We are all like the ladies of Paris; they live sumptuously without knowing what goes into the stew. Similarly we enjoy bodies without knowing of what they consist. What is the body made of? Of parts, and these parts resolve themselves into other parts. What are these last parts? Always bodies: you divide endlessly and never advance.
Voltaire, Philosophical Dictionary (1764), entry on 'Corps'
In Chapter 1 and again in Chapter 2 we saw that two corollaries were traditionally supposed to follow from the actual parts doctrine. The actual parts doctrine was thought to entail (1) that each body has a determinate number of parts, and (2) that each body has ultimate parts. These two corollaries then underpin the array of classic paradoxes of infinite m-divisibility, each of the paradoxes resting on the one or the other corollary, or perhaps on both taken together. We also saw (in preliminary overview) one traditional argument from the actual parts doctrine to corollary (1), and two traditional arguments from the actual parts doctrine to corollary (2). Each of these arguments enjoyed a wide currency during the Enlightenment.
First there was (i) the argument from actual parts to a determinate number of parts. This stressed that, since all the parts into which a body can be m-divided are given in advance (assuming the actual parts doctrine), the entire collection of parts must be determinate in number rather than indefinite or open-ended. This establishes corollary (1): given the actual parts doctrine, each body has a determinate number of parts.