (independent of computations).
 

Dear Quentin,

    My interest is philosophy so I am asking questions in an attempt to learn about peoples ideas. Now I am learning about yours. Your sentence here implies to me that only "objects" (considered as capable of being separate and isolated from all others) can "exist". Only "objects" exist and not, for example, processes. Is this correct?

No, it depends what you mean by existing. When I say "in comp the universe per se does not exist", I mean it does not exist ontologically as it emerge from computations. Existence means different thing at different level.

Does a table exist ? It depends at which level you describe it.

Dear Quentin,

    I am trying to understand exactly how you think and define words.

    By "exist" are you considering capacity of the referent of a word, say table, of being actually experiencing by anyone that might happen to be in its vecinity or otherwise capable of being causally affected by the presence and non-presence of the table?

I still don't understand what you mean by "the idea that the universe is defined/determined ab initio ("in the beginning") is refuted by this".

Regards,
Quentin

    Don't worry about that for now. Let us nail down what "existence" is first.

[Quentin Anciaux]

2012/5/22 Stephen P. King <step...@charter.net>

On 5/21/2012 3:49 PM, Quentin Anciaux wrote:

2012/5/21 Stephen P. King <step...@charter.net>

On 5/21/2012 7:54 AM, Quentin Anciaux wrote:

2012/5/21 Stephen P. King <step...@charter.net>

On 5/21/2012 1:55 AM, Quentin Anciaux wrote:

No it's not a computation, it arises because at every step, computations diverge into new sets of infinite computations, giving rise to the 1p indeterminacy.

Quentin

 Hi Quentin,

   So could we agree that the idea that the universe is defined/determined ab initio ("in the beginning") is refuted by this?

I don't know what you mean here... but in comp the universe per se does not exist, it emerges from computations and is not an object by itself (independent of computations).
 

Dear Quentin,

    My interest is philosophy so I am asking questions in an attempt to learn about peoples ideas. Now I am learning about yours. Your sentence here implies to me that only "objects" (considered as capable of being separate and isolated from all others) can "exist". Only "objects" exist and not, for example, processes. Is this correct?

No, it depends what you mean by existing. When I say "in comp the universe per se does not exist", I mean it does not exist ontologically as it emerge from computations. Existence means different thing at different level.

Does a table exist ? It depends at which level you describe it.

Dear Quentin,

    I am trying to understand exactly how you think and define words.

    By "exist"

Existence is dependent on the level of description, and can be seperated by what exists ontologically and what exists epistemologically. So it depends on the theory you use to define existence.

I would favor a theory which would define existence by what can be experienced/observed. Maybe it's a lack of imagination, but I don't know what it would mean for a thing to exist and never be observed/experienced.
 

are you considering capacity of the referent of a word, say table, of being actually experiencing by anyone that might happen to be in its vecinity or otherwise capable of being causally affected by the presence and non-presence of the table?

I still don't understand what you mean by "the idea that the universe is defined/determined ab initio ("in the beginning") is refuted by this".

Regards,
Quentin

    Don't worry about that for now. Let us nail down what "existence" is first.

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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[meekerdb]

On 5/21/2012 10:56 PM, Quentin Anciaux wrote:

2012/5/22 Stephen P. King <step...@charter.net>

On 5/21/2012 3:49 PM, Quentin Anciaux wrote:

2012/5/21 Stephen P. King <step...@charter.net>

On 5/21/2012 7:54 AM, Quentin Anciaux wrote:

2012/5/21 Stephen P. King <step...@charter.net>

On 5/21/2012 1:55 AM, Quentin Anciaux wrote:

No it's not a computation, it arises because at every step, computations diverge into new sets of infinite computations, giving rise to the 1p indeterminacy.

Quentin

 Hi Quentin,

   So could we agree that the idea that the universe is defined/determined ab initio ("in the beginning") is refuted by this?

I don't know what you mean here... but in comp the universe per se does not exist, it emerges from computations and is not an object by itself (independent of computations).
 

Dear Quentin,

    My interest is philosophy so I am asking questions in an attempt to learn about peoples ideas. Now I am learning about yours. Your sentence here implies to me that only "objects" (considered as capable of being separate and isolated from all others) can "exist". Only "objects" exist and not, for example, processes. Is this correct?

No, it depends what you mean by existing. When I say "in comp the universe per se does not exist", I mean it does not exist ontologically as it emerge from computations. Existence means different thing at different level.

Does a table exist ? It depends at which level you describe it.

Dear Quentin,

    I am trying to understand exactly how you think and define words.

    By "exist"

Existence is dependent on the level of description, and can be seperated by what exists ontologically and what exists epistemologically. So it depends on the theory you use to define existence.

I would favor a theory which would define existence by what can be experienced/observed. Maybe it's a lack of imagination, but I don't know what it would mean for a thing to exist and never be observed/experienced.

You're not likely to experience a quark or even an atom.  What exists is determined by your model of the world.  Even parts of the model that make no possible difference to the experiences the model predicts may be kept because they make the theory simpler, e.g. infinitesimal distances in physics.

Brent

[Quentin Anciaux]

2012/5/22 meekerdb <meek...@verizon.net>

On 5/21/2012 10:56 PM, Quentin Anciaux wrote:

2012/5/22 Stephen P. King <step...@charter.net>

On 5/21/2012 3:49 PM, Quentin Anciaux wrote:

2012/5/21 Stephen P. King <step...@charter.net>

On 5/21/2012 7:54 AM, Quentin Anciaux wrote:

2012/5/21 Stephen P. King <step...@charter.net>

On 5/21/2012 1:55 AM, Quentin Anciaux wrote:

No it's not a computation, it arises because at every step, computations diverge into new sets of infinite computations, giving rise to the 1p indeterminacy.

Quentin

 Hi Quentin,

   So could we agree that the idea that the universe is defined/determined ab initio ("in the beginning") is refuted by this?

I don't know what you mean here... but in comp the universe per se does not exist, it emerges from computations and is not an object by itself (independent of computations).
 

Dear Quentin,

    My interest is philosophy so I am asking questions in an attempt to learn about peoples ideas. Now I am learning about yours. Your sentence here implies to me that only "objects" (considered as capable of being separate and isolated from all others) can "exist". Only "objects" exist and not, for example, processes. Is this correct?

No, it depends what you mean by existing. When I say "in comp the universe per se does not exist", I mean it does not exist ontologically as it emerge from computations. Existence means different thing at different level.

Does a table exist ? It depends at which level you describe it.

Dear Quentin,

    I am trying to understand exactly how you think and define words.

    By "exist"

Existence is dependent on the level of description, and can be seperated by what exists ontologically and what exists epistemologically. So it depends on the theory you use to define existence.

I would favor a theory which would define existence by what can be experienced/observed. Maybe it's a lack of imagination, but I don't know what it would mean for a thing to exist and never be observed/experienced.

You're not likely to experience a quark or even an atom.

Well I didn't say *I*... observer != human. It's something that can interact (with the rest of the world)... And also I agree that what *I* think exists is determined by the model of the world I use... but what really exists doesn't care about what I think or the model I have ;)

Quentin
 

[Stephen P. King]

On 5/21/2012 6:26 PM, Russell Standish wrote:

On Mon, May 21, 2012 at 07:42:01AM -0400, Stephen P. King wrote:

On 5/21/2012 12:33 AM, Russell Standish wrote:

On Sun, May 20, 2012 at 12:06:05PM -0700, meekerdb wrote:

On 5/20/2012 9:27 AM, Stephen P. King wrote:

4) What is the cardinality of "all computations"?

Aleph1.

Actually, it is aleph_0. The set of all computations is
countable. OTOH, the set of all experiences (under COMP) is uncountable
(2^\aleph_0 in fact), which only equals \aleph_1 if the continuity
hypothesis holds.

Hi Russell,

    Interesting. Do you have any thoughts on what would follow from
not holding the continuity (Cantor's continuum?) hypothesis?

No - its not my field. My understanding is that the CH has bugger all
impact on quotidian mathematics - the stuff physicists use,
basically. But it has a profound effect on the properties of
transfinite sets. And nobody can decide whether CH should be true or
false (both possibilities produce consistent results).

Hi Russell,

    I once thought that consistency, in mathematics, was the indication of existence but situations like this make that idea a point of contention... CH and AoC are two axioms associated with ZF set theory that have lead some people (including me) to consider a wider interpretation of mathematics. What if all possible consistent mathematical theories must somehow exist?

Its one reason why Bruno would like to restrict ontology to machines,
or at most integers - echoing Kronecker's quotable "God made the
integers, all else is the work of man".

    I understand that, but this choice to restrict makes Bruno's Idealism even more perplexing to me; how is it that the Integers are given such special status, especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world? Without the physical world to act as a "selection" mechanism for what is "Real", why the bias for integers? This has been a question that I have tried to get answered to no avail.

This is the origin of Bruno's claim that COMP entails that physics is
not computable, a corrolory of which is that Digital Physics is
refuted (since DP=>COMP).

    Does the symbol "=>" mean "implies"? I get confused ...

Yes, that is the usual meaning. It can also be written (DP or not COMP).

    "=>" = "or not"

    I am still trying to comprehent that equivalence! BTW, I was reading a related Wiki article and found the sentence "the truth of "A implies B" the truth of "Not-B implies not-A"". That looks familiar... Didn't I write something like that to Quentin and was rebuffed... I wrote it incorrectly it appears...

Of course in Fortran, it means something entirely different: it
renames a type, much like the typedef statement of C. Sorry, that was
a digression.

    That's OK. ;-) I suppose that it is a blessing to be able to "think in code". ;-)

[Stephen P. King]

Hi!

    What about the existence of numbers? How exactly does interaction between numbers and observers (per Quentin's definition) occur such that we can make claims as to their existence? (Assuming the postulations of Arithmetic Realism.)

[Joseph Knight]

On Tue, May 22, 2012 at 7:36 AM, Stephen P. King <step...@charter.net> wrote:

On 5/21/2012 6:26 PM, Russell Standish wrote:

On Mon, May 21, 2012 at 07:42:01AM -0400, Stephen P. King wrote:

On 5/21/2012 12:33 AM, Russell Standish wrote:

On Sun, May 20, 2012 at 12:06:05PM -0700, meekerdb wrote:

On 5/20/2012 9:27 AM, Stephen P. King wrote:

4) What is the cardinality of "all computations"?

Aleph1.

Actually, it is aleph_0. The set of all computations is
countable. OTOH, the set of all experiences (under COMP) is uncountable
(2^\aleph_0 in fact), which only equals \aleph_1 if the continuity
hypothesis holds.

Hi Russell,

    Interesting. Do you have any thoughts on what would follow from
not holding the continuity (Cantor's continuum?) hypothesis?

No - its not my field. My understanding is that the CH has bugger all
impact on quotidian mathematics - the stuff physicists use,
basically. But it has a profound effect on the properties of
transfinite sets. And nobody can decide whether CH should be true or
false (both possibilities produce consistent results).

Hi Russell,

    I once thought that consistency, in mathematics, was the indication of existence but situations like this make that idea a point of contention... CH and AoC are two axioms associated with ZF set theory that have lead some people (including me) to consider a wider interpretation of mathematics. What if all possible consistent mathematical theories must somehow exist?

Joel David Hamkins introduced the "set-theoretic multiverse" idea (link). The abstract reads: 

"The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous diversity of set-theoretic possibilities, a phenomenon that challenges the universe view. In particular, I argue that the continuum hypothesis is settled on the multiverse view by our extensive knowledge about how it behaves in the multiverse, and as a result it can no longer be settled in the manner formerly hoped for."

 

Its one reason why Bruno would like to restrict ontology to machines,
or at most integers - echoing Kronecker's quotable "God made the
integers, all else is the work of man".

    I understand that, but this choice to restrict makes Bruno's Idealism even more perplexing to me; how is it that the Integers are given such special status, especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world? Without the physical world to act as a "selection" mechanism for what is "Real", why the bias for integers? This has been a question that I have tried to get answered to no avail.

I think Bruno gives such high status to the natural numbers because they are perhaps the least-doubt-able mathematical entities there are. The very fact that talks of a "set-theoretic multiverse" exist makes one ask, how real are sets? Do set theories tell us more about our minds than they do about the mathematical world? (Obviously, as David Lewis pointed out, you need something like a set theory in order to do mathematics at all, and as Russell says, for the average mathematician it really doesn't matter.)

Also: No one here has questioned the reality of the physical world. Should I append this statement to every email until you stop countering it?

 

This is the origin of Bruno's claim that COMP entails that physics is
not computable, a corrolory of which is that Digital Physics is
refuted (since DP=>COMP).

    Does the symbol "=>" mean "implies"? I get confused ...

Yes, that is the usual meaning. It can also be written (DP or not COMP).

    "=>" = "or not"]

Actually "a implies b" is defined as "not a or b". 

 

    I am still trying to comprehent that equivalence! BTW, I was reading a related Wiki article and found the sentence "the truth of "A implies B" the truth of "Not-B implies not-A"". That looks familiar... Didn't I write something like that to Quentin and was rebuffed... I wrote it incorrectly it appears...

Of course in Fortran, it means something entirely different: it
renames a type, much like the typedef statement of C. Sorry, that was
a digression.

    That's OK. ;-) I suppose that it is a blessing to be able to "think in code". ;-)

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

--

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Joseph Knight

[Bruno Marchal]

It is not idealism. It is neutral monism. Idealism would makes mind or ideas primitive, which is not the case.

even more perplexing to me; how is it that the Integers are given such special status,

Because of "digital" in digital mechanism. It is not so much an emphasis on numbers, than on finite. 

especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world?

Not at all. Only "primitively physical" reality is put in doubt. 

Without the physical world to act as a "selection" mechanism for what is "Real",

This contradicts your neutral monism.

why the bias for integers?

Because comp = machine, and machine are supposed to be of the type "finitely describable".

This has been a question that I have tried to get answered to no avail.

You don't listen. This has been repeated very often. When you say "yes" to the doctor, you accept that you survive with a computer executing a code. A code is mainly a natural number, up to computable isomorphism. Comp refers to computer science, which study the computable function, which can always be recasted in term of computable function from N to N.

And there are no other theory of computability, on reals or whatever, or if you prefer, there are too many, without any Church thesis or genuine universality notion. (Cf Pour-Hel, Blum Shub and Smale, etc.)

Bruno

This is the origin of Bruno's claim that COMP entails that physics is
not computable, a corrolory of which is that Digital Physics is
refuted (since DP=>COMP).

    Does the symbol "=>" mean "implies"? I get confused ...

Yes, that is the usual meaning. It can also be written (DP or not COMP).

    "=>" = "or not"

    I am still trying to comprehent that equivalence! BTW, I was reading a related Wiki article and found the sentence "the truth of "A implies B" the truth of "Not-B implies not-A"". That looks familiar... Didn't I write something like that to Quentin and was rebuffed... I wrote it incorrectly it appears...

Of course in Fortran, it means something entirely different: it
renames a type, much like the typedef statement of C. Sorry, that was
a digression.

    That's OK. ;-) I suppose that it is a blessing to be able to "think in code". ;-)

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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

[Stephen P. King]

On 5/22/2012 10:56 AM, Joseph Knight wrote:

On Tue, May 22, 2012 at 7:36 AM, Stephen P. King <step...@charter.net> wrote:

On 5/21/2012 6:26 PM, Russell Standish wrote:

snip

Hi Russell,

    I once thought that consistency, in mathematics, was the indication of existence but situations like this make that idea a point of contention... CH and AoC are two axioms associated with ZF set theory that have lead some people (including me) to consider a wider interpretation of mathematics. What if all possible consistent mathematical theories must somehow exist?

Joel David Hamkins introduced the "set-theoretic multiverse" idea (link). The abstract reads: 

"The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous diversity of set-theoretic possibilities, a phenomenon that challenges the universe view. In particular, I argue that the continuum hypothesis is settled on the multiverse view by our extensive knowledge about how it behaves in the multiverse, and as a result it can no longer be settled in the manner formerly hoped for."

