natural—cannot be supposed capable of being matched term for term, nor can excess and deficiency be supposed in it, unlike its opposite.’ For a discerning investigator knows that reliance on this mental construction to establish the finitude of figures with sides, or of things naturally ordered whose individual members exist simultaneously, rests solely on its implying excess and deficiency between two infinite quantities. This is possible only by supposing an addition beyond an assumed stopping point, whether a particular point in the assumed extension or a particular unit in the assumed number. It is then plainly possible to suppose a stopping point at a particular total of motions and of human souls separated from their bodies, and to imagine adding further instances of the same kind to that total. Thus, the very terms employed in the aforementioned syllogism to establish the argument are equally employed when turning it against his own position, with an identical syllogistic form and no difference.

Furthermore, two collections that differ by a finite amount need not both be finite. Numerical series, for example, have no limit to their numbers, although the first exceed the second by a finite amount. Although these are hypothetical mental constructs, it is clear that the aforementioned syllogism is applied to them in the same manner as it is applied to