Like many people, I am participating in ‘dry January’, meaning that I am not drinking any alcohol during the month of January. I’m also thinking about the Grim Reaper paradox, and have spent much of the year thinking about the infinite future debate between Morriston and Craig. Interestingly, all of these things have come together, in a paradox I shall now dub the ‘dry eternity’ paradox.
Part of the inspiration for this comes from a paper I read recently by Yishai Cohen, called ‘The Endless Future: a Persistent Thorn in the Kalam Cosmological Argument‘(2015). In that, Cohen agrees with Morriston that if a beginningless past is an actual infinite, then so is an endless future, and thus if a beginningless past is impossible for being an actual infinite, so is an endless future. Cohen also argues that if the grim reaper argument shows that the past has to be finite, then a parallel version shows that the future must have an end as well. His argument is critiqued by Jacobus Erasmus in a paper called Cohen on the Kalam Cosmological Argument (2016). Erasmus’ rebuttal is that Cohen’s version of the grim reaper argument presupposes that it is possible for God to actualise an ungrounded causal chain, which can be plausibly denied.
I think that the ‘dry eternity’ paradox escapes Erasmus’ reply.
- Two versions of the Grim Reaper paradox
Here is how Erasmus sets up the grim reaper paradox:
Suppose that the temporal series of past events is actually infinite and that an actually infinite number of Grim Reapers exist. Suppose also that, at each past moment in time, a unique Reaper was assigned to issue a death warrant iff no previous Reaper had already issued a death warrant. (Cohen on the Kalam Cosmological Argument, p. 52)
This results in a contradictory state of affairs. Firstly, for all times tn, there must have been a warrant issued prior to tn. That’s because if no warrant had been issued by tn-1, then the reaper at tn-1 would issue their warrant (resulting in a warrant going out prior to tn).
But, this same reasoning also applies to tn-1 itself, giving us the contrary proposition. That’s because we can also say that the warrant won’t be issued at tn-1, because if it had not been issued by tn-2 it would have been issued by the tn-2 reaper (i.e. before tn-1).
Thus, we have both that the warrant must have been issued at some time prior to tn, but also that there is no time prior to tn at which it could be issued. Contradiction.
Cohen applies this to the endless future. All we need to do is change the relevant tenses in Erasmus’ quote from above to get the following:
Suppose that the temporal series of future events is actually infinite and that an actually infinite number of Grim Reapers exist. Suppose also that, at each future moment in time, a unique Reaper is assigned to issue a death warrant iff no future Reaper will issue a death warrant.
But now we can derive a mirror image contradiction. Suppose that the reaper at t0 checks to see if any future reapers will issue warrants or not. At this point there are two options:
i) no future reaper will issue a warrant (in which case the t0 reaper issues theirs)
ii) some future reaper will issue a warrant (in which case the t0 reaper does nothing)
Suppose that at t0 no future reaper will issue their warrant, meaning that the reaper at t0 can issue theirs. If it were the case that no future reaper issues a warrant at t0, then, in particular, it is also true that at t1 no future reaper will issue a warrant (consider: if it it true today that I will never drink again, then it will also be true tomorrow that I will never drink again). But if it is true at t1 that no future reaper will issue a warrant, this would mean that the reaper at t1 does issue their warrant! And, plainly enough, the reaper at t1 is in the future of the reaper at t0. So if, at t0, no future reaper will issue a warrant, then some future reaper (such as the one at t1) will issue a warrant! Contradiction.
Let’s take the other horn. Suppose at t0 some future reaper will issue their warrant, meaning that the reaper at t0 can stand down. Let’s suppose it is the reaper at t1. Then we are right back to the beginning of the first horn again. For the reaper at t1 will only issue their warrant if none of the future ones will. But if it is true at t1 that none of the future ones will, then this is also true at t2 as well, resulting in that reaper issuing their warrant which in turn brings about another contradiction exactly like the one from above.
Cohen discusses two objections that Koons posed to him in correspondence. The first of these is that in Koons’ version of the paradox, reapers are sensitive to what past reapers have done, but in Cohen’s version they have to be sensitive to what future reapers will do; yet it isn’t possible to have causal sensitivity to future events in the same way as to past ones. The reply Cohen makes to this is that an omniscient God could communicate the future to the reapers such that they know what the others will do, thus overcoming this causal asymmetry. Koons’ second point is that it isn’t possible for God to create beings who embody his omniscience. Even if that is true, the reapers themselves do not have to be omniscient (and can be quite ignorant of, say, how many coins I have in my pocket), just so long as God ensures that they know the behaviour of future reapers. In addition, Cohen points out that Koons’ reason for thinking that the reapers cannot embody omniscience has to do with avoiding causal loops, but it is not clear that there are any causal loops as such in this story (the behaviour of reaper n+1 does not depend on the behaviour of reaper n, etc). Thus it is far from clear that Koons has a successful reply here. One could avoid this by denying the possibility of an omniscient being that knows the future and can communicate it to reapers, of course, but a theist (in particular a Christian theist) will be unlikely to pick that option.
2. Erasmus’ objection
Erasmus’ objection comes at this from a different angle. He says that Cohen’s version of the grim reaper paradox (GRP) requires the following two principles:
K1. It is possible for God to predetermine an endless future
K2. It is possible for God to actualise an ungrounded causal chain
An ‘ungrounded causal chain’ “has a non-well founded relation (xRy, zRx, zRv, wRv, … ) because the chain lacks a first cause” (Erasmus, 2016, p 53). The behaviour of the reaper at t0 is determined by (or grounded in) the behaviour of reapers that are in its future. But the behaviour of the reapers in its future, such as the one at at t1, are themselves determined by (or grounded in) the behaviour of reapers in the future of them as well. Thus there is no ‘first cause’, or grounding, for the behaviour of the reapers. Let us suppose that this is an ungrounded causal chain, and that it is also (metaphysically?) impossible for God to actualise such a causal chain.
