First, it seems that one can be instrumentally irrational without having any intentions based on false beliefs (or lacking any intentions because of false beliefs).  John Broome provides an example: suppose I know the hotel is on fire and that the only escape involves my intending to go through the open window, and, though I intend to live, I sit on the windowsill singing happily until the flames consume me.  This is a clear case of instrumental irrationality, despite my not having any false beliefs (Broome 1997). Indeed, one could fail to intend the means believed necessary for one’s ends because of rage, depression, distraction, grief, or other causes which don’t necessarily involve any false beliefs (Korsgaard 1986).  Hume would have to conclude either that such cases are impossible, or that they involve no instrumental irrationality.