How exactly does this answer the question?
The set of non-ethical categorical imperatives is non-empty.
I agree. Epistemic imperatives are categorical, but non-empty.
The set of non-ethical hypothetical imperatives is non-empty. Hypothetical imperatives include instrumental rules, you have to use X to achieve Y, game-laying rules, etc.
Right, those are examples where non-ethical hypothetical imperatives often show up.
So how does this add up to a reason to think there is a case against categorical imperatives that doesn't equally well count against hypothetical imperatives?
I don't think so. You ought to use a hammer to drive in nails even if you don't want to dive in nails. Anyone who is playing chess should move the bishop diagonally.That doesn't mean you are playing chess.
Again, you're assuming that the rule 'if you're driving in nails, use a hammer' is worth following, and that the rule 'if you're playing chess, move bishops diagonally' is worth following. A nihilist would reject both of those rules as having any normative authority, and say that just because a game has rules it doesn't mean that game-players ought to follow those rules, at most it means that lots and lots of rule-violations make the game go away.
I think you must be mistaken about categorical imperatives and ends.
In the Groundwork, Kant deems rational nature ('humanity' in us) to be an end in itself which can ground a categorical imperative, in the 2nd Critique, he deems the highest good (happiness in proportion to virtue) to be a necessary end of practical reason, and in the Metaphysics of Morals, he deems one's own perfection and the happiness of others to be ends that are also duties. For Kant, the categorical imperative of morality is directed at ends, but it is not a mere hypothetical imperative grounded in subjective ends.
And leaving Kant aside, plenty of moral systems aspiring to categorical force have ends at their center. Classic utilitarianism picks out the greatest overall balance of pleasure over pain as the one and only end of morality. Eudaimonist virtue ethics has as its end a well-lived flourishing life for the agent. Thomist ethics says an intellectual vision of God in the afterlife is the ultimate end of humans. These systems do not traffic in merely hypothetical imperatives: they present these ends as objectively worth pursuing, regardless of the agent's personal preferences.
But if your main point is simply that my 'reduction' assumes that the end ought to be pursued, and that this assumption is a form of cheating, then I agree. I've left the normativity unexplained and unreduced. But then in exactly the same way, your reduction of hypothetical imperatives assumes that effective means to one's ends ought to be taken, and this assumption is also a form of cheating. You have also left the normativity unexplained and unreduced.
So I don't see how hypothetical imperatives are any more fit for naturalistic reduction than categorical imperatives.
I take it you want to reduce a hypothetical imperative like "If you want to stretch, then you ought to stand" into a physically-kosher causal claim like "standing is causally necessary for satisfying your desire to stretch". Now, I'm skeptical about this reduction, simply because I don't see how a mere causal claim could provide any normative direction whatsoever. But in any case, it seems that you could equally well reduce a categorical imperative like "Regardless of what you personally want, if you are the only one around a drowning child, then you ought to help save it from drowning" into a physically-kosher causal claim like "your help is causally necessary for the survival of the drowning child". Both causal claims are equally physicalistic, and both seem equally relevant to their respective imperative, so both physicalistic reductions seem equally promising.
Of course, the question "why should I assume that the drowning's child survival actually matters?" seems reasonable enough. But so does the question "why should I assume that satisfying my desire to stretch actually matters?" If the first question jeopardizes the reduction of the categorical imperative, then the second question would also jeopardize the reduction of the hypothetical imperative.
Hypothetical "ought" statements do not require any special metaphysical apparatus to explain them, they just require rules and payoffs. Categorical imperatives are another story.
Rules and payoffs explain "ought" statements only if you assume that the rules are worth following and the payoffs worth pursuing. But if hypothetical imperatives can help themselves to such assumptions (assuming e.g. that one's own desires ought to be satisfied), then categorical imperatives can help themselves to such assumptions (assuming e.g. that everyone's desires ought to be satisfied, or that everyone's happiness ought to be maximized, or that everyone ought to develop certain character traits).
What reasons are there for doubting the existence of categorical imperatives that do not equally count against the existence of hypothetical imperatives? I can understand rejecting both, I can understand accepting both, but I can't understand treating them differently.
Perhaps so, but then the normativity stems from premise 1, leaving premise 2 as non-normative as ever. But the question is whether premise 2 could be a plausible reduction basis for normative claims.
Well, I'll acknowledge that you could change premise 2 into an inference rule. But notice that you could change either premise 2—the pro-desire-satisfaction one and the pro-desire-frustration one—into an inference rule. Indeed, you could change any normative claim into an inference rule: you could change "people who want to have gay sex ought to go see a trained Baptist minister to get cured" into an inference rule, and then validly go from "I want to have gay sex" to "I ought to go see a trained Baptist minister to get cured". So from the fact that premise 2 could be changed into an inference rule, I don't think anything follows that might jeopardize its status as a full-blooded normative claim.
On the second point, I thought lukeprog was discussing direct conceptual reduction. But if he wants to provide hypothetical imperatives with a synthetic reduction, he'll need a theory of reference capable of explaining why the normative claim turns out to make reference to (and have its truth-conditions provided by) simple causal facts. And on this score, I think hypothetical imperatives and categorical moral imperatives are on an equal footing: since reductionist moral realists have a hard time with synthetic reductions, I would expect reductionist 'instrumental realists' to have a hard time as well.
I don't think hypothetical imperatives can be reduced. The if-ought of a hypothetical imperative is a full-blooded normative claim. But you can't reduce that to a simple if-then about cause and effect.
To see why, consider a nihilist about oughts. She recognizes the causal connections between calorie consumption/burning and weight loss. But she doesn't accept any claim about what people ought to do, even hypothetical imperatives about people who desire weight loss. This seems perfectly coherent: she accepts causal claims, but not normative claims, and there's no contradiction or incoherence there. But this means the causal claims she accepts are not conceptually equivalent to the normative claims she rejects.
For another way to see why, consider the causal claim "less calorie consumption and more calorie burning leads to weight loss". This causal claim points in no normative direction. It doesn't recommend anything, or register any approval, or send any positive or negative messages. Of course, we can take it in one direction or another, but only by combining it with separate normative claims:
Premise 2 is what provides the normativity. It points us in the direction of satisfying desires. But we could easily take things in the opposite direction.
Again, premise 2 is what provides the normativity. But it points us in the opposite direction, viz. the direction of frustrating desires.
So it's pretty clear that premise 1 has no normativity in it. It can't be reduced to either of the two 3's. For we cannot arrive at a 3 without a 2.
So, on your use of 'end', an 'end' cannot be objective and unconditional? I think that's a highly uncommon use of the term.
But if you go this way, it seems like it's less of a reduction of 'ought' and more of a misinterpretation, like reducing 'Santa Claus'-talk into talk about Christmas cheer, or 'God'-talk into talk of love.
After all, one important constraint on any interpretation of any 'ought to X' is that it should be positive towards X as opposed to negative or neutral, in favor of some action or attitude as opposed to against it or indifferent. But a mere predictive causal claim doesn't have any valence at all: it's just a neutral claim about what will probably lead to what, without anything positive or negative. So any attempt to reduce oughts to predictive causal claims seems doomed to failure.
EDIT: For the record, I'm an expressivist about normativity, and I think any attempt to understand it in terms of some actual or hypothetical ontology that could serve as the truth-conditions for a descriptive belief is a mistake. The mystery, I would say, lies in a descriptive interpretation of normativity, not in normativity itself.