He then goes on to show that K2 is doing all the work in generating the paradox because it also applies to ungrounded causal chains that are purely spatial in character. Here is his spatial version of the example:
For example, suppose that time had a beginning and has an end. Accordingly, the predetermined series of future events is finite. Suppose further that space is inhabited only by an actually infinite row of successive Grim Reapers such that (1) there is a first Reaper but no last Reaper, (2) each Reaper is located at a unique spatial point, and (3) all the Reapers are facing the same direction. Now, suppose that God has predetermined that, at noon tomorrow, each Reaper will swing his scythe iff no Reaper in front of him swings his scythe. Accordingly, the same contradiction as above will result at noon tomorrow, namely, regardless of whether the first Reaper swings his scythe, it is both true and false that some Reaper in front of the first Reaper swings his scythe. The contradiction disappears, however, if (K2) is false. (Ibid)
Erasmus’ conclusion then is that denying K1 is not enough to block the contradiction, as it reappears in the spatial case. But denying K2 blocks both contradictions, and as such K1 is not the offending assumption. In effect, he is saying that Cohen’s GRP doesn’t show that the future must have an end. Rather, it just shows that God cannot actualise ungrounded causal sequences.
3. The Dry Eternity Paradox
Now is time to present my version of the paradox that does works even if K2 is false. It does not require that God actualises any ungrounded causal sequences. All that it requires in addition to K1, is one additional assumption:
K3. God can act based on his (presently available) knowledge of future events.
Suppose God has decided to undertake an infinite version of dry January. That is, he has decided to stop drinking (say) holy water forever. However, he enjoys a drop of holy water (who doesn’t?), and wants to to have one final sip. Accordingly, he determines to obey the following rule:
Every day, God will check his comprehensive knowledge of all future events to see if he will ever drink again. If he finds that he does not ever drink again, he will celebrate with his final drink. On the other hand, if he finds that his final drink is at some day in the future, he does not reward himself in any way (specifically, he does not have a drink all day).
Again, we are caught in a dilemma:
Firstly, suppose that, at t0, God consults his comprehensive knowledge of the future, and discovers that he never again drinks after t0. He immediately downs a shot to celebrate (who wouldn’t?). But in that case, when he does his check the next day, at t1, he then will (again) discover that he will never have another drink, and immediately pour himself a drink to celebrate! So even though he rewarded himself yesterday for never having another drink, he is having another drink! Contradiction.
On the other horn, suppose that, at t0, God consults his comprehensive knowledge of the future, and discovers that he does indeed have a drink at some day after t0. Accordingly, he doesn’t celebrate by having a drink on t0. But in that case, there must be some future day at which he has a drink. Suppose it is t1. In that case, it must be that at t1 God will check to see if he will have any subsequent drinks, and find that he will not, resulting in him pouring the last drink. But now we are back at the start of the first horn, because his check at at t2 will also reveal a dry eternity ahead, at which point he will reward himself with another final drink! Contradiction again.
So we clearly have the exact same paradox again. This time however, it is not clear that God has actualised an ungrounded causal chain. After all, at each day God knows the future, and can merely consult his own (presently available) knowledge to see what happens in the coming days. We can imagine him writing it all down in a big book and every day he consults the book. Whatever causal story that happens each day that he consults the book, it is not clear that it is an ungrounded causal chain.
One might deny that God can check his own knowledge to see what he knows about the future and act on it (K3). This would be weird. Why can’t God do that? Does he not know what he foreknows? Is he repressing it? Can he not act on what he knows? He seems to act on his foreknowledge on most versions of theism (specifically any where he has a plan, or reveals the future in prophecy, etc). Denying K3 leaves only the most austere versions of deism, it seems to me. Christianity seems hard to reconcile with its denial in any case.
Objecting to the possibility of the book doesn’t help unless it is really an objection to God’s omniscience, which a theist probably isn’t going to opt for (apart from Open Theists). Denying the possibility of an omniscient being would avoid the paradox of dry eternity though.
One could avoid the problem by denying the possibility of an endless future. The whole point of Morriston’s original reply to Craig was to say that if the past must have a beginning, then the future must have an end. This would vindicate Morriston’s challenge against Craig. It would show that either time has both a beginning and an end, or no beginning and no end, but that there is no third option.
The seemingly only other target we can find is the rule that God undertakes to obey. Perhaps it is not a proper rule, and that somehow it isn’t possible for God to undertake to obey it. Yet this seems rather strange. Consider this similar rule:
Every day, God will check his comprehensive knowledge of all future events to see if he will ever drink again. If he finds that he does not ever drink again, will celebrate with a chocolate bar. On the other hand, if he finds that his final drink is at some day in the future, he does not reward himself in any way (specifically, he does not have a chocolate bar).
Nothing paradoxical follows from this rule. Obeying this rule means that God drinks every day up to the day when he has his final drink, after which he eats chocolate bars every day. God can obviously follow that rule.
But what could stop him from undertaking to follow the rule obtained by merely swapping out the word ‘chocolate bar’ with ‘have his final drink’? Of course, it would lead to contradiction if he were to go this route, and that is a reason to think that it is (somehow) metaphysically impossible for him to swap those words around and undertake to follow the resulting rule. On the other hand, that is just to say that this is one of the things that could be denied to avoid the paradox. It doesn’t motivate thinking that it is impossible. We could ad hoc postulate anything is metaphysically impossible to avoid any paradox.
Something has to go to avoid the paradox of dry eternity.