On 12/9/2011 9:43 AM, Bruno Marchal wrote:

On 09 Dec 2011, at 13:34, Stephen P. King wrote:

On 12/9/2011 4:06 AM, Bruno Marchal wrote:

On 09 Dec 2011, at 08:47, meekerdb wrote:

On 12/8/2011 6:35 PM, Stephen P. King wrote:
On 12/8/2011 9:01 PM, meekerdb wrote:
On 12/8/2011 5:48 PM, Stephen P. King wrote:
On 12/8/2011 6:45 PM, meekerdb wrote:
On 12/8/2011 3:04 PM, Craig Weinberg wrote:
On Dec 8, 4:44 pm, "Stephen P. King"<stephe...@charter.net> wrote:
On 12/8/2011 4:22 PM, Craig Weinberg wrote:
To suppose computation requires a material process would be
materialism, wouldn't it?
Hi Craig,

Not quite, a dualist model would require that some form of material process occur for computations and would go even further in prohibiting computations from not having a physical component but would not specify which it was. This way we preserve computational universality without
having to drift off into idealism and its own set of problems.

True, it could be dualism (or an involuted monism) too, but I wouldn't
call a theory of mind which depends on material processes
computationalism.

You might if you thought that's all that was needed to make a mind, in contrast to some supernatural soul stuff. It basically boils down to whether you suppose there are some things that are real (e.g. some things happen and some don't, or some stuff exists and some doesn't) and some aren't or you suppose that everything happens and exists. In the latter case there's really no role for ur stuff whose only function is to mark some stuff as existing and the rest not.

Brent

Hi Brent,

Interesting role that you have cast the physical world into, but ironically "stuff whose only function is to mark some stuff as existing and the rest not" and "everything happens and exists" do not sleep together very well at all. The "everything happens and exists" hypothesis has a huge problem in that is has no way of sorting the "Tom sees this and not that" from the " from "Dick sees this and not that" and "Jane sees this and not that", where as the "stuff whose only function is to mark some stuff as existing and the rest not" can be coherently defined as the union of what Tom, Dick and Jane see and do not see. The idealists would have us believe that along with numbers their operations there exists some immaterial stratifying medium that sorts one level of Gedel numbering from another. I am reminded of a video I watched some time ago where a girl had three sealed jars. One contained nothing, one contained 4 6-die and the third contained 1,242,345,235,235 immaterial 6-die. ... The physical world is very much real, even if it vanishes when we look at it closely enough. But we might consider that just as it vanishes so too does the ability to distinguish one set of numbers from another. If the ability to distinguish this from that itself vanishes, how are we to claim that computations exist "independent of physics"? Seriously!?!

Where did I claim that. I was just pointing out the genesis of "everything theories"; you did notice that this is called the "everything-list" didn't you?

Brent
HI Brent,

I commented on what you wrote. Care to respond or will you beg my question? How does immaterial based "everything theories" deal with this problem that I just outlined?

You should ask a proponent of such theories; like Bruno. But as I understand it, the ultimate application of Ocaam's razor is to refuse to make any distinctions, so that we theorize that everything exists. But the unqualified everything doesn't seem to be logically coherent. So Bruno backs off to an "everything" that is well defined and still possibly comprehensive, i.e. everything that is computable. Within this plenuum there are various states (numbers in arithmetic) and some principle will pick out what part we experience. Computation includes an uncountable infinity of states and relations between states - so whatever we experience must be in there somewhere.

Good answer. The distinction asked by Stephen King are done, in the relative way, by the universal numbers themselves.

Hi Bruno and Brent,

Sorry, I do not accept that as a "good answer" since it would be cut to shreds by the razor itself.

?

[SPK]
I take Occam <http://en.wikipedia.org/wiki/Occam%27s_razor> to say "in any explanation do not multiply entities beyond necessity."



Postulating that everything exists without a means to even demostrate necessity is to postulate an infinite (of unknown cardinality!) of entities, in direct contradiction to Occam's razor.

Occam razor asks for the minimal number of assumption in a theory. It does not care about the cardinal of the models of the theory. That is why the many worlds is a product of occam principle.

Sure, but the necessity of the plurality of "actual worlds" given that we can only observe one requires additional evidence. Some say that the interference of particles "with themselves" in the two-slit experiment is amble evidence for these, but MWI does nothing to explain why we observe the particular universe that we do. It has its basis problem as your result has its measure problem. I suspect that these two problems are in the same family.




Even when we reduce this to a countable infinite of entities,

Which is indeed the case for the comp ontology, but the epistemology can and will be bigger. It is a sort of Skolem phenomenon, that I have often described.


the need for necessitation remains unanswered. Why do numbers exist?

Nobody can answer that. We cannot prove the existence of the numbers in a theory which do not assume them at the start, implicitly or explicitly.

So it is OK to postulate that numbers exists and from such argue that the physical world is unnecessary epiphenomena and yet is required for your result to run. All I ask is that you consider the world of numbers to not have an existence independent of the possibility of knowledge of it. I separate "existence" from "properties". The mere existence of an object does not necessitate any propeties whatsoever. Numbers have properties, they have relative value... Where do those properties derive?




