On 17 Sep 2011, at 19:07, Stephen P. King wrote:

On 9/16/2011 2:30 PM, Bruno Marchal wrote:


On 15 Sep 2011, at 23:06, Stephen P. King wrote:

On 9/15/2011 2:43 PM, Bruno Marchal wrote:


On 14 Sep 2011, at 06:13, Stephen P. King wrote:

On 9/13/2011 11:28 AM, Bruno Marchal wrote:


On 12 Sep 2011, at 22:16, Craig Weinberg wrote:

To say that complex things can result from very simple rules is true enough, but it's circular reasoning that distracts from the relevant
questions: What are 'rules' and where do they come from?

You are the one assuming some physical reality. But mechanism can explains where such physical rules come from. They are consequences of addition and multiplication. More exactly, their appearances for the average universal machine are consequences of 0, +, and *.



    Dear Bruno,

Could you give us a sketch of exactly how 'physical rules' or the appearance thereof are the "consequences of 0, + and *"? I think that there is more to the explanation than the fact that 0, + and * exist.... This is the part of your work that I still do not understand.

Well, it is the second part. the one I call AUDA.

In a sketch.
1) define provable-by-machine-PA in the arithmetical language {0, s, +, *, "E", "A", etc.}. Like in Gödel 1931. This gives Bp (for beweisbar <some arithmetical proposition>. This will play the role of the "scientific rational opinion of the machine". 2) Solovay: the truth about the logic of Bp is given by G*. The provable part of it is given by G. 3) define the knowledge of the machine by Bp & p. (Theatetus) The logic of Bp & p is given by S4Grz (a logic of a form of intuitionist evolving antisymmetrical knowledge.
4) define observable by Bp & Dt  (logic Z and Z*-
5) define feel-able by Bp & Dt & p (logic X and X*)
Note that the splitting proof/truth (G/G*) extends to Bp & Dt, and to Bp & Dt & p; that is the observable and the feel-able.

Then (eneter the arithmetical UD): restrict the arithmetical realization of the sentence letters p to the sigma_1 sentence. You get the logic Z1* (quanta and qualia). the quanta appears in the non communicable part, and are particular case of qualia, and this assure our coherence: we share histories (this is what Everett confirms the most: we are collectively multiplied by huge factor, and symmetry and linearity appears at the arithmetical quantum bottom.

If comp is correct, and if the Theatetus's idea is correct, Z1* gives the probability one, and you can deduce the other probabilities from there (von Neumann old criteria for a genuine quantum logic).

I hope I was not too sketchy. Use this to dig on the second part (the interview of the LUM, it is AUDA) of the sane04 paper.

Bruno

snip

Umm, OK. David Deutsch discusses ideas in his new book that seem to strongly ague against this idea that an equation, even a sigma_1 sentence that is very elaborate, alone can act as a proof.

I have never said that. A proof is a sequence, or a graph, or a diagram, but always amenable to a sequence, of formula, starting from other formula.

[SPK]
    So how do you avoid infinite regress?

By sthe second recursion theorem of Kleene. Or, more simply, by diagonalization. If Dx gives xx, then DD gives DD. This simple idea explain how numbers can be self-referential relatively to universal numbers.



You seem posit as primitive some form of number and then build a structure upon it that serves as an explanatory model for 'everything', including the appearance of a physical world with laws, all the while not explaining how it is that the primitives have the properties that they have other than pointing to our experience of mathematical entities.

I postulate only two things:
1) that I can survive with a digital brain in this mundane consensual reality (the nature of which I am neutral about) 2) that elementary proposition on natural numbers are true independently of me and you. All scientists do this.





This is circular! In my thinking we can embrace circularity to some extent, via non-well founded sets/logics, but even there we cannot violate basic principles of contradiction and identity.

Where do I violate principles of contradiction and identity?



I distinguish between the implementation of a representation of a proof - given in terms of some configuration of matter - and the relations and structure of the proof itself.

