A Variation on the Grim Reaper Paradox
In one of my earlier posts, I addressed the Grim Reaper paradox and offered my input on a possible resolution of the thought experiment’s curious implications. However, some of my readers may have been dissatisfied with my answer, thinking that it sidestepped around the issue rather than addressing the conundrum directly. A few people asked me why I thought that obscure philosophy on the nature of Time might have any relevance to the question, in the first place. To that end, I have decided to offer a bit more clarification and to attempt to illustrate why I think the Grim Reaper paradox is inherently flawed.
Consider this slightly modified version of the thought experiment…
Fred is sitting in a room at 8:00 am. There exist four Grim Reapers along with Fred, each of which is currently dormant. When any individual Grim Reaper becomes activated, if Fred is not going to be killed by the next Reaper in the order, then this Reaper will instantaneously kill Fred; otherwise, this Reaper will return to a dormant state and continue to do nothing. Each of the Grim Reapers is timed to activate at a specific time after 8:00 am. The first Reaper will activate at 8:15 am. The second activates at 8:30 am. The third activates at 8:45 am. The fourth activates at 9:00 am.
Now, 8:15 arrives and the first Reaper activates. Does it kill Fred or not? If it does kill Fred, because the second Reaper is not going to kill Fred, then the 3rd Reaper in the line is not going to kill Fred– it can’t, obviously, since Fred is already dead. However, if that’s the case, then the second Reaper is going to kill Fred (since those conditions are met) and the first Reaper’s conditions are no longer valid. So, even though we started assuming that the first Reaper killed Fred, we’ve learned that this cannot be the case. Indeed, the same holds true for the second Reaper– if the second Reaper kills Fred, then the fourth Reaper cannot kill Fred meaning that the third Reaper should kill Fred, violating our initial assumption. So, we see that the second Reaper is not going to kill Fred. But if the second Reaper isn’t going to kill Fred, then the first Reaper should– except that we’ve already seen this cannot happen.
Unlike Pruss’s formulation of the paradox, this problem cannot be resolved by simply claiming that actual infinites cannot exist. We’re not relying on actual infinities, here. We are looking at a finite number of Grim Reapers. Nor does is seem reasonable to come to the sort of conclusion which Pruss does in his proposed solution to the paradox. If a person tried to claim that the number “four” cannot actually be a number which applies to the real world because of this paradox, we would all laugh in their faces.
It’s a little bit easier to see the point I was trying to make in my other post, now. Regardless of whether one is an A-Theorist or a B-Theorist as far as Time is concerned, both camps agree that events which lie in the future do not alter the ontology of events in the present. On the A-Theory view of things, I cannot make a decision based upon a future which has not yet been actualized. Things which are not yet actual cannot affect that which is actual, and as such, it is clear that my version of the Grim Reaper Paradox violates this view of things.
Similarly, on the B-Theory, causality is a description of a relation between two events, but it doesn’t affect the ontology of those events. So an event in the future cannot alter the ontology of something in the present. Both events are actualized and static, and my version of the Grim Reaper Paradox violates this precept. However, this also means that events in the present do not alter the ontology of events in the future. The future is just as actual and static as are the past and present, on the B-Theory. As such, it becomes immediately clear that Pruss’ version of the Grim Reaper Paradox violates this same precept, since it is dependent upon the idea that an event can affect the ontology of future events.
I do not think that Pruss’ version of the Grim Reaper paradox shows that actual infinities are inapplicable to the real world any more than my version of this thought experiment shows that the number “four” is inapplicable to the real world. In fact, it seems to me that the paradox is best resolved by abandoning an antiquated and untenable idea of the nature of Time. Apologists like William Lane Craig have attempted to cite the Grim Reaper paradox in order to support the Kalam Cosmological Argument. Ironically, it may be the case that the Grim Reaper Paradox actually undermines the KCA, since that argument is entirely dependent upon the tensed A-Theory of Time.