Footwork

Dion is a person, a whole man. Theon is that part of Dion that does not include the left foot. Theon is a “proper part” of Dion — he’s part of Dion but not identical with him.

Now suppose we remove Dion’s left foot. What has happened? Do we now have two numerically different objects composed of the same matter and occupying the same place? If not, then either Theon or Dion has ceased to exist. Which? How?

(From Chrysippus.)