On 09 Dec 2011, at 17:55, Stephen P. King wrote:

[SPK]I take Occam to say "in any explanation do not multiply entitiesbeyond necessity."

See Brent's answer.

Postulating that everything exists without a means to evendemostrate necessity is to postulate an infinite (of unknowncardinality!) 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

`Nobody can observe one universe. Physicists measure numbers and`

`relates those numbers by inductive inference on quantitative relations`

`among them.`

requires additional evidence.

`"one physical universe" requires as much evidences and explanations`

`than 0, 2, 3, infinity, ... The everything idea is that "all possible`

`universes" is conceptually simpler than one real universe among all`

`the possible one.`

Some say that the interference of particles "with themselves" in thetwo-slit experiment is amble evidence for these, but MWI doesnothing to explain why we observe the particular universe that we do.

`Comp explains this completely, by explaining why you cannot understand`

`that you are the one ending in Washington instead as the one ending in`

`Moscow. It explains contingencies by consistent extensions.`

It has its basis problem as your result has its measure problem.

`I don't think there is any basis problem in the quantum MW, nor is`

`there any "initial theory" problem in comp. And the mind-body problem`

`is transformed into a body problem, itself becoming a measure problem,`

`but that is what makes those theories interesting.`

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 theepistemology can and will be bigger. It is a sort of Skolemphenomenon, 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 thenumbers in a theory which do not assume them at the start,implicitly or explicitly.So it is OK to postulate that numbers exists

`We need only to postulate that zero (or one if you prefer) is a`

`number, and that the successor of a number is a number. This is less`

`than postulating sets or categories, as you need for talking about`

`Stone duality.`

and from such argue that the physical world is unnecessaryepiphenomena

`It is a phenomenon. Why would it be an epiphenomenon? I have argue`

`that this does not make sense.`

and yet is required for your result to run.

The phenomenon is required. Not its primitivity.

All I ask is that you consider the world of numbers to not have anexistence independent of the possibility of knowledge of it.

`In which sense. With comp, the numbers (N, +, *) entails the existence`

`of the knowledge of the numbers by some universal numbers. The "Bp &`

`p" concerns numbers relatively to universal numbers.`

I separate "existence" from "properties".

`Me too. Existence is handled by the quantifier "E", and properties are`

`handled by arithmetical predicate.`

The mere existence of an object does not necessitate any propetieswhatsoever. Numbers have properties, they have relative value...Where do those properties derive?

`From the (non trivial) additive and multiplicative properties, which`

`are among the postulates (recursive laws of addition and`

`multiplication).`

Why numbers and not Nothing?Because with Nothing in the ontology, you can't prove the existenceof anything, not even illusion which needs some illusionnedsubject. 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" andgo from there.

`We have discussed this. "existence exists" does not make sense for me.`

`Existence of what? You are the one transforming existence into a`

`property here.`

To postulate one particular type of entity and not any otherrequires special explanations.

`We assume simple principles and no more than what we need, and with`

`comp we need only combinators, of lambda-terms, or natural numbers.`

What makes numbers special over spaces?

They are conceptually far simpler.

At least with the Stone-type dualism we have a way to show thenecessity of numbers via bisimulations between different instancesof Boolean algebras and, dually, via causality between Stonespaces and thus do not violate Occam blindly.Assuming different instances of boolean algebra is assuming morethan the natural numbers (like assuming finite and infinite sets).Are two Boolean algebras that have different propositionalcontent one and the same? If this is true then there is no variationis algorithms, it is to say that all algorithms are identical inevery way.

?

Comprehensability requires the co-existence of that which iscomprehended with that which is doing the comprehension, thatnumbers can comprehend themselves without additional structureseem to me to be ruled out even by your result.Not all. The relevant part of computer science is embedded inarithmetic. The one doing the comprehension are the universalnumbers, and they need only addition and multiplication for doingthat. That can be derived easily from Godel's 1931 paper.The notion of computation is not inherent in the independentexistence of numbers.

It is. This is a consequence of Church thesis.

