I don’t think it an overstatement to say that the concept of the infinite plays a key role in the philosophy of religion. There are at least two senses in which ‘infinite’ is used. First, ‘infinite’ is often used to mean maximal, as in God’s infinite power, knowledge, and goodness. Second, many arguments in the philosophy of religion discuss ‘infinite number’ or ‘infinitely many’. It is this second sense of the infinite that I focus on in this post. Here are two recent examples of this second sense of the infinite, from Prosblogion, with select quotes (and links to the full posts):
Grim reapers have recently been employed in an argument against an infinite past (see here and here). I’d like to see if grim reapers may similarly be employed in an argument against uncaused beginnings.
I will begin with a preliminary comment about the modal reasoning involved in a grim reaper argument. Then I’ll review the grim reaper argument against an infinite past. Then I’ll present a new, parallel grim reaper argument against uncaused beginnings.
As I see it, the grim reaper argument against an infinite past is an instance of modal reasoning in which one attempts to subtract credence from a modal claim by “connecting it” with a modal claim that’s evidently false. To illustrate, consider the following argument against the possibility of time travel:
(1) Suppose I could go back in time.
(2) Then I could go back to a time before I was born.
(3) If I could go back to a time before I was born, I could prevent my birth.
(4) If I could prevent my birth, then I could exist without having been born.
(5) I cannot exist without having been born.
(6) Therefore, I cannot go back in time.
In the above example, we start with a somewhat “unclear” (and controversial) modal claim about time travel and then attempt to connect it via a series of (arguably) plausible premises to a claim that is easier to assess. This argument is just an example. Even if this particular argument isn’t sound, you get the gist of the strategy.
The gist (or outline) of a grim reaper argument against an infinite past is something like this.