The main problem of AI is not function approximation itself, or the search for function approximators, but the metatheory of search, I think.
Quite the opposite! there can be no hidden source of truth, there is a mathematically optimal way establish what right you have to place your confidence in a belief, and it follows that there is an optimal way to search for function approximators.
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so would these decision-making optimizations be the calculation of statistical probabilities? and just in addition, this kind of access would really make an AI very different than what's going on in animal intelligence
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Yes, in the sense that they can be derived from a priori principles that allow you to conquer the space of ways of doing statistics. Evolution has been a crude way of sampling that space, until it came up with the first universal computer capable of proving optimality conditions
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