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With automata, something that is turing complete can also do what all lower levels of automata can do. E.g. something that is a turing machine can function as a finite state machine, but it is not just a finite state machine. Likewise, a soul is capable of doing all computations a turing machine can do (this is indisbutably true, otherwise we'd have never been able to make computers in the first place), but it isn't just a turing machine.