 Hi Joseph,

    Thank you for this comment and link! Do you think that there is a possibility of an "invariance theory", like Special relativity but for mathematics, at the end of this chain of reasoning? My thinking is that any form of consciousness or theory of knowledge has to assume that there is something meaningful to the idea that knowledge implies agency and intention...

 

Its one reason why Bruno would like to restrict ontology to machines,
or at most integers - echoing Kronecker's quotable "God made the
integers, all else is the work of man".

    I understand that, but this choice to restrict makes Bruno's Idealism even more perplexing to me; how is it that the Integers are given such special status, especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world? Without the physical world to act as a "selection" mechanism for what is "Real", why the bias for integers? This has been a question that I have tried to get answered to no avail.

I think Bruno gives such high status to the natural numbers because they are perhaps the least-doubt-able mathematical entities there are. The very fact that talks of a "set-theoretic multiverse" exist makes one ask, how real are sets? Do set theories tell us more about our minds than they do about the mathematical world? (Obviously, as David Lewis pointed out, you need something like a set theory in order to do mathematics at all, and as Russell says, for the average mathematician it really doesn't matter.)

    My skeptisism centers on the ambiguity of the metric that defines "the least-doubt-able mathematical entities there are". We operate as if there is a clear domain of meaning to this phrase and yet are free to range outside it at will without self-contradiction. Set theory, whether implicit of explicitly acknowledged seems to be a requirement for communication of the 1st person content. Is it necessary for consciousness itself? Might consciousness, boiled down to its essence, be the act of making a distinction itself?

Also: No one here has questioned the reality of the physical world. Should I append this statement to every email until you stop countering it?

    I frankly have to explicitly mention this because the "reality of the physical world" is, in fact, being questioned by many posters on this list. That you would write this remark is puzzling to me. I think that I can safely assume that you have read Bruno's papers... Maybe the problem is that I fail to see how reducing the physical world to the epiphenomena of numbers does not also remove its "reality".

 

This is the origin of Bruno's claim that COMP entails that physics is
not computable, a corrolory of which is that Digital Physics is
refuted (since DP=>COMP).

    Does the symbol "=>" mean "implies"? I get confused ...

Yes, that is the usual meaning. It can also be written (DP or not COMP).

    "=>" = "or not"]

Actually "a implies b" is defined as "not a or b". 

 

    Thank you for this clarification! Would you care to elaborate on this definition?

[Quentin Anciaux]

2012/5/22 Stephen P. King <step...@charter.net>

On 5/22/2012 10:56 AM, Joseph Knight wrote:

On Tue, May 22, 2012 at 7:36 AM, Stephen P. King <step...@charter.net> wrote:

On 5/21/2012 6:26 PM, Russell Standish wrote:

snip

Hi Russell,

    I once thought that consistency, in mathematics, was the indication of existence but situations like this make that idea a point of contention... CH and AoC are two axioms associated with ZF set theory that have lead some people (including me) to consider a wider interpretation of mathematics. What if all possible consistent mathematical theories must somehow exist?

Joel David Hamkins introduced the "set-theoretic multiverse" idea (link). The abstract reads: 

"The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous diversity of set-theoretic possibilities, a phenomenon that challenges the universe view. In particular, I argue that the continuum hypothesis is settled on the multiverse view by our extensive knowledge about how it behaves in the multiverse, and as a result it can no longer be settled in the manner formerly hoped for."

 Hi Joseph,

    Thank you for this comment and link! Do you think that there is a possibility of an "invariance theory", like Special relativity but for mathematics, at the end of this chain of reasoning? My thinking is that any form of consciousness or theory of knowledge has to assume that there is something meaningful to the idea that knowledge implies agency and intention...

 

Its one reason why Bruno would like to restrict ontology to machines,
or at most integers - echoing Kronecker's quotable "God made the
integers, all else is the work of man".

    I understand that, but this choice to restrict makes Bruno's Idealism even more perplexing to me; how is it that the Integers are given such special status, especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world? Without the physical world to act as a "selection" mechanism for what is "Real", why the bias for integers? This has been a question that I have tried to get answered to no avail.

I think Bruno gives such high status to the natural numbers because they are perhaps the least-doubt-able mathematical entities there are. The very fact that talks of a "set-theoretic multiverse" exist makes one ask, how real are sets? Do set theories tell us more about our minds than they do about the mathematical world? (Obviously, as David Lewis pointed out, you need something like a set theory in order to do mathematics at all, and as Russell says, for the average mathematician it really doesn't matter.)

    My skeptisism centers on the ambiguity of the metric that defines "the least-doubt-able mathematical entities there are". We operate as if there is a clear domain of meaning to this phrase and yet are free to range outside it at will without self-contradiction. Set theory, whether implicit of explicitly acknowledged seems to be a requirement for communication of the 1st person content. Is it necessary for consciousness itself? Might consciousness, boiled down to its essence, be the act of making a distinction itself?

Also: No one here has questioned the reality of the physical world. Should I append this statement to every email until you stop countering it?

    I frankly have to explicitly mention this because the "reality of the physical world" is, in fact, being questioned by many posters on this list.

Who ? It's been more than 10 years that I read this list... never seen anybody who questionned the reality of the physical world... we live in it, so it obviously exist. What is put in question is the reality of *a **primitive** material world*.

Quentin
 

That you would write this remark is puzzling to me. I think that I can safely assume that you have read Bruno's papers... Maybe the problem is that I fail to see how reducing the physical world to the epiphenomena of numbers does not also remove its "reality".

 

This is the origin of Bruno's claim that COMP entails that physics is
not computable, a corrolory of which is that Digital Physics is
refuted (since DP=>COMP).

    Does the symbol "=>" mean "implies"? I get confused ...

Yes, that is the usual meaning. It can also be written (DP or not COMP).

    "=>" = "or not"]

Actually "a implies b" is defined as "not a or b". 

 

    Thank you for this clarification! Would you care to elaborate on this definition?

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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[Joseph Knight]

On Tue, May 22, 2012 at 11:08 AM, Stephen P. King <step...@charter.net> wrote:

On 5/22/2012 10:56 AM, Joseph Knight wrote:

On Tue, May 22, 2012 at 7:36 AM, Stephen P. King <step...@charter.net> wrote:

On 5/21/2012 6:26 PM, Russell Standish wrote:

snip

Hi Russell,

    I once thought that consistency, in mathematics, was the indication of existence but situations like this make that idea a point of contention... CH and AoC are two axioms associated with ZF set theory that have lead some people (including me) to consider a wider interpretation of mathematics. What if all possible consistent mathematical theories must somehow exist?

Joel David Hamkins introduced the "set-theoretic multiverse" idea (link). The abstract reads: 

"The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous diversity of set-theoretic possibilities, a phenomenon that challenges the universe view. In particular, I argue that the continuum hypothesis is settled on the multiverse view by our extensive knowledge about how it behaves in the multiverse, and as a result it can no longer be settled in the manner formerly hoped for."

 Hi Joseph,

    Thank you for this comment and link! Do you think that there is a possibility of an "invariance theory", like Special relativity but for mathematics, at the end of this chain of reasoning?

I am doubtful, simply because, for example, the Continuum Hypothesis and its negation are both consistent with ZF set theory. Ditto for the axiom of choice, of course. 

I find it fascinating that, at this level of the foundations of mathematics, mathematics becomes almost an intuitive science. Questions are asked such as: Ought the axiom of choice be true? Are its consequences in line with how we intuit sets to behave? This is the intersection of minds and mathematics. 

 

My thinking is that any form of consciousness or theory of knowledge has to assume that there is something meaningful to the idea that knowledge implies agency and intention...

 

Its one reason why Bruno would like to restrict ontology to machines,
or at most integers - echoing Kronecker's quotable "God made the
integers, all else is the work of man".

    I understand that, but this choice to restrict makes Bruno's Idealism even more perplexing to me; how is it that the Integers are given such special status, especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world? Without the physical world to act as a "selection" mechanism for what is "Real", why the bias for integers? This has been a question that I have tried to get answered to no avail.

I think Bruno gives such high status to the natural numbers because they are perhaps the least-doubt-able mathematical entities there are. The very fact that talks of a "set-theoretic multiverse" exist makes one ask, how real are sets? Do set theories tell us more about our minds than they do about the mathematical world? (Obviously, as David Lewis pointed out, you need something like a set theory in order to do mathematics at all, and as Russell says, for the average mathematician it really doesn't matter.)

    My skeptisism centers on the ambiguity of the metric that defines "the least-doubt-able mathematical entities there are".

I understand. At the end of the day, it may be up to the individual to decide what is doubt-able and what is not. 

 

We operate as if there is a clear domain of meaning to this phrase and yet are free to range outside it at will without self-contradiction. Set theory, whether implicit of explicitly acknowledged seems to be a requirement for communication of the 1st person content. Is it necessary for consciousness itself? Might consciousness, boiled down to its essence, be the act of making a distinction itself?

This is an extremely interesting line of thought. Sets do seem to be necessary for the communication of mathematical ideas, maybe even the communication of ideas period. I will have to give this more thought. 

 

Also: No one here has questioned the reality of the physical world. Should I append this statement to every email until you stop countering it?

    I frankly have to explicitly mention this because the "reality of the physical world" is, in fact, being questioned by many posters on this list.

Only its status as fundamental is being questioned, to my knowledge. There are a couple of posters whose messages I ignore, however, so I could be missing something.

 

That you would write this remark is puzzling to me. I think that I can safely assume that you have read Bruno's papers... Maybe the problem is that I fail to see how reducing the physical world to the epiphenomena of numbers does not also remove its "reality".

It's "real" because I see it, I interact with it. It's not fake, whatever that could possibly mean. It's just made epiphenomenal by COMP.

 

 

 

This is the origin of Bruno's claim that COMP entails that physics is
not computable, a corrolory of which is that Digital Physics is
refuted (since DP=>COMP).

    Does the symbol "=>" mean "implies"? I get confused ...

Yes, that is the usual meaning. It can also be written (DP or not COMP).

    "=>" = "or not"]

Actually "a implies b" is defined as "not a or b". 

 

    Thank you for this clarification! Would you care to elaborate on this definition?

We understand A to imply B. If A is true, then B should be. If B is false, then A better be too. If A is false, then we don't really care about B.

This is the standard definition of "implies" throughout mathematics -- as a definition, in terms of "not" and "or". 

 

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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Joseph Knight

[Stephen P. King]

 No, Bruno, it is not Neutral monism as such cannot assume any particular as primitive, even if it is quantity itself, for to do such is to violate the very notion of neutrality itself. You might like to spend some time reading Spinoza and Bertrand Russell's discussions of this. I did not invent this line of reasoning.

even more perplexing to me; how is it that the Integers are given such special status,

Because of "digital" in digital mechanism. It is not so much an emphasis on numbers, than on finite.

    So how do you justify finiteness?  I have been accused of having the "everything disease" whose symptom is "the inability to conceive anything but infinite, ill defined ensembles", but in my defense I must state that what I am conceiving is an over-abundance of very precisely defined ensembles. My disease is the inability to properly articulate a written description.

 

especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world?

Not at all. Only "primitively physical" reality is put in doubt.

    Not me. I already came to the conclusion that reality cannot be primitively physical.

Without the physical world to act as a "selection" mechanism for what is "Real",

This contradicts your neutral monism.

    No, it does not. Please see my discussion of neutral monism above.

why the bias for integers?

Because comp = machine, and machine are supposed to be of the type "finitely describable".

    This is true only after the possibility of determining differences is stipulated. One cannot assume a neutral monism that stipulates a non-neutral stance, to do so it a contradiction.

This has been a question that I have tried to get answered to no avail.

You don't listen. This has been repeated very often. When you say "yes" to the doctor, you accept that you survive with a computer executing a code. A code is mainly a natural number, up to computable isomorphism. Comp refers to computer science, which study the computable function, which can always be recasted in term of computable function from N to N.

And there are no other theory of computability, on reals or whatever, or if you prefer, there are too many, without any Church thesis or genuine universality notion. (Cf Pour-Hel, Blum Shub and Smale, etc.)

    I do listen and read as well. Now it is your turn. The entire theory of computation rests upon the ability to distinguish quantity from non-quantity, even to the point of the possibility of the act of making a distinction. When you propose a primitive ground that assumes a prior distinction and negates the prior act that generated the result, you are demanding the belief in fiat acts. This is familiar to me from my childhood days of sitting in the pew of my father's church. It is an act of blind faith, not evidence based science. Please stop pretending otherwise.

[Quentin Anciaux]

2012/5/22 Stephen P. King <step...@charter.net>

On 5/22/2012 11:53 AM, Bruno Marchal wrote:

 Neutral monism, in philosophy, is the metaphysical view that the mental and the physical are two ways of organizing or describing the same elements, which are themselves "neutral," that is, neither physical nor mental.

I don't see how taking N,+,* as primitive is not neutral monism. It is neither physical nor mental.

even more perplexing to me; how is it that the Integers are given such special status,

Because of "digital" in digital mechanism. It is not so much an emphasis on numbers, than on finite.

    So how do you justify finiteness?  I have been accused of having the "everything disease" whose symptom is "the inability to conceive anything but infinite, ill defined ensembles", but in my defense I must state that what I am conceiving is an over-abundance of very precisely defined ensembles. My disease is the inability to properly articulate a written description.

 

especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world?

Not at all. Only "primitively physical" reality is put in doubt.

    Not me. I already came to the conclusion that reality cannot be primitively physical.

You are unclear on what you posit. You always came back to the "physical reality" point, so I don't know what more to say... either you agree physical reality is not ontologically primitive or you don't, there's no in between position.
 

Without the physical world to act as a "selection" mechanism for what is "Real",

This contradicts your neutral monism.

 

    No, it does not. Please see my discussion of neutral monism above.

Yes it does, reading you, you posit a physical material reality as primitive, which is not neutral...

why the bias for integers?

Because comp = machine, and machine are supposed to be of the type "finitely describable".

    This is true only after the possibility of determining differences is stipulated. One cannot assume a neutral monism that stipulates a non-neutral stance, to do so it a contradiction.

Computationalism is the theory that you consciousness can be emulated on a turing machine, a program is a finite object and can be described by an integer. I don't see a contradiction.
 

This has been a question that I have tried to get answered to no avail.

You don't listen. This has been repeated very often. When you say "yes" to the doctor, you accept that you survive with a computer executing a code. A code is mainly a natural number, up to computable isomorphism. Comp refers to computer science, which study the computable function, which can always be recasted in term of computable function from N to N.

And there are no other theory of computability, on reals or whatever, or if you prefer, there are too many, without any Church thesis or genuine universality notion. (Cf Pour-Hel, Blum Shub and Smale, etc.)

    I do listen and read as well. Now it is your turn. The entire theory of computation rests upon the ability to distinguish quantity from non-quantity, even to the point of the possibility of the act of making a distinction. When you propose a primitive ground that assumes a prior distinction and negates the prior act that generated the result, you are demanding the belief in fiat acts. This is familiar to me from my childhood days of sitting in the pew of my father's church. It is an act of blind faith, not evidence based science. Please stop pretending otherwise.

"evidence based science" ??

 

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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[Hal Ruhl]

Hi Everyone:

Unfortunately I have been unable to support a post reading/creation activity
on this list for a long time.

I had started this post as a comment to one of Russell's responses [Hi
Russell] to a post by Stephen [Hi Stephen].

I have a model (considerably revised here) that I have been developing for a
long time and was going to use it to support my comments. However, the
post evolved.

Note:
The next most recent version of the following model was posted to the list
on Friday, December 26, 2008 @ 9:28 PM as far as I can reconstruct events.

A brief model of - well - Everything

SOME DEFINITIONS:

i) Distinction:

That which enables a separation such as a particular red from other colors.

ii) Devisor:

That which encloses a quantity [none to every] of distinctions. [Some
divisors are thus collections of divisors.]


MODEL:

1) Assumption # A1: There exists a set consisting of all possible divisors.
Call this set "A" [for All].

