On 19 Nov 2012, at 19:46, meekerdb wrote:

On 11/19/2012 8:33 AM, Bruno Marchal wrote:and the math shows that this will include some continuous/analogobservable.How does it show that?

`Intuitively: by dovetailing on each programs coupled with real`

`numbers. Each computations are done again with all possible streams of`

`real numbers, oracles, etc. Yes the UD is that dumb.`

`But this is probably needed for the measure question. We can even bet`

`that such a coupling has to be exploited by the "winner program" in`

`some special way, if it exists, because even the white rabbit`

`realities are multiplied into a continuum by the existence of that`

`coupling (which is unavoidable: you can't diagonalize against the UD`

`to build a UD avoiding those couplings).`

`Formally: the existence of such a semantics based on a continuum is`

`reflected in the possible topological semantics of the material`

`hypostases S4Grz1, Z1* and X1*, which gives rise to the arithmetical`

`quantum logics.`

`The formal reasons are different for S4Grz1, and the Z and X logics.`

`The topology is intrinsic to the S4Grz type of semantics, but it might`

`still be discrete at that level. For the X1* and Z1*, it comes in part`

`from the lack of necessitation, and the necessity to have infinite`

`sequences of neighborhood structures à la Scott-Montague.`

`If he quantum logic would have given only by S4Grz1, that would have`

`been an argument for loop gravity, and the continuum would have been`

`restricted to the frequency-statistical operator (like in Preskill and`

`Hartle or Graham).`

`If it would have appeared only in the Z and X logic, that would have`

`suggested that String theory might be the correct comp physics.`

`Amazingly the "arithmetical/comp" quantum logics seems to appear in`

`the three possible candidates (S4Grz1, Z1*, X1*).`

`Needless to say this is suggestive and it remains quite a lot of open`

`problems in logic to proceed. What I hope is that the arithmetical`

`quantum logics will give the quantum logic searched, but not found, by`

`von Neumann, which have the property that the probabilities can be`

`derived from the constrains given by the laws for the case of P(x) =`

`1. If this does not work, it means that we might use a stronger`

`definition of knowledge than the one given by Theaetetus.`

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.