It seems clear to me that customs and agreements involve “something shared” in the sense Wei intends. As a result, it sounds straightforwardly odd to say that “This is our custom, but no one does it that way” or “We agreed on it, though he didn’t know it at the time.” Sentences like these demand some explanation or qualification.
On the other hand, nothing seems obviously weird about saying “You should X, though you wouldn’t accept any standard that would recommend that.” It may be that there are problems with using the word ‘should’ without reference to a shared standard (as opposed to just a standard) but it’s another thing to say that this is packed into the meaning of ‘should’. It sounds awfully like a theory of normativity, rather than an analysis of the meaning of a word. In fact, Wei Dai calls it a theory of normativity, though it seems to me that it must either be such a theory, or a suggestion about the meaning of a word. It can’t be both.
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.
That’s a good point, but consider this contrast:
It seems clear to me that customs and agreements involve “something shared” in the sense Wei intends. As a result, it sounds straightforwardly odd to say that “This is our custom, but no one does it that way” or “We agreed on it, though he didn’t know it at the time.” Sentences like these demand some explanation or qualification.
On the other hand, nothing seems obviously weird about saying “You should X, though you wouldn’t accept any standard that would recommend that.” It may be that there are problems with using the word ‘should’ without reference to a shared standard (as opposed to just a standard) but it’s another thing to say that this is packed into the meaning of ‘should’. It sounds awfully like a theory of normativity, rather than an analysis of the meaning of a word. In fact, Wei Dai calls it a theory of normativity, though it seems to me that it must either be such a theory, or a suggestion about the meaning of a word. It can’t be both.
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.