George, who is quite happy thinking that he has just aced his logic exam (actually, he failed miserably) sees a first-order logic proposition on a board:
- (x)(~toothache(x) → ~(x = George))).
Did George get what he intended? Well, yes: he wanted (1) to be true, and the genie did make (1) be true. But while George got what he intended, he also got a toothache, which he clearly did not intend to get. Thus, one can intend (1) without intending (2). Intention cuts more finely than logical equivalence.
Suppose George were better at logic, so it was obvious to him that (1) and (2) are equivalent? Could he intend (1) without intending (2)? I am inclined to answer affirmatively. Belief does not automatically affect intentions—intentions are a matter of the will, not of the intellect. Of course, if he were better at logic, the toothache would not be a surprise.
Once we admit that intentions can cut this finely, we have to be really careful with Double Effect, lest we end up justifying the unjustifiable. We don't want to allow Janine to get away with murder by saying that she asked the genie to bring it about that either Fred is dead or 2+2=5, and so she never intended Fred to be dead. My way of doing that is to introduce the notion of accomplishment. As long as George intended (1), whether or not he knew that (1) entailed (2), George accomplished his toothache: the toothache was a part of the accomplishment of the action. As long as Janine intended the disjunction, the disjunct (or, more precisely, the truthmaker of the disjunct) which she (through the genie) accomplished is a part of her accomplishment.