Divisibility of Magnitude in De Generatione et Corruptione I.2
The central section of GC I.2 is dedicated to an argument allegedly proving that magnitude cannot be divisible. Offered at 316a14-316b18, the argument against what we may call the divisibility thesis has the form of a reductio claiming to show that absurd consequences are implied by this thesis. Since Philoponus, commentators take this reductio to be an argument by Democritus and Aristotle’s aim in this chapter to refute Democritus. Still, the reductio relies heavily on Aristotelian assumptions and theories that it is doubtful would have been available or acceptable to Democritus.
I argue that in this chapter Aristotle puts forward the claim that divisibility is a capacity of magnitude, which if true would account for the position taken for granted in Phys. III.6 that the infinite is an attribute of magnitude. The reductio in GC I.2 exploits Aristotelian commitments to allege that this claim is incoherent. Dealing with this allegation, as this chapter purports to do, does not require a refutation of Democritus, and none is offered. Besides, Democritus lacks the conceptual tools to construct the reductio, which moreover rests on an argument too obviously flawed to suppose that he would believe it could be used against the divisibility thesis. Apparently propelled by Aristotle’s view on capacities as possessed by subjects the flaw on which the reductio rests is not trivial for Aristotle, but a challenge. To address it Aristotle needs to offer a characterization of what it is to say that magnitude is divisible in capacity, which is precisely what he achieves in this chapter.
