Comment status: I may change my mind on a more careful reading.
Other respondents have mentioned the Mathematical Macrocosm Hypothesis. My take differs slightly, I think. I believe you’ve subtly contradicted yourself. In order for your argument to go anywhere you had to assume that an abstract computation rule exists in the same sense as a real computer running a simulation. This seems to largely grant Tegmark’s version of the MMH (and may be the first premise I reject here). ETA: the other branch of your dilemma doesn’t seem to engage with the functionalist view of qualia, which says that the real internal behavior or relationships within a physical system are what matter.
Now, we’re effectively certain that our world is fundamentally governed by mathematical laws of physics (whether we discover the true laws or not). Dualist philosophers like Chalmers seem to grant this point despite wanting to say that consciousness is different. I think Chalmers freely grants that your consciousness—despite being itself non-physical, on his view—is wholly controlled by physical processes in your brain. This seems undisputed among serious people. (You can just take certain chemicals or let yourself get hungry, and see how your thoughts change.)
So, on the earlier Tegmark IV premise, there’s no difference between you and a simulation. You are a simulation within an abstract mathematical process, which exists in exactly the same way as an arithmetical sequence or the computational functions you discuss. You are isomorphic to various simulations of yourself within abstract computations.
Chalmers evidently postulates a “bridging law” in the nature of reality which makes some simulations conscious and not others. However, this seems fairly arbitrary, and in any case I also recall Chalmers saying that a person uploaded (properly) to a computer would be conscious. I certainly don’t see anything in his argument to prevent this. If you don’t like the idea of this applying to more abstract computations, I recommend you reject Tegmark and admit that the nature of reality is still technically an open problem.
Comment status: I may change my mind on a more careful reading.
Other respondents have mentioned the Mathematical Macrocosm Hypothesis. My take differs slightly, I think. I believe you’ve subtly contradicted yourself. In order for your argument to go anywhere you had to assume that an abstract computation rule exists in the same sense as a real computer running a simulation. This seems to largely grant Tegmark’s version of the MMH (and may be the first premise I reject here). ETA: the other branch of your dilemma doesn’t seem to engage with the functionalist view of qualia, which says that the real internal behavior or relationships within a physical system are what matter.
Now, we’re effectively certain that our world is fundamentally governed by mathematical laws of physics (whether we discover the true laws or not). Dualist philosophers like Chalmers seem to grant this point despite wanting to say that consciousness is different. I think Chalmers freely grants that your consciousness—despite being itself non-physical, on his view—is wholly controlled by physical processes in your brain. This seems undisputed among serious people. (You can just take certain chemicals or let yourself get hungry, and see how your thoughts change.)
So, on the earlier Tegmark IV premise, there’s no difference between you and a simulation. You are a simulation within an abstract mathematical process, which exists in exactly the same way as an arithmetical sequence or the computational functions you discuss. You are isomorphic to various simulations of yourself within abstract computations.
Chalmers evidently postulates a “bridging law” in the nature of reality which makes some simulations conscious and not others. However, this seems fairly arbitrary, and in any case I also recall Chalmers saying that a person uploaded (properly) to a computer would be conscious. I certainly don’t see anything in his argument to prevent this. If you don’t like the idea of this applying to more abstract computations, I recommend you reject Tegmark and admit that the nature of reality is still technically an open problem.