subject:"The limit of all computations"



On 28 May 2012, at 18:35, meekerdb wrote:


On 5/28/2012 1:37 AM, Bruno Marchal wrote:



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.


But the 'worlds' are defined by the axioms and rules of inference.


Not as such. the axioms and rules define only the truth common to all  
models, when the theory is sound (and vice versa if the theory is  
complete). Individual models have their lives of their own. They lives  
in other theories or theories models. The models of PA exists in ZF's  
model. Models (semantics) are beyond the theory.




So you could change or add axioms and get different 'worlds'.  In  
this logicians idea of 'world' it is not the case that you only  
prove things in the one world you're in.


That was my point. We alway "prove" what is true in all worlds.  
Proving is a trans-world notion. G proves <> t -> <>[] f, makes that  
formula true in all worlds of all models based on all finite  
irreflexive realist models, for example.
Here the world can be related to the models, but it leads to a very  
special model. So different completeness theorem are being used in  
that context, and we have to be cautious which one we are talking about.


Bruno


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



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Re: The limit of all computations

2012-05-28 Thread meekerdb


On 5/28/2012 1:37 AM, Bruno Marchal wrote:

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. 


But the 'worlds' are defined by the axioms and rules of inference.  So you could change or 
add axioms and get different 'worlds'.  In this logicians idea of 'world' it is not the 
case that you only prove things in the one world you're in.


Brent

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Re: The limit of all computations



On 28 May 2012, at 11:35, Russell Standish wrote:


On Mon, May 28, 2012 at 10:37:53AM +0200, Bruno Marchal wrote:


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.


Well, I can tell you, it is not intuitive! Perhaps there is some
background understanding that is missing.


Yes. Logic, I am afraid. Logic the field, not logic as we use it  
everyday. Don't worry, virtually all non professional logicians miss  
it.  And logicians miss that non logician miss it. It is a very  
technical field.


But the idea that proof, or Bp, entails truth in all world/model is  
given by the completeness theorem of Gödel, or by Kripke semantics  
(with "all worlds" becoming "all accessible worlds"). See my previous  
post.







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,


[]p means (primarily) true in all worlds. In Kripke semantics, it is
relativised to mean true in all accessible worlds.


Yes.



The meaning of provability is a different interpretation.


Yes. But then there are relations linking them. See my previous post  
on Solovay theorem which makes such a relation, and which can be sum  
up by:  G is the modal logic of provability.












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.


p may be true, but if I don't know it (or can't prove it), I  
shouldn't be

asserting it :).


OK. But the fact is that p might be true in your world, and you can  
know or not that fact, independently of the fact that you can prove it  
or not.
We have to distinguish "p is true" with "p is proved", "p is known",  
"p is observed", etc. All those modalities obeys different logics.
Besides, if you can prove p, this does not make it true in your world,  
as Bp -> p, might be non provable, or even false. In that cse your  
world is not accessible from your world: the accessibility relation is  
not reflexive (that is the case for G).
In a cul-de-sac world, Bf -> f is false for example. Typically, a cul- 
de-sac world does not access to itself, indeed it accesses to no world  
at all.









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.



Even if the proof relied upon some facet that may or may not be true
in all worlds?


Yes, because that facets will need to be 'conditionalized upon' in  
your world ... to have a proof.
A world is a semantic notion, and you cannot refer to it in a proof  
(an error well illustrated by Craig, with all my respect).


Bruno








In what class of logics would such an axiom be taken to be true.


All.




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Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au


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Re: The limit of all computations



On 28 May 2012, at 10:37, Bruno Marchal wrote:



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.


Oops. I realize that you were perhaps alluding to "p->Bp". In that  
case, I should have answered "almost none".


In modal logic "p->Bp" is called TRIV, for "trivial". The reason is  
that before Löb, most modal logic have Bp -> p as an axiom, and with  
both "p->Bp" and "Bp->p", we have p <-> Bp, and so the modal logic can  
collapse into classical propositional logic.


But this actually not true for the provability logics, which are very  
subtle.


