A homomorphism is a “structure preserving map”, and is quite general until you specify what is preserved.
From my brief reading of Chalmers, he’s basically captured my objection. As Risto_Saarelma says, the point is that a mapping merely of states should not count. As long as the sets of object states are not overlapping, there’s a mapping into the abstract computation. That’s boring. To truly instantiate the computation, what has to be put in is the causal structure, the rules of the computation, and these seem to be far more restrictive than one trace of possible states.
Chalmer’s “clock and dial” seems to get around this in that it can enumerate all possible traces, which seems to be equivalent to capturing the rules, but still feels decidedly wrong.
A homomorphism is a “structure preserving map”, and is quite general until you specify what is preserved.
From my brief reading of Chalmers, he’s basically captured my objection. As Risto_Saarelma says, the point is that a mapping merely of states should not count. As long as the sets of object states are not overlapping, there’s a mapping into the abstract computation. That’s boring. To truly instantiate the computation, what has to be put in is the causal structure, the rules of the computation, and these seem to be far more restrictive than one trace of possible states.
Chalmer’s “clock and dial” seems to get around this in that it can enumerate all possible traces, which seems to be equivalent to capturing the rules, but still feels decidedly wrong.