As a first off-the-cuff thought, the infinite regress of conditionality sounds suspiciously close to general recursion. Do you have any guarantee that a fully general theory that gives a decision wouldn’t be equivalent to a Halting Oracle?
ETA: If you don’t have such a guarantee, I would submit that the first priority should be either securing one, or proving isomorphism to the Entscheidungsproblem and, thus, the impossibility of the fully general solution.
I would suggest that the best move would be to attempt to coerce the situation into one where the infinite regress is subject to analysis without Halting issues, in a way that is predicted to be least likely to have negative impacts.
Remember, Halting is only undecidable in the general case, and it is often quite tractable to decide on some subset of computations.
Unless you’re saying “don’t answer the question, use the answer from a different but closely related one”, then a moral problem is either going to be known transformable into a decidable halting problem, or not. And if not, my above question remains unanswered.
I meant something more like “don’t make a decision, change the context such that there is a different question that must be answered”. In practice this would probably mean colluding to enforce some sort of amoral constraints on all parties.
I grant that at some point you may get irretrievably stuck. And no, I don’t have an answer, sorry. Chosing randomly is likely to be better than inaction, though.
Obviously any game theory is equivalent to the halting problem if your opponents can be controlled by arbitrary Turing machines. But this sort of infinite regress doesn’t come from a big complex starting point, it comes from a simple starting point that keeps passing the recursive buck.
I understand that much, but if there’s anything I’ve learned from computer science it’s that turing completeness can pop up in the strangest places.
I of course admit it was an off-the-cuff, intuitive thought, but the structure of the problem reminds me vaguely of the combinatorial calculus, particularly Smullyan’s Mockingbird forest.
As a first off-the-cuff thought, the infinite regress of conditionality sounds suspiciously close to general recursion. Do you have any guarantee that a fully general theory that gives a decision wouldn’t be equivalent to a Halting Oracle?
ETA: If you don’t have such a guarantee, I would submit that the first priority should be either securing one, or proving isomorphism to the Entscheidungsproblem and, thus, the impossibility of the fully general solution.
Hah! Same thought!
What’s the moral action when the moral problem seems to diverge, and you don’t have the compute resources to follow it any further? Flip a coin?
I would suggest that the best move would be to attempt to coerce the situation into one where the infinite regress is subject to analysis without Halting issues, in a way that is predicted to be least likely to have negative impacts.
Remember, Halting is only undecidable in the general case, and it is often quite tractable to decide on some subset of computations.
Unless you’re saying “don’t answer the question, use the answer from a different but closely related one”, then a moral problem is either going to be known transformable into a decidable halting problem, or not. And if not, my above question remains unanswered.
I meant something more like “don’t make a decision, change the context such that there is a different question that must be answered”. In practice this would probably mean colluding to enforce some sort of amoral constraints on all parties.
I grant that at some point you may get irretrievably stuck. And no, I don’t have an answer, sorry. Chosing randomly is likely to be better than inaction, though.
Obviously any game theory is equivalent to the halting problem if your opponents can be controlled by arbitrary Turing machines. But this sort of infinite regress doesn’t come from a big complex starting point, it comes from a simple starting point that keeps passing the recursive buck.
I understand that much, but if there’s anything I’ve learned from computer science it’s that turing completeness can pop up in the strangest places.
I of course admit it was an off-the-cuff, intuitive thought, but the structure of the problem reminds me vaguely of the combinatorial calculus, particularly Smullyan’s Mockingbird forest.
This was a clever ploy to distract me with logic problems, wasn’t it?
No, but mentioning the rest of Smullyan’s books might be.