The question is, given a situation in which intuition A demands action X and intuition B demands action Y, what is the morally correct action? The answer might be “X”, it might be “Y”, it might be “both actions are equally good”, or it might be even “Z” for some Z different from both X and Y. But any answer effectively determines a way to remove the contradiction, replacing it by a consistent overarching system. And, if we actually face that situation, we need to actually choose an answer.
This reminds me of my rephrasing of the description of epistemology. The standard description started out as “the science of knowledge” or colloquially, “how do we know what we know”. I’ve maintained, since reading Bartley (“The Retreat to Commitment”), that the right description is “How do we decide what to believe?” So your final sentence seems right to me, but that’s different from the rest of your argument, which presumes that there’s a “right” answer and our job is finding it. Our job is finding a decision procedure, and studying what differentiates “right” answers from “wrong” answers is useful fodder for that, but it’s not the actual goal.
This reminds me of my rephrasing of the description of epistemology. The standard description started out as “the science of knowledge” or colloquially, “how do we know what we know”. I’ve maintained, since reading Bartley (“The Retreat to Commitment”), that the right description is “How do we decide what to believe?” So your final sentence seems right to me, but that’s different from the rest of your argument, which presumes that there’s a “right” answer and our job is finding it. Our job is finding a decision procedure, and studying what differentiates “right” answers from “wrong” answers is useful fodder for that, but it’s not the actual goal.