"A" encompasses every distinction. "A" is thus itself a divisor by (i) and
therefore contains itself an unbounded number of times.


2) Definition (iii): Define "N"s as those divisors that enclose zero
distinction. Call them Nothings.

3) Definition (iv): Define "S"s as divisors that enclose non zero
distinction but not all distinction. Call them Somethings.

4) An issue that arises is whether or not an individual specific divisor is
static or dynamic. That is: Is its quantity of distinction subject to
change? It cannot be both.

This requires that all divisors individually enclose the self referential
distinction of being static or dynamic.

5) At least one divisor type - the "N"s, by definition (iii), enclose no
such distinction but must enclose this one. This is a type of
incompleteness. That is the "N"s cannot answer this question which is
nevertheless meaningful to them. [The incompleteness is taken to be rather
similar functionally to the incompleteness of some mathematical Formal
Axiomatic Systems - See Godel.]

The "N" are thus unstable with respect to their initial condition. They
each must at some point spontaneously enclose this static or dynamic
distinction. They thereby transition into "S"s.

6) By (4) and (5) Transitions exist.

7) Some of these "S"s may themselves be incomplete in a similar manner but
in a different distinction family. They must evolve - via similar
incompleteness driven transitions - until "complete" in the sense of (5).

8) Assumption # A2: Each element of "A" is a universe state.

9) The result is a "flow" of "S"s that are encompassing more and more
distinction with each transition.

10) This "flow" is a multiplicity of paths of successions of transitions
from element to element of the All. That is (by A2) a transition from a
universe state to a successor universe state.

Consequences:

a) Our Universe's evolution would be one such path on which the "S" has
constantly gotten larger.

b) Since a particular incompleteness can have multiple resolutions, the path
of an evolving "S" may split into multiple paths at any transition.

c) A path may also originate on any incomplete "S" not just the "N"s.

d) Observer constructs such as life entities and likely all other constructs
imbedded in a universe bear witness to the transitions via morphing.

e) Paths can be of any length.

f) Since many elements of "A" are very large, large transitions could become
infrequent on a long path where the particular "S" gets very large. (Few
White Rabbits if both sides of the transition are sufficiently similar).

---------------------------

So far I see no "computation" in my model.

However, as I prepared the post and did more reading of recent posts and
thinking I found that I could add one more requirement to the model and thus
make it contain [but not be limited to] comp as far as I can tell:

Add to the end of (5):

Any transition must resolve at least one incompleteness in the relevant "S".
Equate some fraction of the incompleteness of SOME relevant "S"s to a
snapshot of a computation(s) that has(have) not halted.

The transition path of such an "S" must include (but not limited to)
transitions to a next state containing the next step of at least one such
computation.

Thus I see the model as containing, but not limited to, comp.


Well, the model is still a work in progress.



Hal Ruhl

[Stephen P. King]

On 5/22/2012 6:01 PM, Quentin Anciaux wrote:

2012/5/22 Stephen P. King <step...@charter.net>

 No, Bruno, it is not Neutral monism as such cannot assume any particular as primitive, even if it is quantity itself, for to do such is to violate the very notion of neutrality itself. You might like to spend some time reading Spinoza and Bertrand Russell's discussions of this. I did not invent this line of reasoning.

 Neutral monism, in philosophy, is the metaphysical view that the mental and the physical are two ways of organizing or describing the same elements, which are themselves "neutral," that is, neither physical nor mental.

I don't see how taking N,+,* as primitive is not neutral monism. It is neither physical nor mental.

    If mathematical "objects" are not within the category of Mental then that is news to philosophers...

even more perplexing to me; how is it that the Integers are given such special status,

Because of "digital" in digital mechanism. It is not so much an emphasis on numbers, than on finite.

    So how do you justify finiteness?  I have been accused of having the "everything disease" whose symptom is "the inability to conceive anything but infinite, ill defined ensembles", but in my defense I must state that what I am conceiving is an over-abundance of very precisely defined ensembles. My disease is the inability to properly articulate a written description.

 

especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world?

Not at all. Only "primitively physical" reality is put in doubt.

    Not me. I already came to the conclusion that reality cannot be primitively physical.

You are unclear on what you posit. You always came back to the "physical reality" point, so I don't know what more to say... either you agree physical reality is not ontologically primitive or you don't, there's no in between position.

    We have to start at the physical reality that we individually experience, it is, aside from our awareness, the most "real" thing we have to stand upon philosophically. From there we venture out in our speculations as to our ontology. cosmogony and epistemology. is there an alternative?

 

Without the physical world to act as a "selection" mechanism for what is "Real",

This contradicts your neutral monism.

 

    No, it does not. Please see my discussion of neutral monism above.

Yes it does, reading you, you posit a physical material reality as primitive, which is not neutral...

    No, I posit the physical and the mental as "real" in the sense that I am experiencing them. Telescoping out to the farthest point of abstraction we have ideas like Bruno's.  I guess that I need to draw some diagrams...

why the bias for integers?

Because comp = machine, and machine are supposed to be of the type "finitely describable".

    This is true only after the possibility of determining differences is stipulated. One cannot assume a neutral monism that stipulates a non-neutral stance, to do so it a contradiction.

Computationalism is the theory that your consciousness can be emulated on a turing machine, a program is a finite object and can be described by an integer. I don't see a contradiction.

    I am with Penrose in claiming that consciousness is not emulable by a finite machine.

 

This has been a question that I have tried to get answered to no avail.

You don't listen. This has been repeated very often. When you say "yes" to the doctor, you accept that you survive with a computer executing a code. A code is mainly a natural number, up to computable isomorphism. Comp refers to computer science, which study the computable function, which can always be recasted in term of computable function from N to N.

And there are no other theory of computability, on reals or whatever, or if you prefer, there are too many, without any Church thesis or genuine universality notion. (Cf Pour-Hel, Blum Shub and Smale, etc.)

    I do listen and read as well. Now it is your turn. The entire theory of computation rests upon the ability to distinguish quantity from non-quantity, even to the point of the possibility of the act of making a distinction. When you propose a primitive ground that assumes a prior distinction and negates the prior act that generated the result, you are demanding the belief in fiat acts. This is familiar to me from my childhood days of sitting in the pew of my father's church. It is an act of blind faith, not evidence based science. Please stop pretending otherwise.

"evidence based science" ??

    Yes, like not rejecting the physical necessity involved in a computation. I reject Platonism on these grounds; it is anti-empirical.

[meekerdb]

On 5/22/2012 4:22 PM, Stephen P. King wrote:

On 5/22/2012 6:01 PM, Quentin Anciaux wrote:

2012/5/22 Stephen P. King <step...@charter.net>

 No, Bruno, it is not Neutral monism as such cannot assume any particular as primitive, even if it is quantity itself, for to do such is to violate the very notion of neutrality itself. You might like to spend some time reading Spinoza and Bertrand Russell's discussions of this. I did not invent this line of reasoning.

 Neutral monism, in philosophy, is the metaphysical view that the mental and the physical are two ways of organizing or describing the same elements, which are themselves "neutral," that is, neither physical nor mental.

I don't see how taking N,+,* as primitive is not neutral monism. It is neither physical nor mental.

    If mathematical "objects" are not within the category of Mental then that is news to philosophers...

even more perplexing to me; how is it that the Integers are given such special status,

Because of "digital" in digital mechanism. It is not so much an emphasis on numbers, than on finite.

    So how do you justify finiteness?  I have been accused of having the "everything disease" whose symptom is "the inability to conceive anything but infinite, ill defined ensembles", but in my defense I must state that what I am conceiving is an over-abundance of very precisely defined ensembles. My disease is the inability to properly articulate a written description.

 

especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world?

Not at all. Only "primitively physical" reality is put in doubt.

    Not me. I already came to the conclusion that reality cannot be primitively physical.

You are unclear on what you posit. You always came back to the "physical reality" point, so I don't know what more to say... either you agree physical reality is not ontologically primitive or you don't, there's no in between position.

    We have to start at the physical reality that we individually experience, it is, aside from our awareness, the most "real" thing we have to stand upon philosophically. From there we venture out in our speculations as to our ontology. cosmogony and epistemology. is there an alternative?

 

Without the physical world to act as a "selection" mechanism for what is "Real",

This contradicts your neutral monism.

 

    No, it does not. Please see my discussion of neutral monism above.

Yes it does, reading you, you posit a physical material reality as primitive, which is not neutral...

    No, I posit the physical and the mental as "real" in the sense that I am experiencing them.

The physical world is a model.  It's a very good model and I like it, but like any model you can't *know* whether it's really real or not.  Bruno's model explains some things the physical model doesn't, but so far it doesn't seem to have the predictive power that the physical model does. 

Telescoping out to the farthest point of abstraction we have ideas like Bruno's.  I guess that I need to draw some diagrams...

why the bias for integers?

Because comp = machine, and machine are supposed to be of the type "finitely describable".

    This is true only after the possibility of determining differences is stipulated. One cannot assume a neutral monism that stipulates a non-neutral stance, to do so it a contradiction.

Computationalism is the theory that your consciousness can be emulated on a turing machine, a program is a finite object and can be described by an integer. I don't see a contradiction.

    I am with Penrose in claiming that consciousness is not emulable by a finite machine.

It's instantiated by brains which are empirically finite.  Penrose's argument from Godelian incompleteness is fallacious.

 

This has been a question that I have tried to get answered to no avail.

You don't listen. This has been repeated very often. When you say "yes" to the doctor, you accept that you survive with a computer executing a code. A code is mainly a natural number, up to computable isomorphism. Comp refers to computer science, which study the computable function, which can always be recasted in term of computable function from N to N.

And there are no other theory of computability, on reals or whatever, or if you prefer, there are too many, without any Church thesis or genuine universality notion. (Cf Pour-Hel, Blum Shub and Smale, etc.)

    I do listen and read as well. Now it is your turn. The entire theory of computation rests upon the ability to distinguish quantity from non-quantity, even to the point of the possibility of the act of making a distinction. When you propose a primitive ground that assumes a prior distinction and negates the prior act that generated the result, you are demanding the belief in fiat acts. This is familiar to me from my childhood days of sitting in the pew of my father's church. It is an act of blind faith, not evidence based science. Please stop pretending otherwise.

"evidence based science" ??

    Yes, like not rejecting the physical necessity involved in a computation. I reject Platonism on these grounds; it is anti-empirical.

But it wouldn't be if it made some risky predictions which we found to be true.

Brent

[Quentin Anciaux]

2012/5/23 Stephen P. King <step...@charter.net>

On 5/22/2012 6:01 PM, Quentin Anciaux wrote:

2012/5/22 Stephen P. King <step...@charter.net>

 No, Bruno, it is not Neutral monism as such cannot assume any particular as primitive, even if it is quantity itself, for to do such is to violate the very notion of neutrality itself. You might like to spend some time reading Spinoza and Bertrand Russell's discussions of this. I did not invent this line of reasoning.

 Neutral monism, in philosophy, is the metaphysical view that the mental and the physical are two ways of organizing or describing the same elements, which are themselves "neutral," that is, neither physical nor mental.

I don't see how taking N,+,* as primitive is not neutral monism. It is neither physical nor mental.

    If mathematical "objects" are not within the category of Mental then that is news to philosophers...

If numbers (accepting arithmetical realism) are independent of you, the universe, any mind, it is difficult to see how then can be mental object... the way we discover mathematics is through our mind, that doesn't mean mathematical object are mind object... I discover the physical world through my mind, that doesn't mean the physical world is a mental object.
 

even more perplexing to me; how is it that the Integers are given such special status,

Because of "digital" in digital mechanism. It is not so much an emphasis on numbers, than on finite.

    So how do you justify finiteness?  I have been accused of having the "everything disease" whose symptom is "the inability to conceive anything but infinite, ill defined ensembles", but in my defense I must state that what I am conceiving is an over-abundance of very precisely defined ensembles. My disease is the inability to properly articulate a written description.

 

especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world?

Not at all. Only "primitively physical" reality is put in doubt.

    Not me. I already came to the conclusion that reality cannot be primitively physical.

You are unclear on what you posit. You always came back to the "physical reality" point, so I don't know what more to say... either you agree physical reality is not ontologically primitive or you don't, there's no in between position.

    We have to start at the physical reality that we individually experience, it is, aside from our awareness, the most "real" thing we have to stand upon philosophically.

If you start from physicality it is hardly neutral monism.
 

From there we venture out in our speculations as to our ontology. cosmogony and epistemology. is there an alternative?

 

Without the physical world to act as a "selection" mechanism for what is "Real",

This contradicts your neutral monism.

 

    No, it does not. Please see my discussion of neutral monism above.

Yes it does, reading you, you posit a physical material reality as primitive, which is not neutral...

    No, I posit the physical and the mental as "real" in the sense that I am experiencing them. Telescoping out to the farthest point of abstraction we have ideas like Bruno's.  I guess that I need to draw some diagrams...

why the bias for integers?

Because comp = machine, and machine are supposed to be of the type "finitely describable".

    This is true only after the possibility of determining differences is stipulated. One cannot assume a neutral monism that stipulates a non-neutral stance, to do so it a contradiction.

Computationalism is the theory that your consciousness can be emulated on a turing machine, a program is a finite object and can be described by an integer. I don't see a contradiction.

    I am with Penrose in claiming that consciousness is not emulable by a finite machine.

You claim what you want, you simply reject computationalism then, but I have not to accept your claim without you backing it.

Regards,
Quentin
 

 

This has been a question that I have tried to get answered to no avail.

You don't listen. This has been repeated very often. When you say "yes" to the doctor, you accept that you survive with a computer executing a code. A code is mainly a natural number, up to computable isomorphism. Comp refers to computer science, which study the computable function, which can always be recasted in term of computable function from N to N.

And there are no other theory of computability, on reals or whatever, or if you prefer, there are too many, without any Church thesis or genuine universality notion. (Cf Pour-Hel, Blum Shub and Smale, etc.)

    I do listen and read as well. Now it is your turn. The entire theory of computation rests upon the ability to distinguish quantity from non-quantity, even to the point of the possibility of the act of making a distinction. When you propose a primitive ground that assumes a prior distinction and negates the prior act that generated the result, you are demanding the belief in fiat acts. This is familiar to me from my childhood days of sitting in the pew of my father's church. It is an act of blind faith, not evidence based science. Please stop pretending otherwise.

"evidence based science" ??

    Yes, like not rejecting the physical necessity involved in a computation. I reject Platonism on these grounds; it is anti-empirical.

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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[Bruno Marchal]

On 23 May 2012, at 01:22, Stephen P. King wrote:

On 5/22/2012 6:01 PM, Quentin Anciaux wrote:

2012/5/22 Stephen P. King <step...@charter.net>

 No, Bruno, it is not Neutral monism as such cannot assume any particular as primitive, even if it is quantity itself, for to do such is to violate the very notion of neutrality itself. You might like to spend some time reading Spinoza and Bertrand Russell's discussions of this. I did not invent this line of reasoning.

 Neutral monism, in philosophy, is the metaphysical view that the mental and the physical are two ways of organizing or describing the same elements, which are themselves "neutral," that is, neither physical nor mental.

I don't see how taking N,+,* as primitive is not neutral monism. It is neither physical nor mental.

    If mathematical "objects" are not within the category of Mental then that is news to philosophers...

If mathematical "objects" are within the category of Mental then that is news to mathematicians...

And it is disastrous for those who want study the mental by defining it by the mathematical, as in computer science, cognitive science, artificial intelligence, etc;

even more perplexing to me; how is it that the Integers are given such special status,

Because of "digital" in digital mechanism. It is not so much an emphasis on numbers, than on finite.

    So how do you justify finiteness?  I have been accused of having the "everything disease" whose symptom is "the inability to conceive anything but infinite, ill defined ensembles", but in my defense I must state that what I am conceiving is an over-abundance of very precisely defined ensembles. My disease is the inability to properly articulate a written description.

 

especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world?

