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.



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.

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.



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.



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.



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.



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).

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.

Bruno

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



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