I agree that if we had a general theory of logical uncertainty, then we wouldn’t need to have an answer to Robin’s question.
Counterexample request: can you give me a specific case where it matters which computation I view myself as, given that I’m allowed to make general mathematical inferences?
I think the old True PD example works here. Should I view myself as controlling the computation of both players, or just player A, assuming the two players are not running completely identical computations (i.e. same program and data)? If I knew how I should infer the decision of my opponent given my decision, then I wouldn’t need to answer this question.
What I would generally say at this point is, “What part of this is a special problem to TDT? Why wouldn’t you be faced with just the same problem if you were watching two other agents in the True PD, with some particular partial knowledges of their source code, and I told you that one of the agents’ computations had a particular output? You would still need to decide what to infer about the other. So it’s not TDT’s problem, it legitimately modularizes off into a magical logical inference module...”
(Of course there are problems that are special to TDT, like logical move ordering, how not to infer “A1 has EU of 400, therefore if I output A2 it must have EU > 400”, etc. But “Which computation should I view myself as running?” is not a special problem; you could ask it about any calculator, and if the inference mechanism is sound, “You can use multiple valid abstractions at the same time” is a legitimate answer.)
I agree that if we had a general theory of logical uncertainty, then we wouldn’t need to have an answer to Robin’s question.
I think the old True PD example works here. Should I view myself as controlling the computation of both players, or just player A, assuming the two players are not running completely identical computations (i.e. same program and data)? If I knew how I should infer the decision of my opponent given my decision, then I wouldn’t need to answer this question.
What I would generally say at this point is, “What part of this is a special problem to TDT? Why wouldn’t you be faced with just the same problem if you were watching two other agents in the True PD, with some particular partial knowledges of their source code, and I told you that one of the agents’ computations had a particular output? You would still need to decide what to infer about the other. So it’s not TDT’s problem, it legitimately modularizes off into a magical logical inference module...”
(Of course there are problems that are special to TDT, like logical move ordering, how not to infer “A1 has EU of 400, therefore if I output A2 it must have EU > 400”, etc. But “Which computation should I view myself as running?” is not a special problem; you could ask it about any calculator, and if the inference mechanism is sound, “You can use multiple valid abstractions at the same time” is a legitimate answer.)