Not at all. Only "primitively physical" reality is put in doubt.

    Not me. I already came to the conclusion that reality cannot be primitively physical.

You are unclear on what you posit. You always came back to the "physical reality" point, so I don't know what more to say... either you agree physical reality is not ontologically primitive or you don't, there's no in between position.

    We have to start at the physical reality that we individually experience, it is, aside from our awareness, the most "real" thing we have to stand upon philosophically.

The most "real" things might be consciousness, here and now.  And this doesn't make consciousness primitive, but invite us to be methodologically skeptical on the physical, as we know since the "dream argument".

From there we venture out in our speculations as to our ontology. cosmogony and epistemology. is there an alternative?

So you start from physics? This contradicts your neutral monism.

 

Without the physical world to act as a "selection" mechanism for what is "Real",

This contradicts your neutral monism.

 

    No, it does not. Please see my discussion of neutral monism above.

Yes it does, reading you, you posit a physical material reality as primitive, which is not neutral...

    No, I posit the physical and the mental as "real" in the sense that I am experiencing them.

You can't experience the physical. The physical is inferred from theory, even if automated by years of evolution. 

Telescoping out to the farthest point of abstraction we have ideas like Bruno's.  I guess that I need to draw some diagrams...

Not ideas. Universal truth following a deduction in a theoretical frame. It is just a theorem in applied logic: if we are digital machine, then physics (whatever inferable from observable)  is derivable from arithmetic. Adding anything to it, *cannot* be of any use (cf UDA step 7 and 8).

You are free to use any philosophy you want to *find* a flaw in the reasoning, but a philosophical conviction does not refute it by itself.

If you think there is a loophole, just show it to us.

why the bias for integers?

Because comp = machine, and machine are supposed to be of the type "finitely describable".

    This is true only after the possibility of determining differences is stipulated. One cannot assume a neutral monism that stipulates a non-neutral stance, to do so it a contradiction.

Computationalism is the theory that your consciousness can be emulated on a turing machine, a program is a finite object and can be described by an integer. I don't see a contradiction.

    I am with Penrose in claiming that consciousness is not emulable by a finite machine.

This contradicts your statement that your theory is consistent with comp (as it is not, as I argue to you). You are making my point. It took time.

 

This has been a question that I have tried to get answered to no avail.

You don't listen. This has been repeated very often. When you say "yes" to the doctor, you accept that you survive with a computer executing a code. A code is mainly a natural number, up to computable isomorphism. Comp refers to computer science, which study the computable function, which can always be recasted in term of computable function from N to N.

And there are no other theory of computability, on reals or whatever, or if you prefer, there are too many, without any Church thesis or genuine universality notion. (Cf Pour-Hel, Blum Shub and Smale, etc.)

    I do listen and read as well. Now it is your turn. The entire theory of computation rests upon the ability to distinguish quantity from non-quantity, even to the point of the possibility of the act of making a distinction. When you propose a primitive ground that assumes a prior distinction and negates the prior act that generated the result, you are demanding the belief in fiat acts. This is familiar to me from my childhood days of sitting in the pew of my father's church. It is an act of blind faith, not evidence based science. Please stop pretending otherwise.

"evidence based science" ??

    Yes, like not rejecting the physical necessity involved in a computation.

There is no physical necessity involved in a computation, no more than in an addition or multiplication. You will not find a book on computation referring to any physical notion in the definition. This exists only in philosophical defense on physicalism. The notion of physical computation is complex, and there is no unanimity on whether such notion makes sense or not. With comp, it is an open problem, but it does a priori make sense.

I reject Platonism on these grounds; it is anti-empirical.

As Brent pointed out, it depends on the theory. Comp is platonist, but makes precise prediction (indeed, that the whole of physics is given by precise theories based on self-reference). This illustrates that platonism can be empirical. 

Bruno

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

[Russell Standish]

On Tue, May 22, 2012 at 09:56:24AM -0500, Joseph Knight wrote:
> On Tue, May 22, 2012 at 7:36 AM, Stephen P. King <step...@charter.net>wrote:
>
> > On 5/21/2012 6:26 PM, Russell Standish wrote:
> >
> > Yes, that is the usual meaning. It can also be written (DP or not COMP).
> >
> >
> > "=>" = "or not"]
> >
>
> Actually "a implies b" is defined as "not a or b".
>

Whoops! (#>.<#)

[Bruno Marchal]

On 23 May 2012, at 07:21, Russell Standish wrote:

> On Tue, May 22, 2012 at 09:56:24AM -0500, Joseph Knight wrote:
>> On Tue, May 22, 2012 at 7:36 AM, Stephen P. King <step...@charter.net
>> >wrote:
>>
>>> On 5/21/2012 6:26 PM, Russell Standish wrote:
>>>
>>> Yes, that is the usual meaning. It can also be written (DP or not
>>> COMP).
>>>
>>>
>>> "=>" = "or not"]
>>>
>>
>> Actually "a implies b" is defined as "not a or b".
>>
>
> Whoops! (#>.<#)

To be sure I usually use "->" for the material implication, that is "a
-> b" is indeed "not a or b" (or "not(a and not b)").

The IF ... THEN used in math is generally of that type.

I use a => b for "from a I can derive b, in the theory I am currently
considering".

For any theory having the modus ponens rule, we have that "a -> b"
entails (yet at another meta-level) "a => b". This should be trivial.
For many quite standard logics, the reciprocal is correct too, that
is: "a = > b" entails "a -> b". This is usually rather hard to prove
(Herbrand or deduction theorem). It is typically false in modal logic
or in many weak logics. For example the normal modal logics (those
having Kripke semantics, like G, S4, ...) are all close for the rule a
=> Ba, but virtually none can prove the formula a -> Ba. This is a
source of many errors.

Simple Exercises (for those remembering Kripke semantics):
1) find a Kripke model falsifying "a -> Ba".
2) explain to yourself why "a => Ba" is always the case in all Kripke
models.

I recall that a Kripke model is a set (of "worlds") with a binary
relation (accessibility relation). The key is that Ba is true in a
world Alpha is a is true in all worlds Beta such that (Alpha, Beta) is
in the accessibility relation.

A beginners course in logic consists in six month of explanation of
the difference between "a -> b" and "a => b", and then six month of
proving them equivalent (in classical logic).

"a => b" is often written:

a
_

b

Like in the modus ponens rule

a a -> b
________

b


Bruno

>
> --
>
> ----------------------------------------------------------------------------
> Prof Russell Standish Phone 0425 253119 (mobile)
> Principal, High Performance Coders
> Visiting Professor of Mathematics hpc...@hpcoders.com.au
> University of New South Wales http://www.hpcoders.com.au
> ----------------------------------------------------------------------------
>

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[Bruno Marchal]

On 23 May 2012, at 02:54, meekerdb wrote:

On 5/22/2012 4:22 PM, Stephen P. King wrote:

On 5/22/2012 6:01 PM, Quentin Anciaux wrote:

2012/5/22 Stephen P. King <step...@charter.net>

 No, Bruno, it is not Neutral monism as such cannot assume any particular as primitive, even if it is quantity itself, for to do such is to violate the very notion of neutrality itself. You might like to spend some time reading Spinoza and Bertrand Russell's discussions of this. I did not invent this line of reasoning.

 Neutral monism, in philosophy, is the metaphysical view that the mental and the physical are two ways of organizing or describing the same elements, which are themselves "neutral," that is, neither physical nor mental.

I don't see how taking N,+,* as primitive is not neutral monism. It is neither physical nor mental.

    If mathematical "objects" are not within the category of Mental then that is news to philosophers...

even more perplexing to me; how is it that the Integers are given such special status,

Because of "digital" in digital mechanism. It is not so much an emphasis on numbers, than on finite.

    So how do you justify finiteness?  I have been accused of having the "everything disease" whose symptom is "the inability to conceive anything but infinite, ill defined ensembles", but in my defense I must state that what I am conceiving is an over-abundance of very precisely defined ensembles. My disease is the inability to properly articulate a written description.

 

especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world?

Not at all. Only "primitively physical" reality is put in doubt.

    Not me. I already came to the conclusion that reality cannot be primitively physical.

You are unclear on what you posit. You always came back to the "physical reality" point, so I don't know what more to say... either you agree physical reality is not ontologically primitive or you don't, there's no in between position.

    We have to start at the physical reality that we individually experience, it is, aside from our awareness, the most "real" thing we have to stand upon philosophically. From there we venture out in our speculations as to our ontology. cosmogony and epistemology. is there an alternative?

 

Without the physical world to act as a "selection" mechanism for what is "Real",

This contradicts your neutral monism.

 

    No, it does not. Please see my discussion of neutral monism above.

Yes it does, reading you, you posit a physical material reality as primitive, which is not neutral...

    No, I posit the physical and the mental as "real" in the sense that I am experiencing them.

The physical world is a model.  It's a very good model and I like it, but like any model you can't *know* whether it's really real or not.  Bruno's model explains some things the physical model doesn't, but so far it doesn't seem to have the predictive power that the physical model does. 

Hmm... I agree with all your points in this post, except this one. The comp "model" (theory) has much more predictive power than physics, given that it predicts the whole of physics, and the whole of what that physics predicts (and this without mentioning that it predicts the whole qualia part too, unlike the "physics model"). But it does it in a very more difficult way, without "copying on nature". 

Of course it might be false. It might be that comp leads to a different mass for the electron or to the non existence of electrons. But comp, together with some definition of knowledge, predicts physics quantitatively and qualitatively.

Of course to use comp to predict an eclipse is not yet in its range, if it can ever be. To use comp for this, would be like using string theory to prepare a cup of tea. But the goal is not to do physics, just to formulate the mind-body problem, and figure out the less wrong bigger picture.

Bruno

Telescoping out to the farthest point of abstraction we have ideas like Bruno's.  I guess that I need to draw some diagrams...

why the bias for integers?

Because comp = machine, and machine are supposed to be of the type "finitely describable".

    This is true only after the possibility of determining differences is stipulated. One cannot assume a neutral monism that stipulates a non-neutral stance, to do so it a contradiction.

Computationalism is the theory that your consciousness can be emulated on a turing machine, a program is a finite object and can be described by an integer. I don't see a contradiction.

    I am with Penrose in claiming that consciousness is not emulable by a finite machine.

It's instantiated by brains which are empirically finite.  Penrose's argument from Godelian incompleteness is fallacious.

 

This has been a question that I have tried to get answered to no avail.

You don't listen. This has been repeated very often. When you say "yes" to the doctor, you accept that you survive with a computer executing a code. A code is mainly a natural number, up to computable isomorphism. Comp refers to computer science, which study the computable function, which can always be recasted in term of computable function from N to N.

And there are no other theory of computability, on reals or whatever, or if you prefer, there are too many, without any Church thesis or genuine universality notion. (Cf Pour-Hel, Blum Shub and Smale, etc.)

    I do listen and read as well. Now it is your turn. The entire theory of computation rests upon the ability to distinguish quantity from non-quantity, even to the point of the possibility of the act of making a distinction. When you propose a primitive ground that assumes a prior distinction and negates the prior act that generated the result, you are demanding the belief in fiat acts. This is familiar to me from my childhood days of sitting in the pew of my father's church. It is an act of blind faith, not evidence based science. Please stop pretending otherwise.

"evidence based science" ??

    Yes, like not rejecting the physical necessity involved in a computation. I reject Platonism on these grounds; it is anti-empirical.

But it wouldn't be if it made some risky predictions which we found to be true.

Brent

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[meekerdb]

On 5/23/2012 8:47 AM, Bruno Marchal wrote:
> Hmm... I agree with all your points in this post, except this one. The comp "model"
> (theory) has much more predictive power than physics, given that it predicts the whole
> of physics,

It's easy to predict the whole of physics; just predict that everything happens. But
that's not predictive power.

Brent

[Evgenii Rudnyi]

On 23.05.2012 10:47 Bruno Marchal said the following:

>
> On 23 May 2012, at 01:22, Stephen P. King wrote:

...

>> If mathematical "objects" are not within the category of Mental
>> then that is news to philosophers...
>
> If mathematical "objects" are within the category of Mental then that
> is news to mathematicians...
>

Let us take terms like information, computation, etc. Are they mental or
mathematical?

It might be good simultaneously to extend this question by including
general terms that people use to describe the word. Are mathematical
objects then are different from them?

Evgenii

[Stephen P. King]

On 5/23/2012 4:47 AM, Bruno Marchal wrote:

On 23 May 2012, at 01:22, Stephen P. King wrote:

On 5/22/2012 6:01 PM, Quentin Anciaux wrote:

2012/5/22 Stephen P. King <step...@charter.net>

 No, Bruno, it is not Neutral monism as such cannot assume any particular as primitive, even if it is quantity itself, for to do such is to violate the very notion of neutrality itself. You might like to spend some time reading Spinoza and Bertrand Russell's discussions of this. I did not invent this line of reasoning.

 Neutral monism, in philosophy, is the metaphysical view that the mental and the physical are two ways of organizing or describing the same elements, which are themselves "neutral," that is, neither physical nor mental.

I don't see how taking N,+,* as primitive is not neutral monism. It is neither physical nor mental.

    If mathematical "objects" are not within the category of Mental then that is news to philosophers...

If mathematical "objects" are within the category of Mental then that is news to mathematicians...

And it is disastrous for those who want study the mental by defining it by the mathematical, as in computer science, cognitive science, artificial intelligence, etc;

    Are we being intentionally unable to understand the obvious? Do we physically interact with mathematical objects? No. Thus they are not in the physical realm. We interact with mathematical objects with our minds, thus they are in the mental realm. Not complicated.

even more perplexing to me; how is it that the Integers are given such special status,

Because of "digital" in digital mechanism. It is not so much an emphasis on numbers, than on finite.

    So how do you justify finiteness?  I have been accused of having the "everything disease" whose symptom is "the inability to conceive anything but infinite, ill defined ensembles", but in my defense I must state that what I am conceiving is an over-abundance of very precisely defined ensembles. My disease is the inability to properly articulate a written description.

 

especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world?

Not at all. Only "primitively physical" reality is put in doubt.

    Not me. I already came to the conclusion that reality cannot be primitively physical.

You are unclear on what you posit. You always came back to the "physical reality" point, so I don't know what more to say... either you agree physical reality is not ontologically primitive or you don't, there's no in between position.

    We have to start at the physical reality that we individually experience, it is, aside from our awareness, the most "real" thing we have to stand upon philosophically.

The most "real" things might be consciousness, here and now.  And this doesn't make consciousness primitive, but invite us to be methodologically skeptical on the physical, as we know since the "dream argument".

    The only person that is making it, albeit indirectly by implication, is you, Bruno. You think that you are safe because you believe that you have isolated mathematics from the physical and from the contingency of having to be known by particular individuals, but you have not over come the basic flaw of Platonism: if you disconnect the Forms from consciousness you forever prevent the act of apprehension. You seem to think that property definiteness is an ontological a priori. You are not the first, E. Kant had the same delusion.

From there we venture out in our speculations as to our ontology. cosmogony and epistemology. is there an alternative?

So you start from physics? This contradicts your neutral monism.

    So you do need a diagram to understand a simple idea.

 

Without the physical world to act as a "selection" mechanism for what is "Real",

This contradicts your neutral monism.

 

    No, it does not. Please see my discussion of neutral monism above.

Yes it does, reading you, you posit a physical material reality as primitive, which is not neutral...

    No, I posit the physical and the mental as "real" in the sense that I am experiencing them.

You can't experience the physical. The physical is inferred from theory, even if automated by years of evolution.

    We cannot experience anything directly, except for our individual consciousness, all else is inferred.

Telescoping out to the farthest point of abstraction we have ideas like Bruno's.  I guess that I need to draw some diagrams...

Not ideas. Universal truth following a deduction in a theoretical frame. It is just a theorem in applied logic: if we are digital machine, then physics (whatever inferable from observable)  is derivable from arithmetic. Adding anything to it, *cannot* be of any use (cf UDA step 7 and 8).