Why numbers and not Nothing?

Because with Nothing in the ontology, you can't prove the existence of anything, not even illusion which needs some illusionned subject. That is why all fundamental theories assumes the numbers, (or equivalent) and with comp this can be shown to be enough.


I merely start with the assumption that "existence exists" and go from there. To postulate one particular type of entity and not any other requires special explanations. What makes numbers special over spaces?




At least with the Stone-type dualism we have a way to show the necessity of numbers via bisimulations between different instances of Boolean algebras and, dually, via causality between Stone spaces and thus do not violate Occam blindly.

Assuming different instances of boolean algebra is assuming more than the natural numbers (like assuming finite and infinite sets).

Are two Boolean algebras that have different propositional content one and the same? If this is true then there is no variation is algorithms, it is to say that all algorithms are identical in every way.




Comprehensability requires the co-existence of that which is comprehended with that which is doing the comprehension, that numbers can comprehend themselves without additional structure seem to me to be ruled out even by your result.

Not all. The relevant part of computer science is embedded in arithmetic. The one doing the comprehension are the universal numbers, and they need only addition and multiplication for doing that. That can be derived easily from Godel's 1931 paper.


The notion of computation is not inherent in the independent existence of numbers. You are making the mistake of thinking that "independent of any particular physical implementation" is equivalent to "independent of physical implementation", thus you are free from any physical constraint on the notion of computation and then when tyros like me fail to understand how such an idealist model can have any causal efficacy or limit, then I wonder about its validity. You need to agrees Deutsch's critique directly as to how it is possible for an abstract form of theory proving is possible.



My point is that we cannot tacitly assume the existence of entities that can make the distinctions (for example, between difference Goedelian numberings)

Arithmetical (sigma_1) truth dovetails on all Gödel numbering. The inability for a universal number to really know its coding is part of the reason why their is a first person indeterminacy in arithmetic, and that is part of the explanation of why physical laws will be apparent from the universal numbers points of view.

What you just wrote and its meaningfulness vanishes if there is not physical implementation of it. You cannot dismiss the material world and keep its properties.





and thus the insistence that the physical not exist at the same level as numbers seems to be an error.

The numbers (or other finite entities belonging to universal systems) have to be primitive (they are not derivable by less than themselves). This is *necessary* not the case for physics, *by the UDA*.

No, UDA only proves that the physical world cannot be monic and allow for computations. It does not prove that an idealism can work.









I'm intrigued by David Deutsche's assertion that different physics implies that different things are computable, but I'm doubtful that it's true.

I agree, it is total non sense. Not only it would contradict Church thesis and the immunity of computability for diagonalization, but thanks to David Deutsch quantum computer, it does not even make sense with what we know currently believed in physics, and such a position is a sort of revisionist definition of what is a computation. That's is why I prefer to call Deutsch's "Church Turing principle" the "Deutsch's thesis". And it is an open problem if such a thesis is compatible with Church's thesis.

You are not even showing a valid proof here. Refuting Deutsch's assertion would effectively make Yes Doctor vanish,

Why? The contrary is more plausible. "Yes doctor" should a priori refute Deustch thesis.

If Deutsch is wrong, digital substitution vanishes and so does your result.




leaving your result vacuous. Removing all traces of the physical world removes all possibility of distinguishing a false proof from a true proof.

Trivially so. But comp does not remove any *trace* of the physical worlds. Only the pretension that the physical has a primary ontology.

Two different meanings of the world trace. Please don't play word games.





To contradict this one must show how a "theory of abstract theorem proving" is self-consistent in the absence of a means to distinguish one proposed proof from another. Only the physical world with its chalkboards, computer screens sound waves, etc. offers a medium on and in which we can communicate abstract ideas and concepts such as your result. To believe otherwise is to similar to the belief in perpetual motion machines as it would allow us to do work in contradiction to thermodynamics. The acquisition of Knowledge, via computation or other, requires the generation of entropy.

Not really. QM makes physical implementation of computations not needing generation of entropy, nor any energy. Only erasing information would need that, but you can have Turing universality without erasing information. Quantum computer are based on that idea. Universal computation can be made completely reversible. But all this is not relevant, given that we do assume the existence of numbers with + and *.



Information is not gained for free. If numbers have a unique and a priori existence and the physical world emerges from it then even thermodynamics itself is emergent but this still does not allow us to get 0 to equal 1.

OK.



I am sorry to seem so harsh in my critique but this problem that I am pointing out is far to obvious to be so lackadaisically dismissed. I believe in your result, but it does not prove the physical world to not exist as it requires the existence of the physical world to be communicated. That fact alone should be clear.

I have no problem with the existence of the physical worlds, given that I reduce the mind body problem to the problem of justifying the existence of the physical worlds from numbers. This mean I do not doubt about the existence of the physical worlds (who would do that? really). But I do provide a proof or deductive argument that the physical worlds has no ontological primacy, once we assume brain (even material) brain functions like machine at some level of description.

Bruno


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

    How are numbers more primitive than spaces?

Onward!

Stephen





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