The usual implicit approach is to explore the tree of arguments and counterarguments, using disagreement as a heuristic to prioritize which points to explore in more detail… Often this doesn’t work because Alice and Bob have wildly different intuitions about a whole bunch of different questions… What to do then?
Apologies for being dense, but I would also describe the procedure that you lay out following this bit as a “tree of arguments and counterarguments, using disagreement as a heuristic to prioritize which points to explore”.
What’s the crucial difference between the procedure you describe and the usual approach? Is it that whenever you hit on any subquestion simple enough to resolve, everyone updates their intuitions and you start again from the top?
(“They repeat this process until they reach a state where they don’t have any significant disagreements about subclaims… Alice and Bob then start the process over with their new intuitions.”)
Changed to: “A common (implicit) hope is to exhaustively explore the tree of arguments and counterarguments, following a trail of higher-level disagreements to each low-level disagreement.”
I’m distinguishing between hoping to change your view about the root question by getting to each disagreement in turn and propagating the logical consequences of resolving it, or viewing each disagreement as an observation that can help refine intuition / arbitrate between conflicting intuitions.
Apologies for being dense, but I would also describe the procedure that you lay out following this bit as a “tree of arguments and counterarguments, using disagreement as a heuristic to prioritize which points to explore”.
What’s the crucial difference between the procedure you describe and the usual approach? Is it that whenever you hit on any subquestion simple enough to resolve, everyone updates their intuitions and you start again from the top?
(“They repeat this process until they reach a state where they don’t have any significant disagreements about subclaims… Alice and Bob then start the process over with their new intuitions.”)
Changed to: “A common (implicit) hope is to exhaustively explore the tree of arguments and counterarguments, following a trail of higher-level disagreements to each low-level disagreement.”
I’m distinguishing between hoping to change your view about the root question by getting to each disagreement in turn and propagating the logical consequences of resolving it, or viewing each disagreement as an observation that can help refine intuition / arbitrate between conflicting intuitions.