You are free to use any philosophy you want to *find* a flaw in the reasoning, but a philosophical conviction does not refute it by itself.

If you think there is a loophole, just show it to us.

why the bias for integers?

Because comp = machine, and machine are supposed to be of the type "finitely describable".

    This is true only after the possibility of determining differences is stipulated. One cannot assume a neutral monism that stipulates a non-neutral stance, to do so it a contradiction.

Computationalism is the theory that your consciousness can be emulated on a turing machine, a program is a finite object and can be described by an integer. I don't see a contradiction.

    I am with Penrose in claiming that consciousness is not emulable by a finite machine.

This contradicts your statement that your theory is consistent with comp (as it is not, as I argue to you). You are making my point. It took time.

    You have no idea what "my theory" is.

 

This has been a question that I have tried to get answered to no avail.

You don't listen. This has been repeated very often. When you say "yes" to the doctor, you accept that you survive with a computer executing a code. A code is mainly a natural number, up to computable isomorphism. Comp refers to computer science, which study the computable function, which can always be recasted in term of computable function from N to N.

And there are no other theory of computability, on reals or whatever, or if you prefer, there are too many, without any Church thesis or genuine universality notion. (Cf Pour-Hel, Blum Shub and Smale, etc.)

    I do listen and read as well. Now it is your turn. The entire theory of computation rests upon the ability to distinguish quantity from non-quantity, even to the point of the possibility of the act of making a distinction. When you propose a primitive ground that assumes a prior distinction and negates the prior act that generated the result, you are demanding the belief in fiat acts. This is familiar to me from my childhood days of sitting in the pew of my father's church. It is an act of blind faith, not evidence based science. Please stop pretending otherwise.

"evidence based science" ??

    Yes, like not rejecting the physical necessity involved in a computation.

There is no physical necessity involved in a computation, no more than in an addition or multiplication. You will not find a book on computation referring to any physical notion in the definition. This exists only in philosophical defense on physicalism. The notion of physical computation is complex, and there is no unanimity on whether such notion makes sense or not. With comp, it is an open problem, but it does a priori make sense.

    Oh my, can you not see that the book on computation itself is physical and is thus a case of the necessity of a physical instantiation? You can not seriously tell me that the most obvious fact here is not visible to you.

I reject Platonism on these grounds; it is anti-empirical.

As Brent pointed out, it depends on the theory. Comp is platonist, but makes precise prediction (indeed, that the whole of physics is given by precise theories based on self-reference). This illustrates that platonism can be empirical.

    What ever.

[Quentin Anciaux]

2012/5/23 Stephen P. King <step...@charter.net>

On 5/23/2012 4:47 AM, Bruno Marchal wrote:

On 23 May 2012, at 01:22, Stephen P. King wrote:

On 5/22/2012 6:01 PM, Quentin Anciaux wrote:

2012/5/22 Stephen P. King <step...@charter.net>

 No, Bruno, it is not Neutral monism as such cannot assume any particular as primitive, even if it is quantity itself, for to do such is to violate the very notion of neutrality itself. You might like to spend some time reading Spinoza and Bertrand Russell's discussions of this. I did not invent this line of reasoning.

 Neutral monism, in philosophy, is the metaphysical view that the mental and the physical are two ways of organizing or describing the same elements, which are themselves "neutral," that is, neither physical nor mental.

I don't see how taking N,+,* as primitive is not neutral monism. It is neither physical nor mental.

    If mathematical "objects" are not within the category of Mental then that is news to philosophers...

If mathematical "objects" are within the category of Mental then that is news to mathematicians...

And it is disastrous for those who want study the mental by defining it by the mathematical, as in computer science, cognitive science, artificial intelligence, etc;

    Are we being intentionally unable to understand the obvious? Do we physically interact with mathematical objects? No.

Do you physically interact with the physical ? No ! no mind, no interaction, hence the physical is mental, QED... or what you say is just plain wrong...

Quentin
 

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[Stephen P. King]

Hi Evgenii,

There seems to be a divergence of definitions occurring. It might
be better for me to withdraw from philosophical discussions for a while
and focus just on mathematical questions, like the dependence on order
of a basis...

[Evgenii Rudnyi]

On 23.05.2012 19:43 Stephen P. King said the following:

...

> There seems to be a divergence of definitions occurring. It might be
> better for me to withdraw from philosophical discussions for a while
> and focus just on mathematical questions, like the dependence on
> order of a basis...
>

I believe that to this end, one just needs to number basis vectors, so
we must order them. If I remember correctly, depending on how you order
x, y, z you obtain either a right or left-handed coordinate system.

Evgenii

[Bruno Marchal]

On 23 May 2012, at 19:19, Evgenii Rudnyi wrote:

> On 23.05.2012 10:47 Bruno Marchal said the following:
>>
>> On 23 May 2012, at 01:22, Stephen P. King wrote:
>
> ...
>
>>> If mathematical "objects" are not within the category of Mental
>>> then that is news to philosophers...
>>
>> If mathematical "objects" are within the category of Mental then that
>> is news to mathematicians...
>>
>
> Let us take terms like information, computation, etc. Are they
> mental or mathematical?

Information is vague, and can be both.

Computation is mathematical, by using the Church (Turing Kleene Post
Markov) thesis.

But humans, and any universal machine, can mentally handle and reason
on mathematical notions, implementing or representing them locally.

With comp, trivially, the mental is the doing of a universal numbers.

>
> It might be good simultaneously to extend this question by including
> general terms that people use to describe the word. Are mathematical
> objects then are different from them?

I am not sure I understand what you are asking.

Bruno


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

[Evgenii Rudnyi]

On 23.05.2012 20:01 Bruno Marchal said the following:

I am talking about language that we use to describe the Nature.
Information and computation were just an example. We can however find
also energy, mass, or animal, human being.

I guess that Plato has not limited the Platonia to the mathematical
objects rather it was about ideas. So is my question.

Let me repeat about the fight between realism vs. nominalism. Realism in
this context is different from the modern meaning of the word.

Realism and nominalism in philosophy are related to universals. A simple
example:

A is a person;
B is a person.

Does A is equal to B? The answer is no, A and B are after all different
persons. Yet the question would be if something universal and related to
a term �person� exists objectively (say as an objective attribute).

Realism says that universals do exist independent from the mind,
nominalism that they are just notation and do not exist as such
independently from the mind.

To me this difference "realism vs. nominalism" seems to be related to
the question whether mathematical objects are mental or not.

Evgenii

[Bruno Marchal]

On 23 May 2012, at 19:23, Stephen P. King wrote:

On 5/23/2012 4:47 AM, Bruno Marchal wrote:

On 23 May 2012, at 01:22, Stephen P. King wrote:

On 5/22/2012 6:01 PM, Quentin Anciaux wrote:

2012/5/22 Stephen P. King <step...@charter.net>

 No, Bruno, it is not Neutral monism as such cannot assume any particular as primitive, even if it is quantity itself, for to do such is to violate the very notion of neutrality itself. You might like to spend some time reading Spinoza and Bertrand Russell's discussions of this. I did not invent this line of reasoning.

 Neutral monism, in philosophy, is the metaphysical view that the mental and the physical are two ways of organizing or describing the same elements, which are themselves "neutral," that is, neither physical nor mental.

I don't see how taking N,+,* as primitive is not neutral monism. It is neither physical nor mental.

    If mathematical "objects" are not within the category of Mental then that is news to philosophers...

If mathematical "objects" are within the category of Mental then that is news to mathematicians...

And it is disastrous for those who want study the mental by defining it by the mathematical, as in computer science, cognitive science, artificial intelligence, etc;

    Are we being intentionally unable to understand the obvious? Do we physically interact with mathematical objects? No. Thus they are not in the physical realm.

I can agree, and disagree. Too much fuzzy if you don't make your assumption clear. 

We interact with mathematical objects with our minds, thus they are in the mental realm. Not complicated.

But like programs and music, number can incarnate disks and physical memories, locally. Now you do seem dualist, of the non monist kind.

even more perplexing to me; how is it that the Integers are given such special status,

Because of "digital" in digital mechanism. It is not so much an emphasis on numbers, than on finite.

    So how do you justify finiteness?  I have been accused of having the "everything disease" whose symptom is "the inability to conceive anything but infinite, ill defined ensembles", but in my defense I must state that what I am conceiving is an over-abundance of very precisely defined ensembles. My disease is the inability to properly articulate a written description.

 

especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world?

Not at all. Only "primitively physical" reality is put in doubt.

    Not me. I already came to the conclusion that reality cannot be primitively physical.

You are unclear on what you posit. You always came back to the "physical reality" point, so I don't know what more to say... either you agree physical reality is not ontologically primitive or you don't, there's no in between position.

    We have to start at the physical reality that we individually experience, it is, aside from our awareness, the most "real" thing we have to stand upon philosophically.

The most "real" things might be consciousness, here and now.  And this doesn't make consciousness primitive, but invite us to be methodologically skeptical on the physical, as we know since the "dream argument".

    The only person that is making it, albeit indirectly by implication, is you, Bruno. You think that you are safe

?

because you believe that you have isolated mathematics from the physical and from the contingency of having to be known by particular individuals,

?

but you have not over come the basic flaw of Platonism: if you disconnect the Forms from consciousness you forever prevent the act of apprehension. You seem to think that property definiteness is an ontological a priori. You are not the first, E. Kant had the same delusion.

?

(I only argue, showing the consistency and inconsistency of set of beliefs, in the comp theory).

From there we venture out in our speculations as to our ontology. cosmogony and epistemology. is there an alternative?

So you start from physics? This contradicts your neutral monism.

    So you do need a diagram to understand a simple idea.

 

Without the physical world to act as a "selection" mechanism for what is "Real",

This contradicts your neutral monism.

 

    No, it does not. Please see my discussion of neutral monism above.

Yes it does, reading you, you posit a physical material reality as primitive, which is not neutral...

    No, I posit the physical and the mental as "real" in the sense that I am experiencing them.

You can't experience the physical. The physical is inferred from theory, even if automated by years of evolution.

    We cannot experience anything directly, except for our individual consciousness, all else is inferred.

OK, so we agree on this. (it contradicts your sentence above). I guess it is your dyslexia and that you were meaning:

"No, I posit the physical, and the mental is "real" in the sense that I am experiencing it."

Where I posit means I infer it. 

Telescoping out to the farthest point of abstraction we have ideas like Bruno's.  I guess that I need to draw some diagrams...

Not ideas. Universal truth following a deduction in a theoretical frame. It is just a theorem in applied logic: if we are digital machine, then physics (whatever inferable from observable)  is derivable from arithmetic. Adding anything to it, *cannot* be of any use (cf UDA step 7 and 8).

You are free to use any philosophy you want to *find* a flaw in the reasoning, but a philosophical conviction does not refute it by itself.

If you think there is a loophole, just show it to us.

why the bias for integers?

Because comp = machine, and machine are supposed to be of the type "finitely describable".

    This is true only after the possibility of determining differences is stipulated. One cannot assume a neutral monism that stipulates a non-neutral stance, to do so it a contradiction.

Computationalism is the theory that your consciousness can be emulated on a turing machine, a program is a finite object and can be described by an integer. I don't see a contradiction.

    I am with Penrose in claiming that consciousness is not emulable by a finite machine.

This contradicts your statement that your theory is consistent with comp (as it is not, as I argue to you). You are making my point. It took time.

    You have no idea what "my theory" is.

I can't deny.

 

This has been a question that I have tried to get answered to no avail.

You don't listen. This has been repeated very often. When you say "yes" to the doctor, you accept that you survive with a computer executing a code. A code is mainly a natural number, up to computable isomorphism. Comp refers to computer science, which study the computable function, which can always be recasted in term of computable function from N to N.

And there are no other theory of computability, on reals or whatever, or if you prefer, there are too many, without any Church thesis or genuine universality notion. (Cf Pour-Hel, Blum Shub and Smale, etc.)

    I do listen and read as well. Now it is your turn. The entire theory of computation rests upon the ability to distinguish quantity from non-quantity, even to the point of the possibility of the act of making a distinction. When you propose a primitive ground that assumes a prior distinction and negates the prior act that generated the result, you are demanding the belief in fiat acts. This is familiar to me from my childhood days of sitting in the pew of my father's church. It is an act of blind faith, not evidence based science. Please stop pretending otherwise.

"evidence based science" ??

    Yes, like not rejecting the physical necessity involved in a computation.

There is no physical necessity involved in a computation, no more than in an addition or multiplication. You will not find a book on computation referring to any physical notion in the definition. This exists only in philosophical defense on physicalism. The notion of physical computation is complex, and there is no unanimity on whether such notion makes sense or not. With comp, it is an open problem, but it does a priori make sense.

    Oh my, can you not see that the book on computation itself is physical

No, I cannot see that, and what you say would contradict again that you have just admit that you posit the physical. You infer it, you don't see it. 

Unless you mean by physical "relatively consistent with my most probable local computations".

and is thus a case of the necessity of a physical instantiation?

It is not. I mean not in the primitive sense. 

You can not seriously tell me that the most obvious fact here is not visible to you.

It is not visible. It is inferred abductively, or imagined, conceived, possible, but out of reach of experiments and experience. 

But its appearance can be explained, without needing to make it ontological.

Bruno

I reject Platonism on these grounds; it is anti-empirical.

As Brent pointed out, it depends on the theory. Comp is platonist, but makes precise prediction (indeed, that the whole of physics is given by precise theories based on self-reference). This illustrates that platonism can be empirical.

    What ever.

-- 
Onward!

Stephen

"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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

[Bruno Marchal]

On 23 May 2012, at 19:08, meekerdb wrote:

> On 5/23/2012 8:47 AM, Bruno Marchal wrote:
>> Hmm... I agree with all your points in this post, except this one.
>> The comp "model" (theory) has much more predictive power than
>> physics, given that it predicts the whole of physics,
>
> It's easy to predict the whole of physics; just predict that
> everything happens. But that's not predictive power.

I will take it that you are forgetting the whole argument. When I
say that it predicts the whole physics, I mean it literally. And not
everything happens only something like what is described by the
physical theories, except that physicists derive them from "direct"
observation, and comp derives them by the logic of universal machine
observable.

Physics, with comp, and arguably already with QM, is not at all
"everything happens", but more "everything interfere" leading to non
trivial symmetries and symmetries breaking, etc.

Bruno

>
> Brent
>
>> and the whole of what that physics predicts (and this without
>> mentioning that it predicts the whole qualia part too, unlike the
>> "physics model"). But it does it in a very more difficult way,
>> without "copying on nature".
>>
>> Of course it might be false. It might be that comp leads to a
>> different mass for the electron or to the non existence of
>> electrons. But comp, together with some definition of knowledge,
>> predicts physics quantitatively and qualitatively.
>>
>> Of course to use comp to predict an eclipse is not yet in its
>> range, if it can ever be. To use comp for this, would be like using
>> string theory to prepare a cup of tea. But the goal is not to do
>> physics, just to formulate the mind-body problem, and figure out
>> the less wrong bigger picture.
>>
>> Bruno
>

[meekerdb]

On 5/23/2012 11:28 AM, Bruno Marchal wrote:
>
> On 23 May 2012, at 19:08, meekerdb wrote:
>
>> On 5/23/2012 8:47 AM, Bruno Marchal wrote:
>>> Hmm... I agree with all your points in this post, except this one. The comp "model"
>>> (theory) has much more predictive power than physics, given that it predicts the whole
>>> of physics,
>>
>> It's easy to predict the whole of physics; just predict that everything happens. But
>> that's not predictive power.
>
> I will take it that you are forgetting the whole argument. When I say that it predicts
> the whole physics, I mean it literally. And not everything happens only something like
> what is described by the physical theories, except that physicists derive them from
> "direct" observation, and comp derives them by the logic of universal machine observable.
>
> Physics, with comp, and arguably already with QM, is not at all "everything happens",
> but more "everything interfere" leading to non trivial symmetries and symmetries
> breaking, etc.
>
> Bruno

I don't see that comp has predicted anything except uncertainty. Can comp explain the
reason QM is based on complex Hilbert space instead or real, or quaternion, or octonion?
Can it explain where the mass gap comes from? Can it predict the dimensionality of
spacetime? Can it tell whether spacetime is discrete at some level?