Indeed, with B = Gödel's provability (the talk of the Löbian machine),  
although p -> Bp is usually false (cf p = Dt and incompleteness) we  
still have that "p -> Bp" is true for all p = sigma_1 arithmetical  
sentence.
You can intuit this easily. If p = "ExP(x)" with P decidable, the the  
truth of p makes it provable, because if a number has a verifiable  
property, you can find it by testing 0, 1, 2, 3, ... That is exactly  
what all universal machine can do. Sigma_1 completeness (= "p->Bp"  
with p sigma_1) is a provability characterization of Turing  
universality.


So by adding "p->Bp" we characterize the logic of provability of the  
sigma_1 sentences, and that is how I model the UD in arithmetic.


The miracle is that this does not make the modal logic collapsing. I  
can come back on this issue some later day. Perhaps in the FOAR list,  
or here, depending of the comments.


But this is very exceptional, and illustrates that G and G*, and  
S4Grz, etc. are very special logics, quite counter-intuitive.
"p-> Bp", added to G adds the quantum p->BDp to the intensional  
variants, and makes the "intelligible and sensible matter" obeying  
arithmetical quantum logics, leading to the beginning of the  
extraction of physics from arithmetic.


Bruno








(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






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Re: The limit of all computations

2012-05-28 Thread Russell Standish

On Mon, May 28, 2012 at 10:37:53AM +0200, Bruno Marchal wrote:
> 
> 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.

Well, I can tell you, it is not intuitive! Perhaps there is some
background understanding that is missing.

> 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,

[]p means (primarily) true in all worlds. In Kripke semantics, it is
relativised to mean true in all accessible worlds.

The meaning of provability is a different interpretation.


> 
> 
> >
> >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.

p may be true, but if I don't know it (or can't prove it), I shouldn't be
asserting it :).

> 
> 
> >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.
> 

Even if the proof relied upon some facet that may or may not be true
in all worlds?

> 
> >
> >In what class of logics would such an axiom be taken to be true.
> 
> All.
> 
> 

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


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Re: The limit of all computations

2012-05-28 Thread Evgenii Rudnyi


On 27.05.2012 19:24 Bruno Marchal said the following:


On 27 May 2012, at 09:46, Evgenii Rudnyi wrote:


...


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.


It well might be that I have pre-Gödelian conceptions, as I am not a 
mathematician and I cannot distinguish between different mathematical 
theories.






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."




..


Interesting quote. Thanks.



You will find the book at

http://www.lambsound.com/Reading/books/Christian_Faith_and_Natural_Philosophy.pdf

It is a good overview of the science development as a fight between 
three different world views among Christians:


"If Aristotelianism portrayed God as the Great Logician, and 
neo-Platonism as the Great Magus/Artisan, then mechanistic philosophy 
portrayed Him as the Great Mechanical Engineer."


Nowadays God seems to be the Great Programmer.

Evgenii


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Re: The limit of all computations

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 hpco...@hpcoders.com.au
University of New South Wales http://www.hpcoders.com.au

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Re: The limit of all computations

2012-05-27 Thread 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).


-- 


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


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Re: The limit of all computations

2012-05-27 Thread 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

Re: The limit of all computations

2012-05-27 Thread 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/



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Re: The limit of all computations

2012-05-27 Thread 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

Re: The limit of all computations

2012-05-27 Thread 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?


-- 


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


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Re: The limit of all computations

2012-05-27 Thread 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

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Re: The limit of all computations

2012-05-26 Thread 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/



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Re: The limit of all computations

2012-05-26 Thread Pzomby


On Saturday, May 26, 2012 7:48:41 AM UTC-7, 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 
> 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. 
>
> 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.  

 

>
> 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 
>

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Re: The limit of all computations

2012-05-26 Thread 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

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Re: The limit of all computations

2012-05-26 Thread 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/



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Re: The limit of all computations

2012-05-25 Thread 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 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. 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

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Re: The limit of all computations

2012-05-25 Thread Bruno Marchal



On 24 May 2012, at 19:48, meekerdb wrote:


On 5/24/2012 6:42 AM, Bruno Marchal wrote:


On 24 May 2012, at 09:07, Russell Standish wrote:


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.


