In the following I am not considering substance dualism or idealism, but only materialist/physicalist theories.
The Church-Turing thesis states:
Every ‘function which would naturally be regarded as computable’ can be computed by the universal Turing machine.
The Church-Turing-Deutsch principle is a stronger version of the original Church-Turing thesis, that states:
Every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means
A Turing machine functions using the basic laws of logic, and even very small Turing machines are universal (i.e. capable of simulating any other Turing Machine).
As I mentioned earlier, discounting the existence of non-physical entities, this means that anything finite in the universe can be simulated by and therefore reduced to, a very small set of rules. It seems to me that this just a restatement of reductionism.
My question is: If you agree with the Church-Turing-Deutsch principle, are you implicitly subscribing to reductionism (therefore disavowing non-reductionist materialist views such as emergentism)?