Brent

[Hal Ruhl]

Hi Brent:

What you appear to be asking for are predictions of the physics of a
particular universe.

My belief is that the best we can do is to predict the components of physics
common to every evolving universe.

My efforts have focused on understanding why there is a dynamic within the
Everything [such as UDs] and what "observers" in a universe containing them
are observing.

In my model I have identified a dynamic driver [incompleteness] and what
observers observe [TRANSITIONS between universe states].

Since I do not prohibit computations, I believe Comp [including any
prediction of QM in many universes] is allowed within my model but is not
the only descriptor of universe evolution. Many evolving universes may
contain no such computational component.

Hal Ruhl

[meekerdb]

On 5/23/2012 1:20 PM, Hal Ruhl wrote:

Hi Brent:

What you appear to be asking for are predictions of the physics of a
particular universe.

It's the other extreme from 'predicting' everything happens. Since we only have the one physical universe against which to test the prediction, it's the only kind of prediction that means anything.

Brent

[Hal Ruhl]

Hi Brent:

 

I ask if it is reasonable to propose that a theory of everything must be able to list ALL the aspects of the local physics for each one of a complete catalog of universes?

 

Suppose ours is just number 9,876,869,345 in the catalog.  Would we ever complete such a project within the “observers present”  lifetime of our universe? 

 

My current belief is that Comp is a broad brush description of a subset of universes within my own model.  If Bruno thinks his approach is more precise than that I do not have a problem with that.

 

My model appears to answer my questions about the basis of dynamics within the everything and a response as to what “observers” observe.

 

Perhaps this sort of level is all we can expect, but it is, I believe, necessary to police the results so that most individuals can eventually “sign on” some day.  For example we sure need in my opinion a substantially increased level of comprehension of economics which is actually a result of any local physics.  I can’t accomplish this re most of Bruno’s work since I am definitely not “adequate” in the relevant logic disciplines.

 

Hal Ruhl

 

 

From: everyth...@googlegroups.com [mailto:everyth...@googlegroups.com] On Behalf Of meekerdb
Sent: Wednesday, May 23, 2012 4:41 PM
To: everyth...@googlegroups.com
Subject: Re: The limit of all computations

 

On 5/23/2012 1:20 PM, Hal Ruhl wrote:

--

[meekerdb]

On 5/23/2012 4:42 PM, Hal Ruhl wrote:

Hi Brent:

 

I ask if it is reasonable to propose that a theory of everything must be able to list ALL the aspects of the local physics for each one of a complete catalog of universes?

But I wasn't asking for ALL the aspects, just a few very general ones which are questions in current research, meaning there's a chance we might be able to check the predictions.

Brent

[Hal Ruhl]

Hi Brent:

 

I shall try to respond tomorrow.

 

Hal Ruhl

 

From: everyth...@googlegroups.com [mailto:everyth...@googlegroups.com] On Behalf Of meekerdb
Sent: Wednesday, May 23, 2012 8:41 PM
To: everyth...@googlegroups.com
Subject: Re: The limit of all computations

 

On 5/23/2012 4:42 PM, Hal Ruhl wrote:

--

[Bruno Marchal]

On 23 May 2012, at 21:51, meekerdb wrote:

> On 5/23/2012 11:28 AM, Bruno Marchal wrote:
>>
>> On 23 May 2012, at 19:08, meekerdb wrote:
>>
>>> On 5/23/2012 8:47 AM, Bruno Marchal wrote:
>>>> Hmm... I agree with all your points in this post, except this
>>>> one. The comp "model" (theory) has much more predictive power
>>>> than physics, given that it predicts the whole of physics,
>>>
>>> It's easy to predict the whole of physics; just predict that
>>> everything happens. But that's not predictive power.
>>
>> I will take it that you are forgetting the whole argument. When I
>> say that it predicts the whole physics, I mean it literally. And
>> not everything happens only something like what is described by the
>> physical theories, except that physicists derive them from "direct"
>> observation, and comp derives them by the logic of universal
>> machine observable.
>>
>> Physics, with comp, and arguably already with QM, is not at all
>> "everything happens", but more "everything interfere" leading to
>> non trivial symmetries and symmetries breaking, etc.
>>
>> Bruno
>
> I don't see that comp has predicted anything except uncertainty.

UDA predicts indeterminacy, non locality and non cloning. But also
"physics", which physicists take for granted. That UDA explains why
there are appearance of a physical reality (despite its lack of
ontology).

But AUDA does the same thing, + the set of all precise experience
which could refute comp.

> Can comp explain the reason QM is based on complex Hilbert space
> instead or real, or quaternion, or octonion?

Yes. It should. Probably by showing that they provides the canonical
semantics for the arithmetical quantum logic.
But if you grasp the proof, you know that physics is entirely
derivable from arithmetic.

> Can it explain where the mass gap comes from? Can it predict the
> dimensionality of spacetime? Can it tell whether spacetime is
> discrete at some level?

Yes. it has too, or comp is wrong. Now, in AUDA, some variation are
possible, by adopting more constrained definition of knowledge.

Now the goal was not doing physics, but understanding where physics
comes from, and why it separates into quanta and qualia. UDA reduces
the mind-body problem into that type of explanation. physicists just
ignore such question, for they take both the physical universe for
granted and primitive, and they assume an identity thesis, or a
supervenience thesis, which presuppose implicitly non Turing
emulability of the mind.

Bruno


>
> Brent

[Bruno Marchal]

> and related to a term “person” exists objectively (say as an

> objective attribute).
>
> Realism says that universals do exist independent from the mind,
> nominalism that they are just notation and do not exist as such
> independently from the mind.

But that distinction is usually made in the aristotelian context,
where some concrete physical universe is postulated. With comp we know
this is not possible.
You can restate it by saying that the natural numbers are concrete,
but that a property like 'being prime" is abstract. Then
mathematicians are mostly realist, because they believe that "being
prime" is an independent property of natural numbers.
for a mechanical generable set, like the set of prime numbers, you can
come back to nominalism through Gödel numbering, and through the
identification of the concept of primes with the number (machine)
which generates all and only the prime numbers. But this leads to
difficulties for the non mechanically generable sets of numbers, which
*do* play a role in the machine/numbers points of view.

>
> To me this difference "realism vs. nominalism" seems to be related
> to the question whether mathematical objects are mental or not.

But with comp, mental is a number's attributes. And eventually
"physical" is a collection of number attribute. If you make
mathematical object mental, and *only* mental, you have to tell me
what you assume at the start in the theory. If you chose something
physical, then you have to abandon comp, and you have to tell how you
relate mental and physical, by using provably non Turing emulable
components. You will lose also the explanation of why something
physical exist, and why it hurts.

Bruno


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

[Russell Standish]

On Wed, May 23, 2012 at 04:41:56PM +0200, Bruno Marchal wrote:
>
> To be sure I usually use "->" for the material implication, that is
> "a -> b" is indeed "not a or b" (or "not(a and not b)").
>
> The IF ... THEN used in math is generally of that type.
>
> I use a => b for "from a I can derive b, in the theory I am
> currently considering".

Actually, thinking about your thesis, I don't recall you ever once
using the symbol =>. Instead, you tend to write

a
-
b

I do appreciate the distinction, though!

>
> For any theory having the modus ponens rule, we have that "a -> b"
> entails (yet at another meta-level) "a => b". This should be
> trivial.
> For many quite standard logics, the reciprocal is correct too, that
> is: "a = > b" entails "a -> b". This is usually rather hard to
> prove (Herbrand or deduction theorem). It is typically false in
> modal logic or in many weak logics. For example the normal modal
> logics (those having Kripke semantics, like G, S4, ...) are all
> close for the rule a => Ba, but virtually none can prove the formula
> a -> Ba. This is a source of many errors.
>
> Simple Exercises (for those remembering Kripke semantics):
> 1) find a Kripke model falsifying "a -> Ba".
> 2) explain to yourself why "a => Ba" is always the case in all
> Kripke models.
>
> I recall that a Kripke model is a set (of "worlds") with a binary
> relation (accessibility relation). The key is that Ba is true in a
> world Alpha is a is true in all worlds Beta such that (Alpha, Beta)
> is in the accessibility relation.
>

Why is a => Ba true in Kripke models? Surely, it is possible for a to
be true, yet false in some successor world?

[Bruno Marchal]

You are right, but this shows only that "a -> Ba" is false in the
world you are in.

But "a => Ba" is a valid rule for all logic having a Kripke semantics.
Why? Because it means that a is supposed to be valid (for example you
have already prove it), so a, like any theorem, will be true in all
worlds, so a will be in particular true in all worlds accessible from
anywhere in the model, so Ba will be true in all worlds of the model,
so Ba is also a theorem.

"->" is the implication, but "=>" concerns deduction. In fact "a =>
Ba" should not be said true, or false, only valid, or non valid. It is
a rule of inference. It means for example that from a proof of a, you
can deduce a proof of Ba. And this is correct in the Kripke model,
because a proof of a makes a true in *all* worlds (of the appropriate
Kripke structure).

Bruno


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

[meekerdb]

Isn't "a=>Ba" trivially true since every axiom is a theorem?

>>>
>>> I recall that a Kripke model is a set (of "worlds") with a binary
>>> relation (accessibility relation). The key is that Ba is true in a
>>> world Alpha is a is true in all worlds Beta such that (Alpha, Beta)
>>> is in the accessibility relation.
>>>
>>
>> Why is a => Ba true in Kripke models? Surely, it is possible for a to
>> be true, yet false in some successor world?
>
> You are right, but this shows only that "a -> Ba" is false in the world you are in.

I'm confused. ~[a->Ba] means a is true but not provable (i.e. Ba is false) in the world
you are in? Why is proof relative to the world you are in?

> it means that a is supposed to be valid (for example you have already prove it), so a,
> like any theorem, will be true in all worlds, so a will be in particular true in all
> worlds accessible from anywhere in the model, so Ba will be true in all worlds of the
> model, so Ba is also a theorem.
>
> "->" is the implication, but "=>" concerns deduction. In fact "a => Ba" should not be
> said true, or false, only valid, or non valid. It is a rule of inference. It means for
> example that from a proof of a, you can deduce a proof of Ba.

Doesn't that last sentence say Ba=>BBa?

> And this is correct in the Kripke model, because a proof of a makes a true in *all*
> worlds (of the appropriate Kripke structure).

So Ba->a but ~[(a=>Ba)->a]?

Brent

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

[Bruno Marchal]

"a" alone can be read as "a is true".
If "a => Ba" was a valid rule, and reading B as provable, it would
mean that if a is true then a is provable. Incompleteness provide a
counter-example. Dt is true (for PA), but not provable (by PA).
So "a => Ba" is not a valid rule, and "a -> Ba" is not always a true
proposition (Dt -> BDt is false).

Note that a -> Ba is true if a is a sigma_1 proposition, and B is the
provability modality of any sigma_1 complete theory.

x -> Bx asserts a form of completeness, like Bx -> x asserts a form of
correctness or soundness.

>
>>>>
>>>> I recall that a Kripke model is a set (of "worlds") with a binary
>>>> relation (accessibility relation). The key is that Ba is true in a
>>>> world Alpha is a is true in all worlds Beta such that (Alpha, Beta)
>>>> is in the accessibility relation.
>>>>
>>>
>>> Why is a => Ba true in Kripke models? Surely, it is possible for a
>>> to
>>> be true, yet false in some successor world?
>>
>> You are right, but this shows only that "a -> Ba" is false in the
>> world you are in.
>
> I'm confused. ~[a->Ba] means a is true but not provable (i.e. Ba is
> false) in the world you are in? Why is proof relative to the world
> you are in?

By definition of the Kripke semantics. Truth is relativized to worlds.
Then, for the Gödelian provability, it just happens, by Solovay
theorem, that it obeys a normal modal logic, (G), which means it has a
Kripke semantics. You can interpret a world by a model (in the sense
of model theory).

>
>> it means that a is supposed to be valid (for example you have
>> already prove it), so a, like any theorem, will be true in all
>> worlds, so a will be in particular true in all worlds accessible
>> from anywhere in the model, so Ba will be true in all worlds of the
>> model, so Ba is also a theorem.
>>
>> "->" is the implication, but "=>" concerns deduction. In fact "a =>
>> Ba" should not be said true, or false, only valid, or non valid. It
>> is a rule of inference. It means for example that from a proof of
>> a, you can deduce a proof of Ba.
>
> Doesn't that last sentence say Ba=>BBa?

It does imply it, but if B is self-referential, it is equivalent with
Ba -> BBa.

>
>> And this is correct in the Kripke model, because a proof of a makes
>> a true in *all* worlds (of the appropriate Kripke structure).
>
> So Ba->a but ~[(a=>Ba)->a]?

This is meaningless, as you can't mix "=>" and "->".
~[(a=>Ba)->a] is neither a formula, nor a rule.

Bruno


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

[Evgenii Rudnyi]

On 24.05.2012 09:52 Bruno Marchal said the following:

>
> On 23 May 2012, at 20:19, Evgenii Rudnyi wrote:

...

>> nominalism that they are just notation and do not exist as such
>> independently from the mind.
>
> But that distinction is usually made in the aristotelian context,
> where some concrete physical universe is postulated. With comp we
> know this is not possible. You can restate it by saying that the
> natural numbers are concrete, but that a property like 'being prime"
> is abstract. Then mathematicians are mostly realist, because they
> believe that "being prime" is an independent property of natural
> numbers. for a mechanical generable set, like the set of prime

> numbers, you can come back to nominalism through G�del numbering, and

> through the identification of the concept of primes with the number
> (machine) which generates all and only the prime numbers. But this
> leads to difficulties for the non mechanically generable sets of
> numbers, which *do* play a role in the machine/numbers points of
> view.
>
>
>>
>> To me this difference "realism vs. nominalism" seems to be related
>> to the question whether mathematical objects are mental or not.
>
> But with comp, mental is a number's attributes. And eventually
> "physical" is a collection of number attribute. If you make
> mathematical object mental, and *only* mental, you have to tell me
> what you assume at the start in the theory. If you chose something
> physical, then you have to abandon comp, and you have to tell how you
> relate mental and physical, by using provably non Turing emulable
> components. You will lose also the explanation of why something
> physical exist, and why it hurts.
>

In my view, it would be nicer to treat such a question historically.
Your position based on your theorem, after all, is one of possible
positions. In your paper to express your position you employ a normal
human language. Hence I believe that that the question about general
terms in the human language is the same as about the natural numbers.

Again, the ideal world of Plato was not designed for natural numbers only.

Evgenii

[Bruno Marchal]

On 26 May 2012, at 08:47, Evgenii Rudnyi wrote:

> On 24.05.2012 09:52 Bruno Marchal said the following:
>>
>> On 23 May 2012, at 20:19, Evgenii Rudnyi wrote:
>
> ...
>
>>> nominalism that they are just notation and do not exist as such
>>> independently from the mind.
>>
>> But that distinction is usually made in the aristotelian context,
>> where some concrete physical universe is postulated. With comp we
>> know this is not possible. You can restate it by saying that the
>> natural numbers are concrete, but that a property like 'being prime"
>> is abstract. Then mathematicians are mostly realist, because they
>> believe that "being prime" is an independent property of natural
>> numbers. for a mechanical generable set, like the set of prime

>> numbers, you can come back to nominalism through Gödel numbering, and

>> through the identification of the concept of primes with the number
>> (machine) which generates all and only the prime numbers. But this
>> leads to difficulties for the non mechanically generable sets of
>> numbers, which *do* play a role in the machine/numbers points of
>> view.
>>
>>
>>>
>>> To me this difference "realism vs. nominalism" seems to be related
>>> to the question whether mathematical objects are mental or not.
>>
>> But with comp, mental is a number's attributes. And eventually
>> "physical" is a collection of number attribute. If you make
>> mathematical object mental, and *only* mental, you have to tell me
>> what you assume at the start in the theory. If you chose something
>> physical, then you have to abandon comp, and you have to tell how you
>> relate mental and physical, by using provably non Turing emulable
>> components. You will lose also the explanation of why something
>> physical exist, and why it hurts.
>>
>
> In my view, it would be nicer to treat such a question historically.
> Your position based on your theorem, after all, is one of possible
> positions.

