I think the reference to cellular automata is a bit misplaced. Yes, Rule 110 is Turing complete, but I don't think this has anything to do with the sort of lookup table that Searle is appealing to. You can
write programs with Rule 110, by arranging an initial state and letting the rules mutate it. However, a lookup table that merely contains terminal endpoints can't do that. It doesn't have the necessary self-reference.
People always like to say this about Matthew Cook's result on Rule 110 and connect it to Searle's argument, but they are just totally different things. If Searle instead talked about encoding a general purpose AI program to translate sentences, and his substrate of computation happened to be a cellular automata, that's fine, but it would be no different than him postulating an imaginary C++ program that translates the sentences, meaning he would be assuming a solution to A.I. completeness from the start, whether it is via cellular automata or some typical programming language or whatever.
But the type of lookup table he is talking about is just an ordinary hash table, it's just a physical store of fixed immutable data which is not interpreted as self-referencing in a programmatic sense, but instead which simply holds onto, and is "unaware" of, translation replies for each possible input.
People always like to say this about Matthew Cook's result on Rule 110 and connect it to Searle's argument, but they are just totally different things. If Searle instead talked about encoding a general purpose AI program to translate sentences, and his substrate of computation happened to be a cellular automata, that's fine, but it would be no different than him postulating an imaginary C++ program that translates the sentences, meaning he would be assuming a solution to A.I. completeness from the start, whether it is via cellular automata or some typical programming language or whatever.
But the type of lookup table he is talking about is just an ordinary hash table, it's just a physical store of fixed immutable data which is not interpreted as self-referencing in a programmatic sense, but instead which simply holds onto, and is "unaware" of, translation replies for each possible input.