You are making the mistake of thinking that "independent of anyparticular physical implementation" is equivalent to "independent ofphysical implementation",

`I do not assume this. This is what the MGA proves or is supposed to`

`prove. Perhaps that is the error of Benjayk, and other people who does`

`not see that immateriality is proved in the 8th step, and not use`

`before.`

thus you are free from any physical constraint on the notion ofcomputation and then when tyros like me fail to understand how suchan idealist model can have any causal efficacy or limit, then Iwonder about its validity.

`The causal efficacy comes from the fact that addition and`

`multiplication makes the basic ontology Turing universal. Machines`

`have causal efficacy by themselves.`

You need to agrees Deutsch's critique directly as to how it ispossible for an abstract form of theory proving is possible.

`It is up to Deutsch to explain what is the role of primitive stuff in`

`our experience. With comp, MGA prevents such kind of explanation.`

My point is that we cannot tacitly assume the existence ofentities that can make the distinctions (for example, betweendifference Goedelian numberings)Arithmetical (sigma_1) truth dovetails on all GĂ¶del numbering. Theinability for a universal number to really know its coding is partof the reason why their is a first person indeterminacy inarithmetic, and that is part of the explanation of why physicallaws will be apparent from the universal numbers points of view.What you just wrote and its meaningfulness vanishes if there isnot physical implementation of it.

`On the contrary, if you introduce primitively physical implementation`

`you have the problem to explain what you mean by that, and how to`

`relate them with consciousness. this is explained entirely in the comp`

`theory. Primitive matter is used by materialist like a God-explanation`

`gap. It is a postulate of something on which we are asking to not ask`

`further question. Even if comp did not detroy that notion, I would not`

`find it as having an explanatory purpose.`

You cannot dismiss the material world and keep its properties.

`Why? I can explain its properties without introducing an`

`unintelligible primitive matter in the picture.`

and thus the insistence that the physical not exist at the samelevel as numbers seems to be an error.The numbers (or other finite entities belonging to universalsystems) have to be primitive (they are not derivable by less thanthemselves). This is *necessary* not the case for physics, *by theUDA*.No, UDA only proves that the physical world cannot be monic andallow for computations. It does not prove that an idealism can work.

`It proves that IF mechanism is true, only idealism can work. Anything`

`we might add will be like invisible horse. Remember that nobody has`

`ever seen "primitive matter": it is a theological abstract notion. It`

`is not even used in physics, except as a way to put the mind-body`

`problem under the rug, usually with mechanism. My main point is`

`negative: that can't work.`

I'm intrigued by David Deutsche's assertion that differentphysics implies that different things are computable, but I'mdoubtful that it's true.I agree, it is total non sense. Not only it would contradictChurch thesis and the immunity of computability fordiagonalization, but thanks to David Deutsch quantum computer, itdoes not even make sense with what we know currently believed inphysics, and such a position is a sort of revisionist definitionof what is a computation. That's is why I prefer to callDeutsch's "Church Turing principle" the "Deutsch's thesis". Andit is an open problem if such a thesis is compatible withChurch's thesis.You are not even showing a valid proof here. Refuting Deutsch'sassertion would effectively make Yes Doctor vanish,Why? The contrary is more plausible. "Yes doctor" should a priorirefute Deustch thesis.If Deutsch is wrong, digital substitution vanishes

Why?

and so does your result.

I have no clue about what you are saying.

leaving your result vacuous. Removing all traces of the physicalworld removes all possibility of distinguishing a false proof froma true proof.Trivially so. But comp does not remove any *trace* of the physicalworlds. Only the pretension that the physical has a primary ontology.Two different meanings of the world trace. Please don't playword games.

You might elaborate. I thought I was using trace in your sense.

How are numbers more primitive than spaces?

`Which spaces? Define them axiomatically, so we can compare. But either`

`you will axiomatize a very poor notion of space (porr= non Turing`

`universal), or you will define just another universal system, which`

`will be equivalent (ontologically) with the numbers.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- 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. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.