Dear Bruno,
Does your thesis survive without the notion of duplicatability or copying? As I have pointed out, QM does not allow duplication and I am hard pressed to understand how duplication can be carried out in classical physics.
If computationalism is true, it's possible in principle to implement a CA on our boring (i.e. non-quantum, classical) computers that contains conscious beings. Since we would have access to every single bit of information in this CA universe, we could make exact, bit-level copies of these conscious beings. This alone is enough to open the door to all of the philosophical issues we discuss on this list. We can make one copy of the CA and send it to a computer in Moscow, while we leave one copy running here in Washington... and so on.
Presumably, these CA beings would be hard pressed to make copies of themselves while working within the constraints of their own physics; similarly, we may never figure out how to construct matter transmitters and matter copiers within our own physics. But that doesn't change that fact that, in principle, an exact copy of me could be made - say, by a "being" outside of this universe who has total access to this universe's state information and the ability to change it. (Of course, this is a very single-world way of looking at things - imagining that our universe is like a single-history deterministic or indeterministic CA that can be viewed and changed by some outside computer programmer. In actual fact, I take a more complex multi-worlds view, but that view only makes sense after you work out the consequences of "copying". The easiest way to work that out is to concentrate on simple single-world scenarios, like CA worlds that we have perfect information about.)
If we merely consider the Platonia of mathematics we find only a single example of each and every number. If we assume digital substitutability there would be one and only one number for each and every physical object. Where does duplication obtain in Platonia?
The suggestion that there is only "a single example" of each number in Platonia is so ontologically wispy that I don't even know how to label it true or false. Presumably every real number - that is, every possible infinite string of 0s and 1s - "exists" in Platonia. Even if we insist that each real number exists "only once", it follows that any given integer - that is, any given finite string of 1s and 0s - will appear an infinite number of times within the digits of these real numbers. So in fact, we can just as easily say that each integer exists "an infinite number of times" in Platonia.
This is not an idle example. Every possible history of every possible CA exists in Platonia, and even if we insist that each of these unique histories exists "only once", it still follows that some particular *finite* pattern of bits which represents a conscious being will appear innumerable times within these CAs. Within some of these universes there will be beings who create large "computers" in their worlds, and run CAs on them which contain other beings, and they will be able to make perfect copies of these beings. All of the philosophical questions about copying and identity and 1st person vs. 3rd person views apply here.
-- Kory
