Hi Bruno

On 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 of the 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 the role of
> believability for the ideally correct machines.
>
>
> How come Bp->p is not a theorem?

>
>
>
>
>  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?

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

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

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

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