In my earlier post, I gave a Grim Reaper based argument against an infinite past. Here I want to give two more arguments. Unlike the earlier argument, these two arguments are not going to be useful for arguing for the existence of God, since they make use of premises that the atheist is likely to deny (in one case, a version of the Principle of Sufficient Reason, and in the other, the existence of God). But they are useful in a broader sense, namely they help show what might be wrong with an infinite past.
Argument 1. If there is an infinite past, we could imagine that each January 1 in the infinite past somebody looks around and checks if there are any rabbits. If there are, she does nothing. If there aren’t, she makes a breeding pair. Of course, once a breeding pair of rabbits exists, there will be rabbits forever. Nobody and nothing but one of these potential rabbit-makers makes a rabbit. The setup entails that there have always been rabbits, and the rabbits have not been made by anybody or anything, contrary to a causal version of the Principle of Sufficient Reason.
Argument 2. If there is an infinite past, the following scenario should be possible. The universe contains nothing but bobs, and at no time is there more than one. A bob is an asexually reproducing person who lives for a century. At the end of the century he dies, but at the end of his existence he has a choice whether to reproduce or not, and can choose either way. If he freely chooses to reproduce, a new bob comes into existence out of the old bob’s body after death. So, this is a universe where every bob has always chosen to reproduce, though they could have chosen otherwise. But now consider the following very plausible Thesis:
(*) Necessarily, if a world contains at least one contingent being, then there exists something in that world determined into existence by God’s will.
But the story in Argument 2 seems to violate (*), since each bob’s existence is partly dependent on the free choice of the preceding bob. Maybe God has determined, then, not the fact that there is a bob, but that there is some initial infinite sequence of bobs, without determining which initial infinite sequence there is. But even that there is an initial infinite sequence of bobs already depends on bob-made choices.
Argument 2 won’t impress theological compatibilists.