Karl Svozil, "Randomness & Undecidability in
Physics", World Scientific, 1993, [chapters 10.2 - 10.5]
also speaks about the simulaton argument.
It is not unreasonable - he says - to speculate about the
logico-algebraic structure of "automaton" universes (universes
If there is a hidden computing entity, and if this computing
entity is "universal", there is no reason to exclude the so
called (intrinsic) "calculus of propositions".
Physical properties corresponding to _experimental_ propositions
are identified - in the quantum domain - with "projection"
operators on the Hilbert space. Thus Hilbert "lattice" corresponds
to a lattice of experimental propositions. Algebraic relations and
operations between these experimental propositions are called
"calculus of propositions". Hilbert lattice and calculus of propositions
_should_ be equivalent, even in the quantum domain. (Lattice theory
is a framework for organizing structures such as experimental
or logical statements). There is no _recursive_ enumeration
of the axioms of Hilbert lattices.
It is not unreasonable asking something like: do we live in a
(quantum) universe created by some "universal" computation ?
Thus, to test such speculation, we must look for _phenomena_
which correspond to "automaton" calculus of propositions _not_
contained in a Hilbert lattice (or its subalgebras).