Another way I like to phrase this thought (without getting into the details about whether Aristotle and Nietzsche agree or disagree), is that morality is a syst

Another way I like to phrase this thought (without getting into the details about whether Aristotle and Nietzsche agree or disagree), is that morality is a system of rules for making decisions. Turing machines and computation more generally allow for the implementation of arbitrary decision procedures. However, if you want that those decision procedures to be consistent, you need something else, namely a set of axioms. Goedel, Turing, Church, etc. have proved (more or less) that there is no set of axioms that gives universally true answers for all decisions, so there can be no provably objective system of morality. Thus, we must choose our axioms, if we do not, we usually choose implicitly (which I think is related to Nietzsche's abhorrence of slave morality). Aristotle represents a set of axioms that are practically applicable to many human relations, representing a pretty good default, if you have to choose one. Nietzsche says, (to use the words of another) 'choose again.'