Nice. me too.



I see this as a basic duality between abstract algebras and concrete structures, taking neither as primitive.

What do you take as primitive?





I am having to reevaluate my thinking of UDA and AUDA as I read The Beginning of Infinity...

This means you have not understand them. It is just a question of understanding. You might decide to reevaluate the truth of the mechanist assumption, but I am not really interested in that question. The reasoning shows that mechanism is incompatible with phsyicalism/naturalism, and it need to be understood, not evaluate, nor reevaluate, nor accepted. But understood or perhaps to be shown containing a flaw, or a missing step, or something unclear.
[SPK]
I see a difference between understanding an idea and believing that it is true.

The point is that there is no idea, and certainly no truth assertion at all. But you cannot understand a proof and still doubt that the conclusion does follow from the premises. Once you understand the proof that there is no natural numbers x and y such that x^2 = 2* y^2, you stop to pretend that such numbers exist, or you are irrational. It is the same with mechanism: it shows that substance-matter is a concept void of any explanative power in physics, and that the physical laws are not primitive and evolve in a precise way in arithmetic.



My problem boils down to being asked to believe that an abstract version of a perpetual motion machine can exist without problems.

?



A Platonic turing machine, or equivalent in Post, Peano, Goedel, etc. terms, is defined in ways that ignore all requirements of physical reality.

I don't postulate a physical reality, but even if I did, it is a fact that computer can exist without violating any law of physics. The physical requirements are explained in a non physical theory.



They can perform computations (which I interpret as transformations of information) without any reliance on the ability of a physical system to implement them. I know that this is explicit in their definition, but it is this definition that I have a problem with!

This is basic and well explained in elementary textbook in theoretical computer science. It is no more mysterious than the truth of elementary arithmetical propositions.



How are we to take literally an idea, used to explain and predict physical and psychical phenomena, that violates the simple principle that 'there is not such thing as a free lunch', without some explanation - other than some musings about the ideas of some famous Greek fellow?

If you doubt in the independence of the arithmetical truth, then explain me the law of dependence, and explain me what are your primitive elements in your theory.



We can recast this problem in terms of explaining the appearance of change in a universe that is static.

This is something else. This is explained by the indexical approach to time, and is as much a problem for a physicalist than an objective idealist. It concerns any block-conception of reality. With mechanism the explanation is that the "Bp & p" is a logic of subjective duration. Consciousness select histories and glue them into conception of realities.





UDA shows that mechanism is not compatible with physicalism. David Deutsch is both mechanist and physicalist, so its theory/world-view is inconsistent/non-sensical (like the current widespread mechanist Aristotelianism).



I still suspect that you are neglecting the role that you are playing with regard to your work. Without a person (or something like an entity to whom meaningfulness can obtain) to interpret the sigma_1 sentences, they are not different from a random configuration of marks on a chalkboard or pixels on a computer monitor.

You confuse a formula (a mathematical object in metamathematics) and a representation of a formula.


Am I? How do you explain the relation between the two? Oh, I forgot, you claim that the physical stuff is just a 'dream of the numbers'...

I am not claiming that. I am claiming that it follows logically from the mechanist assumption. I am not saying that the mechanist assumption is true.



Forgive my cynical tone, but I have invested a lot of time reading and thinking about your ideas as expressed in your posts and papers, please consider that I am trying very hard not to argue against a straw man version of your idea.

I am used to cynical tone. The problem is that it is never clear if your idea are presented for doubting mechanism (my working assumption) or doubting that there is no flaw in the reasoning.






The problem of Boltzmann Brains in infinite universes seems related to this problem that I am seeing!

The UD can be considered as a strong and precise generalization of that idea. That is the comp mind-body problem. A transformation of the mind-body problem into a purely arithmetical body problem. The solution already found shows that the picture of the epistemological reality of the machine is a theology in the greek sense of the term: a theory of everything explaining the origin of God, souls, intellect, the observable realm and the feel-able dynamics/interactions.

