I have been reading your paper "Computation, Consciousness and the
Quantum" and am puzzled by the statement:
"...I mention we loose, with the Z logics, the necessitation rule. Because
of that we loose the facilities of Kripke world-semantics, and in fact, at
this stage it can be argued that we loose $all$ the universes."
Why this puzzles me is that it seems obvious that if we "loose $all$ the
universes" we also loose the one that we experience. How is it possible to
have even 1-indeterminancy without the existence of at least one universe,
even if it is a "solipsist's one"? How is it possible for me to even justify
my belief that I am actually sitting in front of my keyboard and computer
monitor and writting these words if "we loose $all$ the universes"?
It could be that I do not understand how you reconstruct an appearence
of a 1-person expereince with only arithmetical realism and the church
thesis. Your thesis (and that of Schmidhuber and others) explicitly excludes
any reality to the "hardware" required to "implement" the "objects"
represented by UTM's or equivalents and merely assumes the existence of a
"Platonia" that exists a priori.
This is mere hypostatiation and since we can prove, via your our
reasoning, the non-existence of the Necessitation rule for Z logics, what
difference does it make if we can merely point at pixels on our Monitors or
spots of ink on our hardcopies and claim: "See "S4Grz = S4Grz*", that thus
... "truth is provability, provability is truth"". We can make any claim we
like but if our theories themselves forbid the very exixtence of a universe,
such as the one containing 1-person experiences and some 3-indeterminant
version of space-time-momentumenergy, this is all academic sophistry!
Please help me understand what I am missing!