A false principle concerning desire

I am not the first to discover this particular fallacy—in fact, part of this post is based on ideas I got in conversion from somebody who got them from something he read. But the ideas are no less fun for being mainly not mine.

Consider the following argument for psychological hedonism, the doctrine that the only thing we pursue is pleasure:

1. Whenever we pursue something other than pleasure, we pursue it because it gives us pleasure. (Premise)
2. Therefore, what we really pursue is the pleasure it affords to us.

Not only is (1) false, but (2) does not follow from it. The following inference is invalid:

3. We pursue x because it gives us y.
4. Therefore, what we really pursue is y.

In fact, taken literally, (4) contradicts (3), since if "what we really pursue" is y, and y is not x, then we are not pursuing x (to pursue is the same as to really pursue). But even if we weaken (4) to:

5. Therefore, we pursue y

the inference is still invalid. If I am trying to find a woman who offers water to my camels (cf. Genesis 24), it does not follow that what I am really pursuing is water for my camels. Perhaps I just want the kind of woman who gives water to my camels. Likewise, one might want a particular fig tree in the garden because it yields figs, not because one wants the figs, but because yielding figs is largely constitutive of the health of a tree, and one wants only healthy trees in the garden.

Perhaps the inference works better if we replace (1) by:

6. Whenever we pursue something other than pleasure, we pursue it only because it gives us pleasure.

It's easier to see how (2) might be thought to follow, but (6) now begs the question against the non-hedonist. In any case, the inference is still logically invalid.

In fact, it is even incorrect to conclude from the claim that I seek x solely because it yields y that I want y at all. Suppose that, whimsically, I desire a magical hat that yields rabbits. I only want the hat because it yields rabbits—my whim is that I want to have rabbits pop into existence out of a hat. I can want such a hat for such a reason without having any desire for the rabbits. The rabbits themselves are a nuisance, and I would have no interest at all in rabbits that come into existence in any way other than out of a hat.

It might be objected that then I don't want the hat just because it yields rabbits, but I want the hat because it is a hat that yields rabbits, and so this isn't a counterexample to the inference type. But if so, then the non-hedonist need only say that she doesn't want x just because it yields pleasure, but she wants an x because it is an x that yields pleasure.

The fallacy here also occurs in the Lysis in the argument that if I am friends with x because x yields y, then what I am really friends with is y.