[SPK]
The problem with Boltzmann Brains is how is it that the computational content of one is related to the content of another in some sequential way?

On the contrary. The BB problems comes from the assumption of mechanism, which indeed can glue infinities of BB in ways which could lead to contradiction with the known physics. With comp this is made into a precise mathematical problem (the measure on the sigma_1 proposition and their constructive proofs (computations).



Any given BB is only instanciated for a moment by chance... So we need an infinite ensemble of BBs and an explanation that is not regressive of how their computations are connected.

Comp explains that there is a statistical connexion which drives the consciousness fluxes.


Does your UD do this?

The UD generates the computations on which the statistic bear, and consciousness build the epistemological realities, including the physical one.



BTW, this thought-experiement does not have the 'free lunch' problem because it involves a physical/thermodynamic component..

But that is a problem, because it assumes comp, and comp forbids the reference to a primitive universe.




You seem to rely to much on a hypothetical 3p to act as an abstract version of a "perceiver of meaningfulness" without admitting this reliance.

It is explicit in the act of saying "yes to the doctor", which is part of the explicit assumption. The 'hypothetical 3p", arithmetic, is taught in schools since Pythagorus (at least). The human intuition about it is probably as old as music.


[SPK]
"Yes Doctor' explicitly requires the existence of a physical entity to make the choice

A person makes the choice. It is not a physical entity. You confuse a person with one of its local body.



and this cannot be abstracted away in some limit of computational sequences.

Then UDA is wrong. Where?



The same goes for the copy/clone scheme that is used to explain 1p indeterminancy.

Only for pedagogical purpose. This is explicitly eliminated at step 7 and 8.






If 3p is truly independent of any 1p,

It is, by arithmetical realism. If you believe that "17 is prime" depends on humans, I will ask you to define "humans" and to show explicitly the functional dependence.


[SPK]
This is why I have a problem with realism. It fails to provide an explanation of how the 3p and 1p are correlated other than pointing to the fact that we humans do in fact experience something that is like having an experience of something.

It is the relation between Bp and Bp & p. It is trivial for the ideally correct machines, which use of is enough to explain the origin of the physical laws, in a way coherent with the immaterialist consequences of mechanism.





then how are they related such that we can, as individual minds, have a subjective experience of 3p aspects of existence?

The 3p physical aspects is the 1p plural person views of the 3p arithmetic, when seen from inside. (Consequence of UDA).

[SPK]
I agree this this, but cannot you see that this inside/outside relation is the very same relation that I am promoting as a form of dualism?

I have already agree on this many times. You are the one throwing doubt on that connection. Mechanism leads to phenomenological octalism (the eight hypostases). Your dualism is well approximated by the dualism between Bp and Bp & p. It is made precise by taking into account the communicable and non communicable parts explicitly.



This dualism vanishes in the limit of existence itself, but at the level of existence itself we have a neutral monism;

Yes, and with mechanism, the neutral monist ontology is given by any first-order logical specification of any universal system. they all leads to the same number theology, including physics. Physics is made 100% theory and observer independent, despite it being a construction of "program" consciousness.



difference itself vanishes there. There is not such thing as number or anything else at that level!

So what are the elements of your neutral monism?




With AUDA we can say more. The 1p/3p relations come, in the machines' perspectives, from ignoring that Bp is equivalent with Bp & p, which true equivalence is known only by the "divine intellect" (G*). This gives a theory of non syntactical knowledge, obeying the admitted knowledge theory (S4) , equivalent with the correct opinion of the correct machine, but not in a way such that the machine can know this, except by betting on comp and its own correctness, and this, at its own risk and peril.

[SPK]
    Sure, but this is just the abstract half of the duality!

I don't see what is missing, and I realize I have no clue about what is your primitive ontology.

Bruno

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



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