Beginning with Aristotle’s statement in Physics II.2 that motion must be continuous to be for the sake of an end, I argue that properly understood, continuity is actually a sufficient condition for the goal- directedness of any motion in Aristotle’s teleology. I establish this conclusion first for the simple motions discussed in Physics V-VI, and then for complex changes such as the generation and development of a living thing. In both steps of the argument, the notion of καθ’ αυτό agency serves as a key link between continuity and goal-directedness. The understanding of Aristotle’s teleology that emerges from the consideration of continuity, finally, fits Aristotle’s discussion of that for the sake of which in Generation and Corruption II.9 and Physics II.8.
Mirus, Christopher, "To Hou Heneka and Continuous Change" (2004). The Society for Ancient Greek Philosophy Newsletter. 401.