Undetached PartsHere's a puzzle that continues to tease metaphysicians. 1 Dion is a human being and Theon is his left-foot-complement, i.e., that proper part of Dion which is composed of the atoms that compose Dion except for those which overlap his left foot. We know that Dion is distinct from Theon, since they have different properties. For example, Dion has two feet but Theon has one. But suppose Dion's left foot is cut off and destroyed. Dion seems to survive this ordeal, since a person can survive losing a minor part such as a foot. Theon seems to survive too, since it would be strange for Theon to 1 The puzzle can be traced back as far as Philo of Alexandria and Chryssipus (Sedley 1982; Long & Sedley 1987: 171-172). A version of it also appears in William of Sherwood (1968: 60-61). Another instance of the problem was introduced to the literature by Wiggins (1968), who -perhaps mistakenly -took it to be a version of the puzzle due to Geach (1980: §110) which is now known as the problem of the many. 2 be destroyed by a mere extrinsic change, viz., ceasing to be attached to a foot. But with Dion's left foot gone, Dion and Theon are now in exactly the same place at exactly the same time, and they seem to be composed of all the same atoms. In short, they seem to be coincident. When numerically distinct objects are coincident, I will say that they are co-located. Since Dion and Theon are distinct, it follows that, if they are coincident, then they are also co-located. Unfortunately, the idea that material objects can be colocated does not sit well with common intuitions.This problem has spawned a wide array of creative and interesting solutions. 2 Simons (1987) observes that it "brings together a number of crucial ontological issues, and has elicited the most varied responses. It is almost a touchstone for finding out important facts about a philosopher's ontology" (118). One solution, which I will call the conservative solution, distinguishes between ordinary and extraordinary undetached parts.Ordinary undetached parts are parts which are recognized in folk metaphysics, and extraordinary undetached parts are parts which are not recognized in folk metaphysics. (I will have something to say about the vagueness of this distinction in Section 2.) The conservative solution claims that only ordinary undetached parts exist. 3 Theon's existence is then denied on the grounds that Theon is an extraordinary undetached part, not an ordinary one, and this dissolves the puzzle. After all, there is no reason to worry that Dion is coincident with Theon if Theon doesn't exist. An important objection to the conservative solution is that it doesn't generalize 2 Various solutions are defended by Wiggins (1968);