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In response to a request, I am going to do some basic unpacking of second-order desire, or "metawanting". Basically, a second-order desire or metawant is a desire about a first-order desire.
Example 1: Suppose I am very sleepy, but I want to be alert. My desire to be alert is first-order. Suppose also that there is a can of Mountain Dew handy. I know that Mountain Dew contains caffeine and that caffeine will make me alert. However, I also know that I hate Mountain Dew1. I do not want the Mountain Dew, because I know it is gross. But it would be very convenient for me if I liked Mountain Dew: then I could drink it, and I could get the useful effects of the caffeine, and satisfy my desire for alertness. So I have the following instrumental belief: wanting to drink that can of Mountain Dew would let me be alert. Generally, barring other considerations, I want things that would get me other things I want - I want a job because I want money, I want money because I can use it to buy chocolate, I want chocolate because I can use it to produce pleasant taste sensations, and I just plain want pleasant taste sensations. So, because alertness is something I want, and wanting Mountain Dew would let me get it, I want to want the Mountain Dew.
This example demonstrates a case of a second-order desire about a first-order desire that would be instrumentally useful. But it's also possible to have second-order desires about first-order desires that one simply does or doesn't care to have.
Example 2: Suppose Mimi the Heroin Addict, living up to her unfortunate name, is a heroin addict. Obviously, as a heroin addict, she spends a lot of her time wanting heroin. But this desire is upsetting to her. She wants not to want heroin, and may take actions to stop herself from wanting heroin, such as going through rehab.
One thing that is often said is that what first-order desires you "endorse" on the second level are the ones that are your most true self. This seems like an appealing notion in Mimi's case; I would not want to say that at her heart she just wants heroin and that's an intrinsic, important part of her. But it's not always the case that the second-order desire is the one we most want to identify with the person who has it:
Example 3: Suppose Larry the Closet Homosexual, goodness only knows why his mother would name him that, is a closet homosexual. He has been brought up to believe that homosexuality is gross and wrong. As such, his first-order desire to exchange sexual favors with his friend Ted the Next-Door Neighbor is repulsive to him when he notices it, and he wants desperately not to have this desire.
In this case, I think we're tempted to say that poor Larry is a gay guy who's had an alien second-order desire attached to him via his upbringing, not a natural homophobe whose first-order desires are insidiously eroding his real personality.
A less depressing example to round out the set:
Example 4: Suppose Olivia the Overcoming Bias Reader, whose very prescient mother predicted she would visit this site, is convinced on by Eliezer's arguments about one-boxing in Newcomb's Problem. However, she's pretty sure that if Omega really turned up, boxes in hand, she would want to take both of them. She thinks this reflects an irrationality of hers. She wants to want to one-box.
1Carbonated beverages make my mouth hurt. I have developed a more generalized aversion to them after repeatedly trying to develop a taste for them and experiencing pain every time.