How about, “You should X, and you should accept a standard that would recommend it?” Thereby appealing to a third (shared) standard, possibly one having to do with rationality of moral beliefs. Applying an analogous moral version of Aumann’s Agreeement Theorem could lead us to a theory which suggests that you can never say this quoted sentence unless you’re willing to believe that you should accept the standard you recommend.
I do hope to avoid discussion about the common usage of “should” in favor of a theory that would allow us (if no one else) to use it consistently to refer to some shared standard, and I believe this can be done without paradox. So long as a community shares a sufficiently basic belief, it will be possible to extract shared consequences of that belief. In the same sense that a group of rationalists cannot convince non-Baysians that they should apply Aumann’s Agreement Theorem, we cannot convince an analogous group that our word “should” refers to our internally normative values. In neither case should we worry.
How about, “You should X, and you should accept a standard that would recommend it?” Thereby appealing to a third (shared) standard, possibly one having to do with rationality of moral beliefs. Applying an analogous moral version of Aumann’s Agreeement Theorem could lead us to a theory which suggests that you can never say this quoted sentence unless you’re willing to believe that you should accept the standard you recommend.
I do hope to avoid discussion about the common usage of “should” in favor of a theory that would allow us (if no one else) to use it consistently to refer to some shared standard, and I believe this can be done without paradox. So long as a community shares a sufficiently basic belief, it will be possible to extract shared consequences of that belief. In the same sense that a group of rationalists cannot convince non-Baysians that they should apply Aumann’s Agreement Theorem, we cannot convince an analogous group that our word “should” refers to our internally normative values. In neither case should we worry.