Is the past finite or infinite? Can objects have infinite causal histories? The Grim Reaper paradox sets out to show that this cannot be the case, and others have since added onto the discussion. I will start by presenting three formulations of the Grim Reaper paradox, the Pruss and Koon's Grim Reaper formulation, Koons Paper Passer version, and Daniel Linford's version.
Pruss and Koons Grim Reaper Paradox - text from WLC (www.reasonablefaith.org/writings/question-answer/grim-reaper-paradox#_edn1)
Imagine that there are denumerably infinitely many Grim Reapers.
You are alive at midnight.
Grim Reaper #1 will strike you dead at 1:00 a.m. if you are still alive at that time.
Grim Reaper #2 will strike you dead at 12:30 a.m. if you are still alive then.
Grim Reaper #3 will strike you dead at 12:15 a.m., and so on.
Such a situation seems clearly conceivable—given the possibility of an actually infinite number of things—but leads to an impossibility:
You cannot survive past midnight, and yet you cannot be killed by any Grim Reaper at any time.
You cannot point to any particular Grim Reaper as the one that killed you as there will always have been a different Grim Reaper that should have done the job, yet you also must be dead.
Paper Passer Version - text from Trent Horne (https://www.catholic.com/audio/cot/debate-gods-existence-trent-horn-vs-alex-oconnor)
Imagined beings called paper passers who exist at every January 1st in the past.
So there’s one at January 1st, 2020, one at January 1st, 2019, and so on into an infinite past.
Their job is to receive a piece of paper from the passer who held it during the year before them and to see if it’s blank.
If the paper is blank, then they write a unique number assigned to them on it.
If the paper they receive already has a number on it, however, then they just pass the paper along to the next paper passer at the end of the year.
Now here’s the question, what number is written on the paper given to the paper passer at January 1st, 2020?
There has to be some number written on it because if it were blank then the 2020 paper passer would write his number on it.
But it can’t be blank because if it were, the 2019 paper passer would have written his number on it.
But the 2019 paper passer could not have written his number on it because if the paper were blank when he got it, the 2018 paper passer would have written his number on it.
If there are an infinite number of paper passers, then we have a paradox.
If there are an infinite number of paper passers, then we have a paradox.
Daniel Linford's Version - text (https://useofreason.wordpress.com/2020/01/05/the-grim-reaper-paradox-and-the-original-solution-part-1/)
This one isn't so much a formulation of the Paradox to show the problem but to raise issue with a potential solution.
Malpass tries to formulate Hawthorne's objection to work against the Pruss and Koons formulation of the Grim Reaper Paradox.
Essentially, the objection is that while we might not know where the first moment the person is dead at we can say that we know where the last moment they are alive is at.
To quote from Malpass's blog,
"Hawthorne first considers the case of a ball rolling towards an open-infinite Zeno-sequence of walls. 2 miles away there is a wall; 1 and 1/2 miles away is another wall; 1 and 1/4 miles away is another wall; 1 and 1/8 miles away there is another wall, etc. Thus, there is an infinite sequence of walls, ever closer to the point that is exactly one mile away. There is no wall which is the ‘closest’ to the one mile point (which makes it an open sequence). Suppose the walls are impenetrable and cannot be knocked over (etc). The ball is rolled towards the walls. What happens as it arrives at the one mile mark? Hawthorne’s answer is as follows:
“The ball does not proceed beyond a mile and it does not hit a wall.” (p. 625)"
So, the solution proposed is that despite no Reapers actually doing to killing that the person still dies.
Daniel Linford responds by proposing the following,
Let’s suppose that an infinitude of guns is pointed at Fred and an infinitude of guns is pointed at Sue.
Let’s assume that if a gun fires at Fred, then Fred is killed, and if a gun fires at Sue, then Sue is killed.
After one minute has elapsed, if no gun has yet fired at Fred, then gun 1 will fire at Fred.
After half a minute has elapsed, if no gun has yet fired at Fred, then gun 2 will fire at Fred.
And so on — after 1/n of a minute, if no gun has yet fired at Fred, then gun n will fire at Fred.
No guns ever fire at Sue.
After the time interval, Fred has been killed yet — if the Hawthorne solution is to be believed — no bullets struck Fred and no guns were ever fired.
After the time interval, Fred has been killed yet — if the Hawthorne solution is to be believed — no bullets struck Fred and no guns were ever fired.
Fred and Sue are in the same situation because while an infinitude of guns were pointed at both of them, no gun was ever fired.
What explains the difference between Fred and Sue?
This is, I believe, a powerful objection. Neither Fred nor Sue were fired at. If they were they would die, yet by Hawthorne's solution Fred is dead anyways despite the same course of events happening to him as happened to Sue. How is this justified?
The answer tends to be, as argued by philosophers like Craig, Koons, Pruss, etc. that there simply cannot be an infinite causal past. There must always be some sort of first cause, as otherwise a paradox arises. This is a view I am very sympathetic to, and so I want to ask what your thoughts are on this topic. Do you think there can be an infinite causal past? What is your solution to the Grim Reaper Paradox if you wish to preserve an infinite causal past?
