A Commentary on Stephen Puryear's response to Andrew Loke and Travis Dumsday

Puryear's response essay is called Finitism, Divisibility, and the Beginning of the Universe: Replies to Loke and Dumsday. 

In this commentary, we'll see if Puryear's response to Loke and Dumsday holds up, but I also want to see if what I said in the previous blog is still defensible. 

Puryear says:

My argument has elicited replies from Andrew Ter Ern Loke [2016] and Travis Dumsday [2016]. Here I address the three basic objections to emerge from those replies.

The first two, due to Dumsday, concern the distinction between infinite magnitudes and infinite multitudes, and the distinction between extensively and intensively infinite progressions. 

The third objection, which both Loke and Dumsday urge in one form or another, concerns the possibility that time might be continuous yet naturally divide into smallest parts of finite duration.

That third objection I'm especially interested in. But I am very interested in the first two objections as well. Let's dive in. 

Commentary on Stephen Puryear's "Finitism and The Beginning of the Universe"

It's always exciting to read new criticisms of William Lane Craig's Kalam Cosmological Argument. In this blog, I'll be providing commentary on Stephen Puryear's "Finitism and The Beginning of the Universe". Here is the abstract: 

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 antifinitist objection, but argue that it also subverts the very argument against an eternal past it was intended to save.