It seems to me that COMP is more general that computationalism since it seems to include certain unfalsifiable postulations that are independent of computationalism per say, AR, to be specific.
A can be unfalsifiable, and B can be unfalsifiable, but this does not entail that A & B is unfalsifiable. Take A = "god exists", and B = "God does not exist" as an exemple. I don't know if AR per se is unfalsifiable, but I do show that comp is falsifiable. But you don't have begin to criticize the proof ...
My own difficulties with Bruno's thesis hinges on this postulation. I see it as an avoidance of a fundamental difficulty in Foundation research, how to account for the 1st person experience of time if one assumes that Existence in itself is Time-less.
I would like to stay modest, but this is well explained once you realise that the simplest thaetetus definition of knowledge, where
(I know p) = (p and (I prove p))
leads directly toward an antisymmetric form of branching time modal theory, (S4Grz), very akin to Brouwer's theory of time/consciousness.
This is somewhere else that I trip over and fall in my thinking of your work, Bruno. Is this "no mechanism can compute the output of any self-duplication" a classical version of the "no-cloning" theorem?
Not so directly, but yes I do think those are related. (But it's a little out of the scope we are presently discussing).
Does my comment above about how to bridge this gap of emulating a brain
and emulating the entire universe? If it does it would seem to dramatically
increase the computational power requirements of the emulating computation
on top of the exponential slowdown.
One technical question I have about this is: if we assume that the
emulated universe is finite, what would be the equation showing the required
computational power of the emulator given an estimate of the total
algorithmic and/or information content of the universe?
The main idea on which most agrees in this list is that the information content of the "everything" (or the multiverse, or UD*, ....) is zero.
Additionally, what are we to make of results such as the Kochen-Specker theorem that show that given any quantum mechanical system that has more than two independent degrees of freedom can not be completely represented in terms of Boolean algebra?
You should say "can not be completely represented with a logical morphisme in
a boolean algebra. But that does not entail that some other representation will
not work. This is obvious: the theory "quantum mechanics" *is* a boolean theory;
the hilbert spaces are classical mathematical object, etc. Or better, take the
Goldblatt theorem (which plays a so prominent role in my thesis). It says that
(where B is some modal logic):
Quantum Logic proves a formula A iff the classical modal theory B proves []<>A.
It's like the theorem of Grzegorczyk which says that Intuitionistic Logic proves a formula A iff the classical modal theory S4Grz proves []p.
The transformation A =====> []<>A is just not a morphism in the Kochen & Specker sense.
The "physical reality" I extract from comp cannot itself be embedded in a boolean algebra, apparently (I have not yet a totally clean proof of that statement, but let us say that only a high logical conspiracy would make boolean the "arithmetical quantum logic").
Bruno
http://iridia.ulb.ac.be/~marchal/