Isn't "a=>Ba" trivially true since every axiom is a theorem?


"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/



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Re: The limit of all computations

2012-05-24 Thread meekerdb


On 5/24/2012 6:42 AM, Bruno Marchal wrote:


On 24 May 2012, at 09:07, Russell Standish wrote:


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.


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/





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Re: The limit of all computations

2012-05-24 Thread Bruno Marchal



On 24 May 2012, at 09:07, Russell Standish wrote:


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?


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/



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Re: The limit of all computations

2012-05-24 Thread 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?


-- 


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


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Re: The limit of all computations

2012-05-24 Thread Bruno Marchal



On 23 May 2012, at 20:19, Evgenii Rudnyi wrote:


On 23.05.2012 20:01 Bruno Marchal said the following:


On 23 May 2012, at 19:19, Evgenii Rudnyi wrote:



...


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.


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.


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/



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Re: The limit of all computations

2012-05-24 Thread 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

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RE: The limit of all computations

2012-05-23 Thread Hal Ruhl

Hi Brent:

 

I shall try to respond tomorrow. 

 

Hal Ruhl

 

From: everything-list@googlegroups.com
[mailto:everything-list@googlegroups.com] On Behalf Of meekerdb
Sent: Wednesday, May 23, 2012 8:41 PM
To: everything-list@googlegroups.com
Subject: Re: The limit of all computations

 

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

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Re: The limit of all computations


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

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RE: The limit of all computations

2012-05-23 Thread 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: everything-list@googlegroups.com
[mailto:everything-list@googlegroups.com] On Behalf Of meekerdb
Sent: Wednesday, May 23, 2012 4:41 PM
To: everything-list@googlegroups.com
Subject: Re: The limit of all computations

 

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

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Re: The limit of all computations


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

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RE: The limit of all computations

2012-05-23 Thread 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

-Original Message-
From: everything-list@googlegroups.com
[mailto:everything-list@googlegroups.com] On Behalf Of meekerdb
Sent: Wednesday, May 23, 2012 3:52 PM
To: everything-list@googlegroups.com
Subject: Re: The limit of all computations

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

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Re: The limit of all computations


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

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Re: The limit of all computations

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

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Re: The limit of all computations



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 

 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 meanin

Re: The limit of all computations

2012-05-23 Thread Evgenii Rudnyi


On 23.05.2012 20:01 Bruno Marchal said the following:


On 23 May 2012, at 19:19, Evgenii Rudnyi wrote:



...


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.


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

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Re: The limit of all computations



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/



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Re: The limit of all computations

2012-05-23 Thread 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

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Re: The limit of all computations

2012-05-23 Thread Stephen P. King


On 5/23/2012 1:19 PM, 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?


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


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...


--
Onward!

Stephen

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


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Re: The limit of all computations

2012-05-23 Thread Quentin Anciaux

2012/5/23 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 
>
>>
>>   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


> 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.
>
>

Re: The limit of all computations

2012-05-23 Thread 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 >



 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

Re: The limit of all computations

2012-05-23 Thread 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

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Re: The limit of all computations


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

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


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Re: The limit of all computations



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 

 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 do

Re: The limit of all computations



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 >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








--


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


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Re: The limit of all computations

2012-05-23 Thread 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 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! (#>.<#)

-- 


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


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Re: The limit of all computations



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 

 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 t

Re: The limit of all computations

2012/5/23 Stephen P. King 

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

Re: The limit of all computations

2012-05-22 Thread 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 mailto:stephe...@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 possibilit

Re: The limit of all computations


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



2012/5/22 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.


*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,

RE: The limit of all computations

2012-05-22 Thread 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

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Re: The limit of all computations

2012/5/22 Stephen P. King 

>  On 5/22/2012 11:53 AM, Bruno Marchal wrote:
>
>
>  On 22 May 2012, at 14:36, Stephen P. King 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?
>
>  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
>
>
>  It is not idealism. It is neutral monism. Idealism would makes mind or
> ideas primitive, which is not the case.
>
>
>  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.

