I had always assumed that only ultimate ends, or telic / final / non-instrumental desires, could be intrinsically irrational. (Think Future Tuesday Indifference.) Instrumental desires, by contrast, may happen to be irrational if based on a false and irrational means-end belief, but then the problem is extrinsic to the desire itself -- the problem instead lies with the false belief, and one could presumably imagine circumstances in which the means-end belief would be true, thus making the instrumental desire in question a perfectly reasonable way of achieving one's goals.
Or so I assumed. (And I think it's a fairly common assumption.)
University of York undergraduate philosophy student Lorin Thompson (mentioned here with permission) drew my attention to an interesting class of counterexamples. We can obtain intrinsically irrational instrumental desires if we consider instrumental desires that are essentially self-defeating. His example is the "desire to think of a number, in order to not think of a number (simultaneously)." The implicit means-end belief -- that one can achieve avoiding thinking of a number, by means of thinking of a number -- is logically incoherent, and the resulting instrumental desire is thus intrinsically (rather than merely extrinsically) irrational.
It's a cool case! At the very least, I'll need to re-write my essay question for future years to ask something like whether there are "unworthy" ultimate ends rather than just "intrinsically irrational desires", as it now turns out that even Humean subjectivists should make room for the latter.
Does anyone know whether such cases have been discussed before, or could it potentially be a new contribution to the literature if Lorin were to write up his paper for an academic journal?