- y is beautiful to x if and only if x takes y to be beautiful.
This cannot be a complete theory about beauty. After all, exactly the same theory can be given for ugliness:
- y is ugly to x if and only if x takes y to be ugly.
Since nothing has been said that distinguishes beauty from ugliness, the theory cannot be complete.
Moreover, there is a further oddness about the theory as I've given it. According to the theory, the fundamental concepts are relational: being beautiful (or ugly) to. But on the right hand side of the biconditionals we have the monadic beautiful (or ugly). If someone fully accepts the theory, she won't take anything to be beautiful simpliciter, but only beautiful to her. So, perhaps the relativist should say:
- y is beautiful to x if and only if x takes y to be beautiful to her.
One serious problem with this is that then nothing is beautiful to the self-conscious objectivist, since the self-conscious objectivist takes nothing to be beautiful to her--she does not have any relational "is beautiful to" predicate.
And consider another problem. Suppose I am essentially logically omniscient, so that if p and q are logically equivalent, then it is an essential property of me that I believe p if and only if I believe q. Applying this to the biconditional, I get:
- It is an essential property of me that: I believe that y is beautiful to me if and only if I believe that I take y to be beautiful to me.
But to take something to be beautiful to me is just to believe it is beautiful to me. So:
- It is an essential property of me that: I believe that y is beautiful to me if and only if I believe that I believe that y is beautiful to me.
But that is surely wrong: logical omniscience should not imply omniscience about my internal states.
Maybe, though, I am being too cognitivist about "takes y to be beautiful to her". Maybe to take y to be beautiful isn't to believe anything about y but to have a certain appreciative attitude to y. That takes care of the problem of the objectivist and the logically omniscient individuals.
But we still have another problem. Imagine that I love Mozart. I go to a Mozart violin concert, and then during the intermission I get a message about a family emergency and I need to go home. The first part of the concert was beautiful to me. Tomorrow I hear that the second half of the concert was even better in the respects I appreciate. I conclude that I missed some beautiful performances. But on the appreciative attitude version of "takes", that's false. For the second half of the concert wasn't beautiful to me, since I didn't take it to be beautiful in the appreciative sense.
A familiar response is to amend the right-hand-side of the biconditional to replace "I take y to be beautiful (to me)" with "I would take y to be beautiful (to me) if I experienced y." But probably not. After all, had I stayed for the second half of the concert, worries about the family emergency and guilt that I am enjoying someone's fiddling while my home burns (literally or figuratively) would have spoiled my enjoyment of the concert. Of course this is just a special case of the problems that go under the head of "the conditional fallacy."
So we would have to idealize: I would take y to be beautiful if I experienced y in ideal observing circumstances. But as the above example shows, the ideal observing circumstances need to include being in the right mental state. We better not define the right mental state as the one in which one's appreciation is correct, since then our theory isn't subjectivist any more. And given that what one appreciates can be so heavily dependent on one's emotional state, it seems that at this point matters are hopeless.
And all the same goes for similar theories about morality.