>
>
>
>
>
>  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 th

Re: The limit of all computations


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


On 22 May 2012, at 14:36, Stephen P. King 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?



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


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


 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.


--
Onward!

Stephen

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

--
You received this messa

Re: The limit of all computations

2012-05-22 Thread Joseph Knight

On Tue, May 22, 2012 at 11:08 AM, Stephen P. King wrote:

>  On 5/22/2012 10:56 AM, Joseph Knight wrote:
>
>
>
> On Tue, May 22, 2012 at 7:36 AM, Stephen P. King 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

Re: The limit of all computations

2012/5/22 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 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 
> agencyand
> 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 ...

Re: The limit of all computations


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



On Tue, May 22, 2012 at 7:36 AM, Stephen P. King 
mailto:stephe...@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?


--
Onward!

Stephen

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

--
You received

Re: The limit of all computations

2012-05-22 Thread Bruno Marchal

On 22 May 2012, at 14:36, Stephen P. King 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?

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

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

--
You received this message because you are subscribed to the Google
Groups "Everything List" group.

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

Re: The limit of all computations

2012-05-22 Thread Joseph Knight

On Tue, May 22, 2012 at 7:36 AM, Stephen P. King 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
>
>  --
> You received this message

Re: The limit of all computations


On 5/22/2012 3:35 AM, Quentin Anciaux wrote:



2012/5/22 meekerdb mailto:meeke...@verizon.net>>

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



2012/5/22 Stephen P. King mailto:stephe...@charter.net>>

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



2012/5/21 Stephen P. King mailto:stephe...@charter.net>>

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



2012/5/21 Stephen P. King mailto:stephe...@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

  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



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 
.)


--
Onward!

Stephen

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

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Re: The limit of all computations


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". ;-)




--
Onward!

Stephen

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

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Re: The limit of all computations

2012/5/22 meekerdb 

>  On 5/21/2012 10:56 PM, Quentin Anciaux wrote:
>
>
>
> 2012/5/22 Stephen P. King 
>
>>  On 5/21/2012 3:49 PM, Quentin Anciaux wrote:
>>
>>
>>
>> 2012/5/21 Stephen P. King 
>>
>>>  On 5/21/2012 7:54 AM, Quentin Anciaux wrote:
>>>
>>>
>>>
>>> 2012/5/21 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?



>>> 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


>   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
>
>
>
>
>> 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
>>
>>   --
>> You received this message because you are subscribed to the Google Groups
>> "Everything List" group.
>> To post to this group, send email to everything-list@googlegroups.com.
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>> everything-list+unsubscr...@googlegroups.com.
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>>
>
>
>
> --
> All those moments will be lost in time, like tears in rain.
> --
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Re: The limit of all computations

2012-05-21 Thread meekerdb


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



2012/5/22 Stephen P. King mailto:stephe...@charter.net>>

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



2012/5/21 Stephen P. King mailto:stephe...@charter.net>>

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



2012/5/21 Stephen P. King mailto:stephe...@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


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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Re: The limit of all computations

2012-05-21 Thread Quentin Anciaux

2012/5/22 Stephen P. King 

>  On 5/21/2012 3:49 PM, Quentin Anciaux wrote:
>
>
>
> 2012/5/21 Stephen P. King 
>
>>  On 5/21/2012 7:54 AM, Quentin Anciaux wrote:
>>
>>
>>
>> 2012/5/21 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?
>>>
>>>
>>>
>> 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
>
>  --
> You received this message because you are subscribed to the Google Groups
> "Everything List" group.
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> everything-list+unsubscr...@googlegroups.com.
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>



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Re: The limit of all computations


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



2012/5/21 Stephen P. King >


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



2012/5/21 Stephen P. King mailto:stephe...@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.


--
Onward!

