On 10/26/2011 12:44 PM, Bruno Marchal wrote:

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On 26 Oct 2011, at 05:34, Stephen P. King wrote:On 10/25/2011 4:40 PM, Russell Standish wrote:On Mon, Oct 24, 2011 at 04:08:38PM +0200, Bruno Marchal wrote:On 23 Oct 2011, at 04:41, Russell Standish wrote:On Fri, Oct 21, 2011 at 02:14:48PM +0200, Bruno Marchal wrote:So the histories, we're agreed, are uncountable in number, but OMs(bundles of histories compatible with the "here and now") aresurelystill countable.This is not obvious for me. For any to computational states which are in a sequel when emulated by some universal UM,there are infinitely many UMs, including one dovetailing on the reals, leading to intermediate states. So I think that the "computational neighborhoods" are a priori uncoutable.Apriori, no. The UMs dovetailing on the reals will have only executeda finite number of steps, and read a finite number of bits for agivenOM. There are only a countable number of distinct UM states making up the OM.The 3-OM. But the first person indeterminacy depends on all the (infinite) computations going through all possible intermediary 3-OMs states.So does the OM I'm referring to. Does that still make is a 3 OM?That fits with the topological semantics of the first person logics (S4Grz, S4Grz1, X, X*, X1, X1*). But many math problems are unsolved there.You will need to expand on this. I don't know what you mean.I have explained this to Stephen a long time ago, when explaining why the work of Pratt, although very interesting fails to address the comp mind body problem. Basically Pratt's duality is recover by the "duality" between Bp (G) and Bp& Dt (Z1*) or Bp& Dt& p (X1*). You might serach what I said by looking at Pratt in the archive, with some luck.This is above my level of understanding at present. Hopefully, there will be some quiet time soon to study this, as it sounds interesting!Hi Russell and Bruno,, I recommend that you read Steve Vickers' "Topology Via Logic" first.I would not have discovered, and take seriously, the materialhypostases without it, I think. I give him full credit in mypublications. Abramski played some role too. Very nice book, but stillquite abstract. I have already commented Pratt at large.The other reason to use the self-reference logics is that it distinguish automatically the quanta (sharable, communicable at least in a first person plural way) from the qualia (not sharable, purely individual), all this by the Gödel-Löb-Solovay proof/truth splitting of the modal logics.Yes - that is interesting, but is true of any modal logic (apart from S4Grz, it would appear).But how do you obtain the mutual orthogonality of observables on aquantum logic? We must address the relationship betweenorthocomplete lattices and Boolean algebras at some point!The ortholattice are the gluing of Boolean algebraic dreams ofuniversal machines (the boolean algebra describing their consistenthistories). It gives the differentiation/fuse structure of the localand partial boolean algebras.But dually the ortholattices can be internalized as structured subsetsin Boolean algebra, or by Kripkean semantics.An apparent conspiracy of nature prevent such "duality" to bealgebraically interesting, in the quantum case. I guess we have tolive with this.In the digital case, it is an open problem. It makes interesting tosolve the digital case, just to see if such conspiracy of nature is aphysical law or a geographical misfortune. This can be translatedmechanically into a set of arithmetical problem, but those are *very*complex (that's the weakness of the interview of the universal machineon such question).Bruno http://iridia.ulb.ac.be/~marchal/

Hi Bruno,

`From what I can tell so far, ortholattices have Boolean algebras in`

`an orthogonal relationship, similar to the independent unit vectors in a`

`linear vector space. Does non-distributivity follow from this? I can see`

`the relation they have to Kripkean semantics but do cannot act as`

`contractuals. I am still studying. Have you written any new papers`

`covering more detail of the material hypostases? I was unable to find`

`your detailed discussion of Pratt's duality in the List archive...`

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