There is in fact such a thing as a learner with a sub-Turing hypothesis class. Such a learner
with such a primitive output as “in the class” or “not in the class” does not engage in
world optimization, that is: its actions do not, to its own knowledge,
skew any probability distribution over future states of any portion of the world outside itself.
…
Now, what we’ve been proposing as an Oracle is even less capable.
which led me to think you were talking about an oracle even less capable than a learner with a sub-Turing hypothesis class.
It would truly have no outputs whatsoever, only input and a debug view. It would, by definition, be
incapable of narrowing the future of anything, even its own internal states.
If the hypotheses it considers are turing-complete, then, given enough information (and someone would give it enough information, otherwise they couldn’t do anything useful with it), it could model itself, its environment, the relation between its internal states and what shows up on the debug view, and the reactions of its operators on the information they learn from that debug view. Its (internal) actions very much would, to its own knowledge, skew the probability distribution over future states of the outer world.
You said
which led me to think you were talking about an oracle even less capable than a learner with a sub-Turing hypothesis class.
If the hypotheses it considers are turing-complete, then, given enough information (and someone would give it enough information, otherwise they couldn’t do anything useful with it), it could model itself, its environment, the relation between its internal states and what shows up on the debug view, and the reactions of its operators on the information they learn from that debug view. Its (internal) actions very much would, to its own knowledge, skew the probability distribution over future states of the outer world.