Stephen

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

--
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Re: The limit of all computations

2012-05-21 Thread 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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Re: The limit of all computations

2012-05-21 Thread 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

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Re: The limit of all computations

2012-05-21 Thread Quentin Anciaux

2012/5/21 Stephen P. King 

>  On 5/21/2012 7:54 AM, Quentin Anciaux wrote:
>
>
>
> 2012/5/21 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?
>>
>>
>>
> 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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Re: The limit of all computations


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



2012/5/21 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?



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?


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Stephen

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~ Francis Bacon

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Re: The limit of all computations

2012-05-21 Thread 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



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).



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Re: The limit of all computations


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



2012/5/21 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?



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.


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Re: The limit of all computations

2012-05-21 Thread Quentin Anciaux

2012/5/21 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?
>
>
>
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

-- 
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>
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>
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> ~ Francis Bacon
>
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Re: The limit of all computations


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?


--
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Stephen

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~ Francis Bacon


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Re: The limit of all computations


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 ...

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Stephen

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~ Francis Bacon


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Re: The limit of all computations

2012-05-21 Thread 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).

-- 

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Re: The limit of all computations

2012-05-21 Thread 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?

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Re: The limit of all computations

2012-05-21 Thread 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

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

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...
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Re: The limit of all computations

2012-05-21 Thread 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


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Re: The limit of all computations

2012-05-20 Thread Quentin Anciaux

2012/5/21 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<http://en.wikipedia.org/wiki/Jenga#Tallest_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?
>

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
>
>  --

Re: The limit of all computations

ogical 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
<http://plato.stanford.edu/entries/democritus/> and Heraclitus
<http://plato.stanford.edu/entries/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 <http://www.thefreedictionary.com/ostensibly>.

"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

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
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Re: The limit of all computations


On 5/20/2012 10:26 PM, meekerdb wrote:

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


Sorry Brent,

You are not grasping what I am talking about.

--
Onward!

Stephen

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


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Re: The limit of all computations

 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 
<http://plato.stanford.edu/entries/democritus/> and Heraclitus 
<http://plato.stanford.edu/entries/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 
<http://www.thefreedictionary.com/ostensibly>.


"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...

--
Onward!

Stephen

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

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Re: The limit of all computations


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

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Re: The limit of all computations

cular 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 
<http://plato.stanford.edu/entries/democritus/> and Heraclitus 
<http://plato.stanford.edu/entries/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 <http://www.thefreedictionary.com/ostensibly>.

"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
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Re: The limit of all computations



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 <http://plato.stanford.edu/entries/democritus/> and 
Heraclitus <http://plato.stanford.edu/entries/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 
<http://www.thefreedictionary.com/ostensibly>.


"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?

--
Onward!

Stephen

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

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Re: The limit of all computations


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

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Re: The limit of all computations

n 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?



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Re: The limit of all computations


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 hugeJenga 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.


--
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Stephen

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

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Re: The limit of all computations


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 hugeJenga tower 
<http://en.wikipedia.org/wiki/Jenga#Tallest_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?



--
Onward!

Stephen

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

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Re: The limit of all computations


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

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.


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Re: The limit of all computations

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
<http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&sqi=2&ved=0CE8QFjAB&url=http%3A%2F%2Fwww.tapir.caltech.edu%2F%7Elindblom%2FPublications%2F10_CommMathPhys.61.87.pdf&ei=G1O5T9y1NYG69QT036GoCg&usg=AFQjCNGQxEJa9DEFbyKnXiub-nS7zvPksw&sig2=9za6duwSbfQp-yZ_Cj6vzA>.
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?

--
Onward!

Stephen

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

Re: The limit of all computations


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



2012/5/20 Stephen P. King <mailto:stephe...@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 
<http://en.wikipedia.org/wiki/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 u/s. 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 th

Re: The limit of all computations


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

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Re: The limit of all computations

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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Re: The limit of all computations

2012-05-20 Thread Quentin Anciaux

2012/5/20 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?
>

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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-- 
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Re: The limit of all computations