What do you mean by "my position"? I don't think I defend a position.
I do study the consequence of comp, if only to give a chance to a real
non-comp theory.

> In your paper to express your position you employ a normal human
> language. Hence I believe that that the question about general terms
> in the human language is the same as about the natural numbers.

? (I can agree and disagree, it is too vague)

>
> Again, the ideal world of Plato was not designed for natural numbers
> only.

Sure. Although it begins with "natural numbers only", and it ended on
this, somehow, because the neoplatonists were aware of the importance
of numbers and were coming back to Pythagorean form of platonism.

Now, with comp, or just with Church thesis, there is a sort of
rehabilitation of the Pythagorean view, for the "non natural numbers"
reappears in the natural number realm as unavoidable epistemic tools
for the natural numbers to understand themselves, and anymore than
numbers (and their basic laws) is not just unnecessary, it is that it
cannot work without adding some explicit non-comp magic.

I am not against non-comp, but I am against any gap-theory, where we
introduce something in the ontology to make a problem unsolvable
leading to "don't ask" policy.

Bruno


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

[Evgenii Rudnyi]

On 26.05.2012 11:30 Bruno Marchal said the following:

>
> On 26 May 2012, at 08:47, Evgenii Rudnyi wrote:

...

>> In my view, it would be nicer to treat such a question
>> historically. Your position based on your theorem, after all, is
>> one of possible positions.
>
> What do you mean by "my position"? I don't think I defend a position.
> I do study the consequence of comp, if only to give a chance to a
> real non-comp theory.

A position that the natural numbers are the foundation of the world. I
agree that you often repeat the assumption for your theorem but I
believe that your answers to my question have been answered exactly from
such a position.

>
>> In your paper to express your position you employ a normal human
>> language. Hence I believe that that the question about general
>> terms in the human language is the same as about the natural
>> numbers.
>
> ? (I can agree and disagree, it is too vague)

When we talk with each other and make proofs we use a human language.
Hence to make sure that we can make universal proofs by means of a human
language, it might be good to reach an agreement on what it is.

>>
>> Again, the ideal world of Plato was not designed for natural
>> numbers only.
>
> Sure. Although it begins with "natural numbers only", and it ended on
> this, somehow, because the neoplatonists were aware of the
> importance of numbers and were coming back to Pythagorean form of
> platonism.
>
> Now, with comp, or just with Church thesis, there is a sort of
> rehabilitation of the Pythagorean view, for the "non natural numbers"
> reappears in the natural number realm as unavoidable epistemic tools
> for the natural numbers to understand themselves, and anymore than
> numbers (and their basic laws) is not just unnecessary, it is that it
> cannot work without adding some explicit non-comp magic.
>
> I am not against non-comp, but I am against any gap-theory, where we
> introduce something in the ontology to make a problem unsolvable
> leading to "don't ask" policy.

We are back to a human language. It seems that you mean that some
constructions expressed by it do not make sense. It well might be but
again we have to discuss the language then.

As for comp, I have written once

Simulation Hypothesis and Simulation Technology
http://blog.rudnyi.ru/2011/09/simulation-hypothesis-and-simulation-technology.html

that practically speaking it just does not work. I understand that you
talk in principle but how could we know if comp in principle is true if
we cannot check it in practice?

I personally find an extrapolation of a working model outside of its
scope that has been researched pretty dangerous.

Evgenii

[Pzomby]

Hi Evgenii

 

Here is another opinion on the need for language: 

 

Simulations, models, emulations, replications, depictions, representations, symbols, are different then existent instantiations, exemplifications of the observable universe that are described by mathematics combined with the human language constructs of units of measurement. 

 

It seems that the existent observable physical universe *encodes* mathematics that human observers combine it with *necessary* language created conventions of units of measurement that can be computed and it (mathematics & language) then describes its appearance. 

[Bruno Marchal]

On 26 May 2012, at 16:48, Evgenii Rudnyi wrote:

> On 26.05.2012 11:30 Bruno Marchal said the following:
>>
>> On 26 May 2012, at 08:47, Evgenii Rudnyi wrote:
>
> ...
>
>>> In my view, it would be nicer to treat such a question
>>> historically. Your position based on your theorem, after all, is
>>> one of possible positions.
>>
>> What do you mean by "my position"? I don't think I defend a position.
>> I do study the consequence of comp, if only to give a chance to a
>> real non-comp theory.
>
> A position that the natural numbers are the foundation of the world.

I don't defend that position. I show it to be a consequence of the
comp hypothesis + occam razor.

> I agree that you often repeat the assumption for your theorem but I
> believe that your answers to my question have been answered exactly
> from such a position.

That is possible, that is why I repeat ad nauseam that I assume comp,
not that I defend that theory, only that that it is testable.
It gives also a rational alternative with less magic notion, like
primitive matter, or consciousness.

UDA is an argument showing that if the brain (in a large sense) is a
machine at some level, then the natural numbers, or their universal
cousins, are the foundation of the web of interfering computations on
worlds supervenes.

>
>>
>>> In your paper to express your position you employ a normal human
>>> language. Hence I believe that that the question about general
>>> terms in the human language is the same as about the natural
>>> numbers.
>>
>> ? (I can agree and disagree, it is too vague)
>
> When we talk with each other and make proofs we use a human
> language. Hence to make sure that we can make universal proofs by
> means of a human language, it might be good to reach an agreement on
> what it is.

This is an impossible task. That is why I use the semi-axiomatic
method (in UDA), and math in AUDA.
If you disagree with a method of reasoning, you have to explain why.
In english, no problem.

>
>>>
>>> Again, the ideal world of Plato was not designed for natural
>>> numbers only.
>>
>> Sure. Although it begins with "natural numbers only", and it ended on
>> this, somehow, because the neoplatonists were aware of the
>> importance of numbers and were coming back to Pythagorean form of
>> platonism.
>>
>> Now, with comp, or just with Church thesis, there is a sort of
>> rehabilitation of the Pythagorean view, for the "non natural numbers"
>> reappears in the natural number realm as unavoidable epistemic tools
>> for the natural numbers to understand themselves, and anymore than
>> numbers (and their basic laws) is not just unnecessary, it is that it
>> cannot work without adding some explicit non-comp magic.
>>
>> I am not against non-comp, but I am against any gap-theory, where we
>> introduce something in the ontology to make a problem unsolvable
>> leading to "don't ask" policy.
>
> We are back to a human language. It seems that you mean that some
> constructions expressed by it do not make sense. It well might be
> but again we have to discuss the language then.

I don't see why we have to discuss language, apart from the machines
and their languages.

>
> As for comp, I have written once
>
> Simulation Hypothesis and Simulation Technology
> http://blog.rudnyi.ru/2011/09/simulation-hypothesis-and-simulation-technology.html
>
> that practically speaking it just does not work. I understand that
> you talk in principle but how could we know if comp in principle is
> true if we cannot check it in practice?

The whole point is that we can check it, at least if you accept the
classical theory of knowledge. Physics arise from number self-
reference in a precise constrained way, and the logic of observable
already give rise to quantum-like logic.
If mechanism is false, we can know it. If it is true we can only bet
on it, and the bet or not on some level of substitution. The facts
(Everett QM) gives evidence that our first person plural is given by
the electronic orbital, our stories does not depend on the precise
position of electron in those orbitals.

>
> I personally find an extrapolation of a working model outside of its
> scope that has been researched pretty dangerous.

I am just showing that computationalism (widespread) and materialism
(widespread) are incompatible. I reason only, and I extrapolate less
than Aristotelians.

Bruno


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

[Evgenii Rudnyi]

On 26.05.2012 21:06 Bruno Marchal said the following:

>
> On 26 May 2012, at 16:48, Evgenii Rudnyi wrote:
>
>> On 26.05.2012 11:30 Bruno Marchal said the following:
>>>
>>> On 26 May 2012, at 08:47, Evgenii Rudnyi wrote:
>>
>> ...
>>
>>>> In my view, it would be nicer to treat such a question
>>>> historically. Your position based on your theorem, after all,
>>>> is one of possible positions.
>>>
>>> What do you mean by "my position"? I don't think I defend a
>>> position. I do study the consequence of comp, if only to give a
>>> chance to a real non-comp theory.
>>
>> A position that the natural numbers are the foundation of the
>> world.
>
> I don't defend that position. I show it to be a consequence of the
> comp hypothesis + occam razor.

I do appreciate the clearness of your position. From this viewpoint, the
language of mathematics allows us to remove ambiguities indeed.

...

>>
>> When we talk with each other and make proofs we use a human
>> language. Hence to make sure that we can make universal proofs by
>> means of a human language, it might be good to reach an agreement
>> on what it is.
>
> This is an impossible task. That is why I use the semi-axiomatic
> method (in UDA), and math in AUDA. If you disagree with a method of
> reasoning, you have to explain why. In english, no problem.

I also agree that human language in a way is a mess. Yet, somehow it
seems to work and this puzzles my, how it could happen when even
mathematicians failed to analyze it.

...

>>> I am not against non-comp, but I am against any gap-theory, where
>>> we introduce something in the ontology to make a problem
>>> unsolvable leading to "don't ask" policy.
>>
>> We are back to a human language. It seems that you mean that some
>> constructions expressed by it do not make sense. It well might be
>> but again we have to discuss the language then.
>
> I don't see why we have to discuss language, apart from the machines
> and their languages.

It seems that there is a gap between the language of mathematics and a
human language. It might be interesting to understand it. It might give
us a hint on how the Universe is made. You see, we must use a human
language to communicate, with the language of mathematics this would not
work. I do not know why.

>>
>> As for comp, I have written once
>>
>> Simulation Hypothesis and Simulation Technology
>> http://blog.rudnyi.ru/2011/09/simulation-hypothesis-and-simulation-technology.html
>>
>>
>>
>> that practically speaking it just does not work. I understand that
>> you talk in principle but how could we know if comp in principle is
>> true if we cannot check it in practice?
>
> The whole point is that we can check it, at least if you accept the
> classical theory of knowledge. Physics arise from number

> self-reference in a precise constrained way, and the logic of

> observable already give rise to quantum-like logic. If mechanism is
> false, we can know it. If it is true we can only bet on it, and the
> bet or not on some level of substitution. The facts (Everett QM)
> gives evidence that our first person plural is given by the
> electronic orbital, our stories does not depend on the precise
> position of electron in those orbitals.
>
>
>>
>> I personally find an extrapolation of a working model outside of
>> its scope that has been researched pretty dangerous.
>
> I am just showing that computationalism (widespread) and materialism
> (widespread) are incompatible. I reason only, and I extrapolate less
> than Aristotelians.

I am afraid that reason only is not enough to understand Nature. I am
browsing now The Soul of Science: Christian Faith and Natural
Philosophy. Let me give a quote that in an enjoyable way expresses my
thought above.

p. 19 "In 1277 Etienne Tempier, Bishop of Paris, issued a condemnation
of several theses derived from Aristotelianism - that God could not
allow any form of planetary motion other than circular, that He could
not make a vacuum, and many more. The condemnation of 1277 helped
inspire a form of theology known as voluntarism, which admitted no
limitations on God�s power. It regarded natural law not as Forms
inherent within nature but as divine commands imposed from outside
nature. Voluntarism insisted that the structure of the universe -
indeed, its very existence - is not rationally necessary but is
contingent upon the free and transcendent will of God."

"One of the most important consequences of voluntarist theology for
science is that it helped to inspire and justify an experimental
methodology. For if God created freely rather than by logical necessity,
then we cannot gain knowledge of it by logical deduction (which traces
necessary connections). Instead, we have to go out and look, to observe
and experiment. As Barbour puts it:

'The world is orderly and dependable because God is trustworthy and not
capricious; but the details of the world must be found by observation
rather than rational deduction because God is free and did not have to
create any particular kind of universe.'"

Evgenii

[Russell Standish]

On Thu, May 24, 2012 at 03:42:15PM +0200, Bruno Marchal wrote:
>
> But "a => Ba" is a valid rule for all logic having a Kripke
> semantics. Why? Because it means that a is supposed to be valid (for
> example you have already prove it), so a, like any theorem, will be
> true in all worlds, so a will be in particular true in all worlds
> accessible from anywhere in the model, so Ba will be true in all
> worlds of the model, so Ba is also a theorem.

I still don't follow. If I have proved a is true in some world, why
should I infer that it is true in all worlds? What am I missing?

[Bruno Marchal]

On 27 May 2012, at 12:15, Russell Standish wrote:

> On Thu, May 24, 2012 at 03:42:15PM +0200, Bruno Marchal wrote:
>>
>> But "a => Ba" is a valid rule for all logic having a Kripke
>> semantics. Why? Because it means that a is supposed to be valid (for
>> example you have already prove it), so a, like any theorem, will be
>> true in all worlds, so a will be in particular true in all worlds
>> accessible from anywhere in the model, so Ba will be true in all
>> worlds of the model, so Ba is also a theorem.
>
> I still don't follow. If I have proved a is true in some world, why
> should I infer that it is true in all worlds? What am I missing?

1) You might be missing the soundness theorem, perhaps.

I give an example with classical propositional logic. Suppose that you
prove some formula, like (p & q)->q, then automatically the formula is
true in all propositional worlds (which are given by the valuation of
the atomic propositions).
Indeed you can verify that (p & q)->q is true in the four type of
possible worlds (those with p true and q true, p true and q false, p
false and q true, and p false and q false).

That is related to the idea that a valid proof does not depend on the
world, or interpretations, or contexts, etc. So if you prove something
it has to be true in all world, and that is why logicians favor
theories having a semantics such that they can prove a soundness
theorem. Of course they are even more happy when they have a theory
with a completeness theorem, which provides the opposite: all
proposition true in all interpretations (model, worlds, ...) can be
proved in the theory. This is the case for all first order theory. So
RA, PA, ZF are complete in that sense. M proves p iff p is true in all
models (interpretation, worlds) of p. Of course they are incomplete in
the "incompleteness" sense. Gödel proved the completeness theory PA,
and actually of all first order theories (in his PhD thesis, 1930),
and the incompleteness of PA (actually of PM, 1931).
So completeness in "completeness theorem and incompleteness theorem",
is used in different sense:

Keep in mind that the completeness theorem asserts that if M proves p,
then p is true in all models of M.

OK?

2) You might perhaps also be missing, or not taking into account
consciously enough, Kripke semantics. In that case we have the same
language as propositional calculus, + the unary connector or operator B.

Unlike ~p, whose truth value depends only of the value of p, Bp value
is not functionally dependent of the truth value of p.

Now, a modal logic theory which has the formula K (for Kripke) B(p->q)-
>(Bp->Bp), and whose set of theorems is closed for the modus ponens
rule (a, a->b) / b, but also the necessitation rule (p / Bp), can be
given a so called Kripke semantics (due indeed to Kripke, around 1968,
I think). [I write (p/BP) instead of p => Bp, to avoid confusion with
"->"].

In that semantics, you have a referential (any set with a binary
relation). The elements of the set are called world and designate by
greek letters, and the relation is called accessibility relation,
often designated by R, and if (alpha, beta) belongs to R, we write as
usual "alpha R beta".

That referential becomes a model when, on each world, you give a
valuation on the atomic sentences p, q, r, ... and you extend, as in
propositional logic the value of the compound formula. All worlds
"obeys" classical propositional logic, so to speak. If a is true in
alpha, and if b is true in alpha, we will have (a & b) is true in alpha.

But this will not provide a valuation for Bp, as Bp does not truth-
functionally depend on the value of p.

