 The question of whether magnitude is perpetually divisible into smaller units, or divisible only down to some atomic magnitude leads to the dilemma of divisibility (Miller 1982), a difficulty that Aristotle necessarily had to face in connection with his analysis of the continuum. In the dilemma’s first, or nihilistic horn, it is argued that, were magnitude everywhere divisible, the process of carrying out this division completely would reduce a magnitude to extensionless points, or perhaps even to nothingness. The second, or atomistic, horn starts from the assumption that magnitude is not everywhere divisible and leads to the equally unpalatable conclusion (for Aristotle, at least) that indivisible magnitudes must exist.