On 20 Apr 2011, at 01:15, Stephen Paul King wrote:

Hi Bruno,You mentioned in a previous mail “the duality between Bp and Bp&p”. Could you elaborate on this? Is it a Stone or a Pontryaginduality? (these are different!)

`Not at all. It is more akin to the cartesian mind-body duality. Bp`

`gives the third person discourse given by the machine, and Bp & p`

`gives the first person knower linked to that machine. Bp is third`

`person self-reference, like when you discuss with your doctor about`

`your temperature and body constitution, and Bp & p is the Plotinus`

`inner god, or soul, which the amchine cannot even name.`

Also, are there any restriction on the content of theproposition p?

p is for any arithmetical proposition (assuming comp)

`p is for any sigma_1 proposition (assuming comp, and assuming that the`

`machine assumes comp too). In that case the hypostases are restricted`

`to the propositions accessed by the Universal Dovetailer.`

Could a model of a possible world be a p?

`No. p are (roughly speaking) finite syntactical object. A model is an`

`infinite structure. p might be satisfied, or not, by a model (true in`

`that model).`

`In the modal context, and in a model, we can use a stone-like duality`

`to "model" a proposition by a set of models. This is useful for the`

`hypostase which have no Kripke semantics. But this is technic. In Bp &`

`p, it is better to think of p as a syntactical arithmetical`

`proposition (it can be a huge one!).`

I ask this because so far you seem to only consider p that aretautologically true (such as 2+2 = 4)

p can be 2+2=5. In that case, the correct machine will not know p.

and thus are trivially independent of observer notions.

`The observer is defined in the third person way by its body/program or`

`relative number (relative to some probable universal environement/`

`history).`

What about the contents of Observer Moments? Could they be p?

`They can be accessible "p", like "I am in Washington" after a self-`

`duplication experience, or in the universal dovetailing.`

I suspect that the in the “&p” (and p is true) is where theconcreteness, that I have referred to before, lies hidden; for insituations where the truth or untruth of a proposition that involvespossible worlds (not just the truth of arithmetic statements) thereis a requirement of a concrete realization between the observer ofthat world and the possible world. This latter idea is explicit inthe Everett and Rovelli Interpretations. (Concreteness is theproperty of being “this and not anything else” that is invariant topoint of view.)

`Perhaps. I would say that the concreteness is in both B and p (in Bp &`

`p). Also the duality above, the cartesian one, extends itself into the`

`duality between Bp & Dt and Bp & p & Dt (or Dp, it is equivalent).`

`The concreteness is then made even more concrete by imposing the`

`existence of a model satisfying the proposition (assuming the machine`

`talk first-order logic, Dt is equivalent with the existence of a model`

`by Gödel's completeness theorem).`

`But remember that, unlike Everett and Rovelli, we do not assume QM,`

`nor the existence of a primitive physical world. A concrete`

`realization is just a local and relative very probable (with the comp-`

`measure) universal number.`

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.