Intuitions and Violinists
One of the most famous intuitionist arguments is Judith Jarvis Thomson's violinist argument. In brief, Thomson asks you to imagine you wake up one day and discover that a group of music lovers have kidnapped you and hooked you up to a famous violinist who is dying of kidney failure. If you unplug yourself, he dies, but if you remain hooked up, he will heal and be ready to live on his own in nine months. Thomson takes it as obvious that there is no moral problem if you decide to unhook yourself, and according to Wikipedia all of her critics share that intuition even if they disagree that this intuition leads to the conclusion that abortion is permissible. Yet my intuition is quite different -- were I in that situation, I would feel a very strong moral compulsion to remain attached for the nine months. This is more than a matter of desiring to do something above and beyond the call of duty -- I would feel guilt for unplugging the violinist similar in kind to what I'd feel if I caused his death more directly. In my mind, the fact of holding such great power over another person's fate entails an obligation to use that power in a way that protects their interests. (Though, if I hadn't blown my cover by writing this post, I wouldn't be above threatening to unplug myself in order to get the music lovers to offer me some compensation for my time, since this is an unusual case in which the person who holds the power does not therefore benefit from the situation.)
Of course, Thomson's larger argument is not directed at me, since I'm quite convinced that a fetus is not morally a person (except perhaps very late in gestation), and therefore already believe abortion is permissible. But it's somewhat disconcerting to find my intuitions at odds with something agreed on by both sides of a major philosophical debate.