A thought about the Grim reaper argument occurred to me, and I wanted to quickly jot it down to see where it goes.

Consider the proposed Grim Reaper paradox in which: Fred is going to be annihilated by a Grim Reaper set to go off at 11:00 am + 1/n minute; it seems absurd that any single Grim Reaper could be the cause of Fred’s death, since before any Grim Reaper could kill Fred, another Grim Reaper would have had the chance to kill Fred.

This argument assumes that time cannot be divided into smallest atomic units (which I accept, but is nonetheless noteworthy). It also presupposes that it is logically possible for Fred to die instantaneously rather than over a finite period of time (which I also accept, and yet is noteworthy). However, supposing I changed the paradox and said that an infinite number of Grim Reapers were set to go off at exactly 11:00 am, and Fred is approaching 11:00 am. Now, it seems to me that at the finite time 11:00 am (if there really is such a finite/atomic time – or even if 11:00 am is but a temporal infinitesimal point in the same way that finite lines are restricted by ‘points’ which mark their borders) an infinite number of Grim Reapers all simultaneously cause Fred to cease existing. However, a single Grim Reaper is sufficient for Fred to cease to exist. Therefore, is there a single Grim Reaper which causes Fred to cease to exist, or do all the infinite Grim Reapers cause Fred to cease to exist? This thought experiment finds its paradoxical analogy in the example of the brick and the bullet both hitting a window at exactly the same instant leading to the question “what caused the window to break?”.

Now, if one says that a single Grim Reaper caused Fred to cease to exist, then there must be some sufficient reason why that Grim Reaper (call it Grim Reaper A) is the cause of Fred’s ceasing to exist rather than any other Grim Reaper. Thus, the Principle of Sufficient Reason, it seems, is in danger of being undermined. On the other hand, if all the Grim Reapers caused Fred to cease to exist then an infinite number of causes exist for one single effect. This conclusion seems to undermine that which the Grim Reaper argument is intended to demonstrate: namely that there cannot be an infinite set of causes for a single effect.

Perhaps an answer to this is that the Grim Reaper argument is only intended to demonstrate that there cannot be an infinite *sequence* of causes for a single effect. That isn’t quite right either though, since the argument Pruss presents is more nuanced that that. For, according to him, it is possible to have an actually infinite sum of objects existing all at once, and thus actual infinities of this sort are possible. Moreover one can say, in response to my thought experiment, that the mereological sum of all Grim Reapers is what caused Fred to die without any apparent difficulty.

Finally, the problem is that the paradox can be instantiated if there is an infinite past, but since the paradox cannot be instantiated (logically), then there cannot be an infinite past.

I suggest that this ‘paradox’ has the same solution (broadly) as Zeno’s ‘Aristotle & tortoise’ paradox, in that it involves:

– an infinite number of (increasingly shorter) coincident events,

– which are contained within a finite, bounded time interval

– with a binary decision occurring ‘at the limit’.

Sure – the infinite sequence goes in a different temporal direction, and the Grim Reaper paradox uses cause-and-effect between the GR’s, but I don’t think those differences change the solution.

Also – could you explain the last line:

“Finally, the problem is that the paradox can be instantiated if there is an infinite past, but since the paradox cannot be instantiated (logically), then there cannot be an infinite past.”

I agree – it can be instantiated with an infinite past.

However, the paradox, as presented, involves a finite past. Should we therefore conclude that there cannot be a finite past?

If not – then why does the ‘infinite past’ version of the paradox exclude the possibility of an infinite past? What is different about it?

I have been meaning to respond to you, but I don’t think I can make much sense of your comments. First, Zeno’s paradox can be solved in a number of ways, none of which do you allude to clearly. It seems to me that one solution to Zeno’s paradox is to deny that there are material atoms (smallest, simple, indivisible parts of all physical reality). That’s a tidy solution which Leibniz opts for (and I’m quite tempted to accept that solution). Perhaps you can explain the dynamics of the solution you have in mind – you are most welcome to.

Now, concerning the paradox itself, it is stipulated by Pruss not with a finite past, but with an infinite past. Perhaps you can explain why you think a finite past could just as well allow for the instantiation of this paradox? The only way I’ve come up with for that to occur is for God to create an infinite number of Grim Reapers all at once (since, according to Pruss, an infinite number of things can really exist).