Hi Brian,

On 24 Sep 2012, at 19:44, Brian Tenneson wrote:

Hi BrunoOn Fri, Sep 14, 2012 at 1:20 AM, Bruno Marchal <marc...@ulb.ac.be>wrote:Hi Brian, On 13 Sep 2012, at 22:04, Brian Tenneson wrote: Bruno, You use B as a predicate symbol for "belief" I think.I use for the modal unspecified box, in some context (in place ofthe more common "[]").Then I use it mainly for the box corresponding to Gödel's beweisbar(provability) arithmetical predicate (definable with the symbols E,A, &, ->, ~, s, 0 and parentheses.Thanks to the fact that Bp -> p is not a theorem, it can plays therole of believability for the ideally correct machines.How come Bp->p is not a theorem?

`If it was, Bf -> f would be a theorem, and thus ~Bf would be a`

`theorem, and this would contradict the second incompleteness theorem.`

`Or by Löb, if Bf -> f is a theorem, then by necessitation B(Bf->f)`

`would be a theorem, and by Löb (B(Bp->p)->Bp) and modus ponens, we`

`would get Bf, and by Bf -> f, we would get f, and the machine would be`

`inconsistent.`

`Bf -> f is a theorem of G*, and so its arithmetical interpretation is`

`true (in the standard model), but this the machine cannot prove.`

What are some properties of B and is there a predicate for knowing/being aware of that might lead to a definition for self-awareness?Yes, B and its variants: B_1 p == Bp & p B_2 p = Bp & Dt B_3 p = Bp & Dt & t, and others. D? B_1? B_2? B_3?

Dp is defined by ~B~p.

`B_1 p is defined by Bp & p, etc. (I mean by their arithmetical`

`interpretation). When I have more time I will give the precise`

`Solovaytheorem, here or on FOAR.`

btw, what is a machine and what types of machines are there?With comp we bet that we are, at some level, digital machine. Thetheory is one studied by logicians (Post, Church, Turing, etc.).I am also curious as to the definition of a digital machine.

`Anything emulable by a Turing machine, or anything definable by a`

`sigma_1 arithmetical relations. This is provably equivalent, and get`

`very general with Church thesis.`

Is there a generic description for a structure (in the math logicsense) to have a belief or to be aware; something likeA |= "I am the structure A" ?Yes, by using the Dx = xx method, you can define a machine havingits integral 3p plan available. But the 1p-self, given by Bp & p,does not admit any name. It is the difference between "I have twolegs" and "I have a pain in a leg, even if a phantom one". G* provesthem equivalent (for correct machines), but G cannot identify them,and they obeys different logic (G and S4Grz).DX = xx?

`I will soon explain this with the phi_i notations. But the basic idea`

`is that you can build a self-referential machine by applying a`

`duplicator to itself. If Dx produces "xx", DD will produce "DD", that`

`is itself. It is an effective diagonalization. See how to build`

`amoeba, and self-regenerating programs with this in my paper "Amoeba,`

`planaria and dreaming machines", where I illustrate in LISP how to use`

`that idea. Some subroutine are explained in the appendice of`

`"conscience & mécanisme".`

Finally, on a different note, if there is a structure for which allstructures can be 1-1 injected into it, does that in itself imply asort of ultimate structure perhaps what Max Tegmark views as thelevel IV multiverse?A 1-1 map is too cheap for that, and the set structure is a too muchstructural flattening. Comp used the simulation, notion, at a nonspecifiable level substitution.This structure I have in mind having the property that allstructures can be injected into it has more structure than a setstructure. See, I have revised my thoughts and put them into afairly short document. You helped me a year or two ago to show mesome flaws with my thoughts in a document. I could send it to you.

`OK. September is busy, but I will have more time (I hope) in october,`

`you can send it to me.`

Best, 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.