A legacy post originally published on OCTOBER 6, 2009 at 8:23 AM
đź”— Two More Arguments Against an Infinite Past by Alexander Pruss
In an 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.
The opening argument is missing a crucial premise: if the past could be infinite, this set-up could obtain. But we have good reason to reject this premise here.
But also, it doesn’t follow that the PSR is violated. For starters, each rabbit has an explanation. You might focus, then, on why there are any rabbits at all, ever. Two responses: there might be something timeless that accounts for why there are any rabbits at all, ever—perhaps Ney, Barbour, and Carroll’s universal wavefunction understood in non-spatiotemporal terms, or maybe some timeless quantum field, or maybe even a God or an impersonal neo-Platonic One. Second, under branching actualism, every possible world shares a history with the actual world. But this entails that if there have always been rabbits, then it is necessarily the case that there are rabbits. But then it’s no longer a contingent uncaused or contingent unexplained thing, and so doesn’t violate the PSR.
Also, consider this parody of the opening argument which shows that an endless future is impossible
If there is an infinite future, we could imagine that on each January 1 in the infinite future, somebody checks whether there will be any rabbits in future years. (How do they know? God reveals to them whether there will be rabbits in future years.) If there will be no rabbits in future years, the person does nothing for the whole year. If there will be rabbits in future years, the person makes no rabbits, kills all the rabbits that there are on Jan 1, and ensures that there are no rabbits up until the beginning of the next year. There are rabbits today. Nobody and nothing but one of these potential rabbit-killers kills or makes rabbits.
The setup entails that there will never be rabbits in any future year.** But there are rabbits now, and only a rabbit-killer could kill the rabbits, and yet the rabbit-killers do literally nothing. (Remember, if there will be no rabbits in future years, each rabbit-killer does nothing.) Thus, the current rabbits die, and yet nothing causes them to die, in violation of the causal PSR.
**Suppose that there will be a rabbit in some future year y. Call this SUPPOSE. Focus on y. y is either such that there will be rabbits in future years, or there will be no rabbits in future years.
If y is such that there will be rabbits in future years—call this assumption RFY—then y’s rabbit-killer kills all the rabbits that there are and ensures that none come to be until year (y+1). But no rabbit-killer ever makes any rabbits, and since only rabbit-killers make rabbits, if the causal PSR is to hold true, rabbits can come to be only if a rabbit-killer makes them. Hence, no rabbit ever comes to be. But then there will never be any rabbits, in contradiction to RFY.
If y is such that there will be no rabbits in future years—call this NRFY—y’s rabbit-killer does nothing. But by SUPPOSE, there’s some rabbit in y, and y’s rabbit-killer does nothing to make it cease to exist. Per the causal PSR, it can only cease if it’s killed in some way, and yet nothing kills it at least up until the next year. Hence, the rabbit exists in the next year. But this contradicts NRFY.
Hence, from SUPPOSE, we derived a dilemma on each horn of which there’s a contradiction. Hence, ~SUPPOSE.
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