Consider the Grim Reaper (GR) paradox. Fred’s alive at midnight. Only a GR can kill him. Each GR has an alarm with a wakeup time. When the alarm goes off, the GR looks to see if Fred’s alive, and if he is, the GR kills him. Otherwise, the GR does nothing. Suppose the alarm times of the GR’s are 12:30 am, 12:15 am, 12:07.5 am, …. Then Fred’s got to be dead, but no GR could have killed him. If, say, the 12:15 GR killed him, that means Fred was alive at 12:07.5, which means the 12:07.5 GR would have killed him.
A Hawthorne answer to the GR paradox is that the GRs together killed Fred, though no one of them did.
Here’s a simple variant that shows this can’t be true. You hang up a stocking at midnight. There is an infinite sequence of Jolly Givers, each with a different name, and each of which has exactly one orange. There are no other oranges in the world, nor anything that would make an orange. When a JG’s alarm goes off, it checks if there is anything in the stocking. If there is, it does nothing. If there is nothing in the stocking, it puts its orange in the stocking. The alarm times are the same as in the previous story.
The analogous Hawthorne answer would have to be that the JGs together put an orange in the stocking. But then one of the JGs would need to be missing his orange. But no one of the JGs is missing his orange, since no one of them took it out of his pocket. So, the orange would have had to come out of nowhere.
And, to paraphrase a very clever recent comment, if it came out of nowhere, why would it be an orange, rather than, say, a pear?
I think the JG paradox also suggests an interesting link between the principle that nothing comes from nothing and the rejection of supertasks.
5 comments:
As it happens, I have just posted a reply to an earlier Grim Reaper post, that I think avoids all Hwthornesque replies, by regarding these paradoxes as variants of the potential versus actual infinity issue.
How did Fred die? Was it a heart attack? It could have been. Fred's heart could have simply stopped at midnight. Did the GRs all have to have been intending to stab him in the heart, for that to be what happened? No. They could have been intending to shoot him in the head.
Suppose they had been intending to shoot Fred in the head unless they found him already shot in the head. Then he would have had to have been shot in the head. Where would the bullet (or bolt or whatever) have come from? Your JG paradox seems to be like that question. Your JGs seem to be able to create anything out of nothing: They could intend to give Fred anything, if they find him without it at their appointed time, and it appears at midnight. Unless infinitely many of them fail to do what they intend to do, that is.
I think that the latter is going to be more plausible than the former a lot of the time. And similarly for the GR. Perhaps the GR are very capable, and a meteorite is perturbed out of the chaos of the night sky by their plan, their infinitude and logic, and it hits Fred in the head at or just before midnight. But there must be some limit to their powers, is what I think the JG paradox shows. (At first I thought that your JG paradox was like Hilbert's Hotel, but then I noticed how different it was. Nothing is created out of nothing in Hilbert's Hotel, it just seems to be.)
Suppose that Fred had a heart attack at midnight. It would not have come from nothing, but it would have had a very strange cause. It is more reasonable to reject the hypothetical scenario, I think.
And similarly with your Jolly Givers: there are infinitely many oranges close enough to my stocking for each of them to be capable of getting into the stocking very very quickly indeed: infinitely many have to be capable of getting there inside a millisecond; indeed, infinitely many inside a nanosecond, etc.
Suppose you give the Jolly Givers special powers to move their oranges arbitrarily quickly, and yet safely, so that there is no bunching up of far too many oranges. Even so, each Jolly Giver has to see the stocking, and see whether it is empty or not. So, there are infinitely many who have to see that inside a nanosecond, and inside any arbitrarily small amount of time. How do they all see so much, in such a short amount of time? Clearly they do not see using photons, but it is quite hard to imagine any other way that would work for them.
In short, such scenarios as Hawthorne's and yours are superficially simple, but are actually absurdly complicated. It is possible to construct scenarios involving similar before-effects in relatively simple Newtonian universes. But would that give you a link between metaphysical principles?
Infinity-1 is infinity+1.
All are full, including the guy one and as the one came from the ontological sum, it was not created.
I was thinking about absurd conclusion objections. I really liked your argument on pages 48-49 and 61-63 of Infinity, Causation, and Paradox. It seems that you generated a contradiction in that the tinkerers were independent and indeterministic and not independent and indeterministic at the same time.
I was thinking about the Prefixed Grim Reaper story. It is very plausible that some things are indeterministic. Imagine there was an indeterministic process that decided between the prefixed grim reaper story and the paradoxical one. The absurd conclusion objection would not rule out the process causing the prefixed grim reaper story. It would rule out it causing the paradoxical one, however. That means that an indeterministic process could only have one result. That is a contradiction. What do you think?
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