A grim reaper (GR) is a device that activates at a pre-set time. It checks if Fred--the victim--is alive. If he is, it kills him. If he isn't alive, it does nothing. For the Grim Reaper Paradox, we're supposed to imagine one GR set for 12:30, another for 12:15, another for 12:07.5, and so on. Before each time for which a GR is set, there is an earlier one. But Fred is alive alive at 12:00. Paradox ensues when we notice that Fred must be dead at 12:30 (else that 12:30 GR would have killed him), but no GR could have killed him, since if he were alive at its activation time, he would have been alive when the previous one activated, and hence would have been killed then at least.
John Hawthorne has claimed that Fred is not killed by any one GR, but by them altogether. More precisely, Fred is killed by their mereological sum.
Here's a gruesome way to see the problem with this solution. We can number the GRs in reverse: the 12:30 GR is number 1, the 12:15 one is number 2, and so on. Then suppose that the odd-numbered GRs kill by decapitating and the even-numbered ones kill by stabbing in the heart. Given the setup, Fred is either decapitated or stabbed in the heart but not both. But which one?! If he were decapitated, he would have been first stabbed. If he were stabbed, he would have been decapitated before that.
7 comments:
Is the GR paradox essentially the same as, for example;
A man is traveling from point A to point B. He is only permitted to go half the distance between points each day.
He will never reach his destination because he can always halve the distance each day..?
No, I think it's pretty different.
(No idea if you get notified of comments on old posts.)
I have a thought about strengthening this:
I have a red ball. A Blue-Maker is a creature that hates the color red and but indifferent to any other color. When it wakes up, if there are any red balls around, it makes the ball turn blue instantly. There are an infinite number of Blue-Makers, who will wake up at 12:30, 12:15, 12:7.5, etc.
Now, if the red ball turns blue after 12:00, even though no Blue-Makers did anything (every Blue-Maker awoke to seeing a blue ball!), that would be strange. But what if the ball turns yellow after 12:00, and never was blue?
I can think of reasons why the ball shouldn't spontaneously turn yellow:
1) There is no thing which caused the ball to be yellow.
2) There is no explanation for why the ball is yellow.
3) In day-to-day experience, red balls don't usually turn into yellow balls.
But every such reason seems to be a reason for why the ball shouldn't spontaneously turn blue.
Therefore, if one thinks that it's impossible for the mereological sum of Blue-Makers to turn a red ball into a yellow ball, then one should think that it's impossible for the mereological sum of Blue-Makers to turn a red ball into a blue ball.
Have a nice day! :)
That's a very nice argument indeed. I like it a lot. I would use it in my book if I had the opportunity for backwards causation. :-)
What I think your argument highlights is that when the causal power of the GR isn't activated, it is completely irrelevant WHAT it would have done had it been activated.
FYI the solution to the paradox is in solving what causation actually is.
You wrote the following in this brilliant paper:
http://alexanderpruss.com/papers/kalaam.pdf
"Once we have causal finitism, then we need only one more ingredient to
establish an uncaused cause: we need to rule out causal circles".
Causal circles are the ONLY thing that cannot be ruled out.
Because causal circles are in fact the ONLY thing that exist fundamentally.
Causal circularity is the uncaused cause. Causal circularity is what a wave(s) fundamentally is. An ontological zero unit.
You wrote...
"Given that there is a plurality of uncaused causes"
The collection of grim reapers shouldn't be thought of as a collection of grim reapers at all.
It should be thought of as a plurality of uncaused causes or a collection of net zero waves or units of causal circularity. A wave summation that fundamentally nets to zero.
"Thus we have good reason to think there is an uncaused cause. The
plurality of uncaused causes, then, can be seen as being at the head of
every causal sequence. And at this point I issue an invitation to the reader,
theist, pantheist, polytheist, agnostic, atheist or other: Given that there is a
plurality of uncaused causes, let’s investigate that plurality together. After
all, the question of what that plurality is like is apt to be one of the most
important explanatory questions there are."
The answer to your challenge is that the strong PSR defines the nature of the singularity to plurality of mathematical waves itself. The head of every causal sequence aka all wave flow is zero and its inherent nature to explore life and/or existence eternally.
Absolute perfection.
Also. Enjoyed your PSR book @Alexander R Pruss.
Thank you for writing it.
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