Stephen Puryear

Many philosophers have argued that the past must be finite in duration because otherwise reaching the present moment would have involved something impossible, namely, the sequential occurrence of an actual infinity of events. In reply, some philosophers have objected that there can be nothing amiss in such an occurrence, since actually infinite sequences are ‘traversed’ all the time in nature, for example, whenever an object moves from one location in space to another. This essay focuses on one of the two available replies to this objection, namely, the claim that actual infinities are not traversed in nature because space, time, and other continuous wholes divide into parts only in so far as we divide them in thought, and thus divide into only a finite number of parts. I grant that this reply succeeds in blunting the anti-finitist objection, but I argue that it also subverts the very argument against an eternal past that it was intended to save.

I argue that Leibniz's treatment of void or empty space in the appendix to his fourth letter to Clarke conflicts with the way he elsewhere treats (metaphysical) evil, insofar as he allows that God has created a world with the one kind of privation (evil), while insisting that God would not have created a world with the other kind of privation (void). I consider three respects in which the moral case might be thought to differ relevantly from the physical one, and argue that none of them succeed in removing the inconsistency. Rather than denying the existence of void, Leibniz should have been led by his treatment of evil to realize that the arguments he deploys in this appendix are dubious, and that the principles to which he appeals do not rule out empty space any more than they rule out evil, darkness, cold, or any other privations.