Kripke defined the truth of Bp in the world alpha, by the truth of p
in all the worlds accessible from alpha.

Bp is true is everywhere I will find myself, p is true. It is natural
with most known modalities (where Bp/Dp ([ ]/<>), with Dp = ~B~p,
corresponds to Necessity/Possibility, Obligation/Permission,
Everywhere/Somewhere, Always/Once, For-all/It-exists, etc.).

If Bp means that p is true in all worlds accessible from the world I
am in, Dp meaning ~B~p, will mean that it is false that ~p is true in
all worlds accessible, and thus that there is a world where p is true.
So, Dp is true in alpha if it exists a world beta with p true in beta
and (alpha R beta).

So here, like provability above, "Bp" is related to true in all
(accessible) worlds.

Then you have the completeness theorem for many modal logic.

K4 proves A iff A is true in all models with R transitive (4 = Bp ->
BBp)
KTproves A iff A is true in all models with R réflexive (T = Bp -> p)
KTB proves A iff A is true in all models with R réflexive and
symmetrical
and
G proves A iff A is true in all finite models with R irreflexive and
realist (realist means that all transitory world accesses to cul-de-
sac, and a world is transitory if it is a not a cul-de-sac, and of
course a cul-de-sac world is a world alpha such that there are no beta
such that alpha R beta.


3) A relation between modal logic and provability by PA (or any Lobian
machine) has been made more precise by Solovay theorem.

Provability (of a rich (Löbian)) machine or axiomatizable theory, like
PA to fix the thing, obeys a modal logic, indeed G, in the following
sense:

We map the modal logic language on arithmetic, by

1) mapping the atomic sentence letters p, q, r, by arithmetical
proposition (p = "1+1=2", q = "Fermat theorem", etc.)
That basic low level mapping is called the realization (for using it
below). In AUDA, comp and the UD is modeled later by restricting this
mapping to the sigma-1 arithmetical propositions.


2) extending this realization to the more complex boolean formula in
the obvious sense (p&q will be mapped on "1+1=2 & Fermat theorem", for
example, ... of course written with only "s" and "0" and "+" and "*"
and the logical symbols.

3) extending this to Bp by mapping it on Beweisbar('p'), that is Gödel
*arithmetical* provability predicate, and 'p' being the Gödel number
encoding of p.

And we can do this for any modal logic, of course, but if we do this
to the modal logic G and G*, we have the two theorems of Solovay (1976):

G prove A iff for all realisations of the atomic formula, PA proves
m(A), with m(A) the mapping described above.

And the "cerise sur le gateau":

G* prove A iff for all realisations of the atomic formula, m(A) is
true, again with m(A) the mapping described above.

So G axiomatizes what Löbian machine can prove about their provability
ability, and G* axiomatizes the truth about them, being provable or
unprovable by the machine.

Is this a reason to identify the models of PA with the Kripke worlds?
Not really. But there are relations which are interesting, but
technically long to be described.

Note that at the modal propositional level G and G* are decidable,
making obvious that a self-observing/inferring machine can produce
many truth about herself despite not being able to prove them. Ideally
correct self-observing/inferring machine get mystical, in that sense.
Unavoidably.

The gap between proof and truth, for machine, gives sense to the
Theaetetus definition of the knower, thanks to

(Bp <-> Bp & p) belongs to G* minus G. True but not provable.

If you map Bp, no more on Beweisbar('p'), but on (Beweisbar('p') & p),
you get a knower associated to the machine. It is a knower, in the
sense that it obeys to the classical logic S4. Indeed it obeys to the
system S4Grz. And the machine cannot give any description of that
knower, so that it verifies well the "mystic theory of knowledge" (by
Brouwer, notably, but also Plotinus and Plato).

Oops... I might have been a bit long, sorry. It sums a bit AUDA.

Bruno

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

[Bruno Marchal]

On 27 May 2012, at 12:15, Russell Standish wrote:

> On Thu, May 24, 2012 at 03:42:15PM +0200, Bruno Marchal wrote:
>>
>> But "a => Ba" is a valid rule for all logic having a Kripke
>> semantics. Why? Because it means that a is supposed to be valid (for
>> example you have already prove it), so a, like any theorem, will be
>> true in all worlds, so a will be in particular true in all worlds
>> accessible from anywhere in the model, so Ba will be true in all
>> worlds of the model, so Ba is also a theorem.
>
> I still don't follow. If I have proved a is true in some world, why
> should I infer that it is true in all worlds? What am I missing?

I realize my previous answer might be too long and miss your question.
Apology if it is the case.

Here is a shorter answer. The idea of proving, is that what is proved
in true in all possible world. If not, a world would exist as a
counter-example, invalidating the argument.

You might want to prove something about your actual world, but this
can only have the form of a conditional like if my world satisfy such
a such propositions then it has to satisfy that or this proposition,
and that conditional has better to be true in all worlds, for we never
really know which world we are in, we can only make theories.

Now, the modal Bp, and proof in math, can be study mathematically, and
that is what I described in the preceding post, and constitutes a bit
of the Arithmetical UDA.

Bruno



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

[Bruno Marchal]

On 27 May 2012, at 09:46, Evgenii Rudnyi wrote:

> On 26.05.2012 21:06 Bruno Marchal said the following:
>>
>> On 26 May 2012, at 16:48, Evgenii Rudnyi wrote:
>>
>>> On 26.05.2012 11:30 Bruno Marchal said the following:
>>>>
>>>> On 26 May 2012, at 08:47, Evgenii Rudnyi wrote:
>>>
>>> ...
>>>
>>>>> In my view, it would be nicer to treat such a question
>>>>> historically. Your position based on your theorem, after all,
>>>>> is one of possible positions.
>>>>
>>>> What do you mean by "my position"? I don't think I defend a
>>>> position. I do study the consequence of comp, if only to give a
>>>> chance to a real non-comp theory.
>>>
>>> A position that the natural numbers are the foundation of the
>>> world.
>>
>> I don't defend that position. I show it to be a consequence of the
>> comp hypothesis + occam razor.
>
> I do appreciate the clearness of your position. From this viewpoint,
> the language of mathematics allows us to remove ambiguities indeed.

Yes, and that is not an argument for the truth of comp, but it is an
argument for the interest of comp. It like looking for your key under
the lamp, because out the light you can't find them.

But another reason, is that comp is more polite, with respect to the
machine, and so if they can be conscious, there is less risk to hurt
them, by betting on that.

>
> ...
>
>>>
>>> When we talk with each other and make proofs we use a human
>>> language. Hence to make sure that we can make universal proofs by
>>> means of a human language, it might be good to reach an agreement
>>> on what it is.
>>
>> This is an impossible task. That is why I use the semi-axiomatic
>> method (in UDA), and math in AUDA. If you disagree with a method of
>> reasoning, you have to explain why. In english, no problem.
>
> I also agree that human language in a way is a mess. Yet, somehow it
> seems to work and this puzzles my, how it could happen when even
> mathematicians failed to analyze it.

No machine at all can develop of semantics for its "living" language.
Language are living phenomenon, containing probably universal "memes".
It can be more clever than us. The brain is the most complex known
object in the universe. And brains (and machine) are already limited
in their self-study for logical reason.

A clever machine is a machine which understands that she know nothing,
really. But beliefs are possible and needed to survive.

>
> ...
>
>>>> I am not against non-comp, but I am against any gap-theory, where
>>>> we introduce something in the ontology to make a problem
>>>> unsolvable leading to "don't ask" policy.
>>>
>>> We are back to a human language. It seems that you mean that some
>>> constructions expressed by it do not make sense. It well might be
>>> but again we have to discuss the language then.
>>
>> I don't see why we have to discuss language, apart from the machines
>> and their languages.
>
> It seems that there is a gap between the language of mathematics and
> a human language.

Don't confuse the formal languages, OBJECT of study of logicians, and
the language of the mathematicians, and logicians, to prove things
about what they are interested in. That language is human language.

Formalism just means that we ask the opinion of some machine. We ask
ZF about the continuum hypothesis, and she answered that she does not
know (somehow).

> It might be interesting to understand it. It might give us a hint on
> how the Universe is made.

What do you mean by Universe? I am a bit skeptical about Universe.

> You see, we must use a human language to communicate, with the
> language of mathematics this would not work.
> I do not know why.

?
There is no language of mathematics. It is the human languages, with
abbreviations. Don't confuse this with the formal languages of
logicians and computer scientist. They are very easy to communicate
with, as they are simpler (and sort of subset) of human language. In
english you will say to the secretary "could you print this document",
but you can ask formally the machine, by "print files" of "CONTROL-
Command", or something.

>
>>>
>>> As for comp, I have written once
>>>
>>> Simulation Hypothesis and Simulation Technology
>>> http://blog.rudnyi.ru/2011/09/simulation-hypothesis-and-simulation-technology.html
>>>
>>>
>>>
>>> that practically speaking it just does not work. I understand that
>>> you talk in principle but how could we know if comp in principle is
>>> true if we cannot check it in practice?
>>
>> The whole point is that we can check it, at least if you accept the
>> classical theory of knowledge. Physics arise from number
>> self-reference in a precise constrained way, and the logic of
>> observable already give rise to quantum-like logic. If mechanism is
>> false, we can know it. If it is true we can only bet on it, and the
>> bet or not on some level of substitution. The facts (Everett QM)
>> gives evidence that our first person plural is given by the
>> electronic orbital, our stories does not depend on the precise
>> position of electron in those orbitals.
>>
>>
>>>
>>> I personally find an extrapolation of a working model outside of
>>> its scope that has been researched pretty dangerous.
>>
>> I am just showing that computationalism (widespread) and materialism
>> (widespread) are incompatible. I reason only, and I extrapolate less
>> than Aristotelians.
>
> I am afraid that reason only is not enough to understand Nature.

All what I explain on comp start from the discovery that reason only
is not enough to understand the natural numbers.
Nor is reason enough to understand reason.

Universal machine can defeat all theories about them.

Just with the numbers we are confronted to the *big* unknown.

I am afraid you might still have a pre-Gödelian conception of machine
and numbers. before Gödel we thought they were easy, now we know that
just about them, we know about nothing, and actually, many are still
in the deny of that situation, apparently.

> I am browsing now The Soul of Science: Christian Faith and Natural
> Philosophy. Let me give a quote that in an enjoyable way expresses
> my thought above.
>
> p. 19 "In 1277 Etienne Tempier, Bishop of Paris, issued a
> condemnation of several theses derived from Aristotelianism - that
> God could not allow any form of planetary motion other than
> circular, that He could not make a vacuum, and many more. The
> condemnation of 1277 helped inspire a form of theology known as

> voluntarism, which admitted no limitations on God’s power. It

> regarded natural law not as Forms inherent within nature but as
> divine commands imposed from outside nature. Voluntarism insisted
> that the structure of the universe - indeed, its very existence - is
> not rationally necessary but is contingent upon the free and
> transcendent will of God."

OK. With comp, and Plotinus; there are three Gods. The outer-God,
which has no will and no power really. The Divine Noùs (Platonia), and
the Inner-God (or divine soul). What you describe might apply to the
inner-god, not the outer-god, which is the origin of both the Noùs and
the soul.

>
> "One of the most important consequences of voluntarist theology for
> science is that it helped to inspire and justify an experimental
> methodology.

Yes. That's excellent. As long as that methodology is not confuse
with an instrumental or positivist philosophy, which leads to the
"don't ask" attitude, and lack of funds for fundamental inquiry.

> For if God created freely rather than by logical necessity, then we
> cannot gain knowledge of it by logical deduction (which traces
> necessary connections). Instead, we have to go out and look, to
> observe and experiment. As Barbour puts it:

That would lead to the confusion of physics (search for universal
laws) and geography (the contingent neighborhood). Not to mention
theology itself, which is put in danger by such moves (as it is the
case).

>
> 'The world is orderly and dependable because God is trustworthy and
> not capricious; but the details of the world must be found by
> observation rather than rational deduction because God is free and
> did not have to create any particular kind of universe.'"

I doubt that the outer god is free. Open problem for me.
The inner god is free, but this is what makes the reality infinitely
complex, for the best and the worst.

Interesting quote. Thanks.

Bruno

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

[Russell Standish]

On Sun, May 27, 2012 at 06:20:29PM +0200, Bruno Marchal wrote:
>
> On 27 May 2012, at 12:15, Russell Standish wrote:
> >I still don't follow. If I have proved a is true in some world, why
> >should I infer that it is true in all worlds? What am I missing?
>
> I realize my previous answer might be too long and miss your
> question. Apology if it is the case.
>
> Here is a shorter answer. The idea of proving, is that what is
> proved in true in all possible world. If not, a world would exist as
> a counter-example, invalidating the argument.

I certainly missed that. Is that given as an axiom? It seems like that
would be written p -> []p.

When I say p is true in a world, I can only prove that p is true in
that world. I am mute on the subject of whether p is true in any other
world (unless I can use an axiom like the above).

In what class of logics would such an axiom be taken to be true. (Of
course it is true in classical logic, but there is only one "world" there).

[Bruno Marchal]

On 28 May 2012, at 04:00, Russell Standish wrote:

> On Sun, May 27, 2012 at 06:20:29PM +0200, Bruno Marchal wrote:
>>
>> On 27 May 2012, at 12:15, Russell Standish wrote:
>>> I still don't follow. If I have proved a is true in some world, why
>>> should I infer that it is true in all worlds? What am I missing?
>>
>> I realize my previous answer might be too long and miss your
>> question. Apology if it is the case.
>>
>> Here is a shorter answer. The idea of proving, is that what is
>> proved in true in all possible world. If not, a world would exist as
>> a counter-example, invalidating the argument.
>
> I certainly missed that. Is that given as an axiom?

That would be a meta-axiom in a theory defining what is logic. But
that does not exist. It is just part of what logic intuitively
consists in.
Logicians are not interested of truth or interpretation of statements.
They are interested in validity. What sentences follow from what
sentences, independently of interpretations, and thus true in all
possible worlds.

> It seems like that
> would be written p -> []p.

This means that if p then p is provable. "p -> Bp", if B = provable,
is completeness (with the meaning of completeness = its meaning in
incompleteness). This is false in non rich theory (by the fact that
their are non rich) and false in rich theory, by the fact that rich
theory obeys to the incompleteness theorem. So, it is true for rare
exception (like the first order theory of real numbers) which is not
rich (not sigma_1 complete).

Take the proposition (a v b) in propositional logic. Take the world
{(a t), (b, f)}, i.e. the world with a true, and b false. Let p = (a v
b). This provides a counter-example to p -> Bp. p is true in that
world (because a v b is true if a is true), yet it is not provable,
because it is false in some other world, like the world with both a
and b false.

Or take p = Dt. Dt -> BDt contradicts immediately the second
incompleteness theorem which says that Dt -> ~BDt.

>
> When I say p is true in a world, I can only prove that p is true in
> that world.

I don't think so. If p is true, that does not mean you can prove it,
neither in your world, nor in some other world.

> I am mute on the subject of whether p is true in any other
> world (unless I can use an axiom like the above).

By the logicians notion of proof, if you prove a proposition, it is
true in all worlds/model/interpretation.

>
> In what class of logics would such an axiom be taken to be true.

All.

> (Of
> course it is true in classical logic, but there is only one "world"
> there).

In classical propositional logic, a world is just anything to which we
attach a valuation t, or f, to the atomic proposition, p, q r, ...
This makes 2^aleph_zero worlds. A world can be identified with a
function from {p, q, r, ...} to {t, f}.
In first order logic, worlds can be identified with interpretations,
or models. All first order theories have many models. In fact for any
cardinal, there is a model having that cardinal. The number of worlds
exceeds the cardinals nameable in set theory.

Bruno

>
>
> --
>
> ----------------------------------------------------------------------------
> Prof Russell Standish Phone 0425 253119 (mobile)
> Principal, High Performance Coders
> Visiting Professor of Mathematics hpc...@hpcoders.com.au
> University of New South Wales http://www.hpcoders.com.au
> ----------------------------------------------------------------------------
>