The main objection to the Grim Reaper paradox as an argument against infinite causal sequences is the Unsatisfiable Pair (UP) objection that notes that paradox sets up an impossible situation—and that’s why it’s impossible!
I’m exploring a response that distinguishes metaphysical and (narrowly) logical unsatisfiability. The Grim Reaper situation is not logically unsatisfiable. The UP objection (well, really, Unsatisfiable Quadruple) notes that the following cannot all be true:
For all n > 0, the nth reaper wakes up at 60/n minutes after 10 am and kills Fred if and only if Fred is alive.
Fred is alive at 10 am.
There are no possible causes of Fred’s death other than those described in (1).
There are no possible causes of Fred’s resurrection.
But all that’s needed to have these four claims hold is for each reaper to kill Fred and then have Fred causelessly come back to life before the next one kills him. And while I think causeless resurrections are metaphysically impossible, they are (narrowly) logically coherent.
In other words, for the UP objection to work, the unsatisfiability must be metaphysical, not merely narrowly logical. But this, I think, negatively affects the force of the UP objection. For instance, in my Infinity book I consider Grim Reapers with adjustable wake-up times, and I note that for some wake-up time settings (say, the nth reaper wakes up 60/n minutes before noon) there is no paradox, and I ask what metaphysical force prevents the wake-up time settings from being the paradoxical ones. Daniel Rubio in a review of the book responds (in the context of a parody) that “no metaphysical thesis is required to explain this impossibility; the fact that it would lead to a contradiction is enough.” But in fact a metaphysical thesis is required to explain the impossibility, since there is no contradiction (in the narrowly logical sense) in (1)–(4).
Perhaps this is not a big deal. After all the metaphysical thesis here, that causeless events are impossible, is one that I do accept. But nonetheless it is a metaphysical thesis, as such on par with causal finitism, and hence when we consider the explanation of the impossibility of the Grim Reaper story and the impossibility of various other of the causal paradoxes that I discuss, there is something appealing about seeing the case as nonetheless offering support for causal finitism, which explains all of them, while the thesis about causeless events being impossible does not.
3 comments:
Dr. Pruss, what other resources do you recommend in responding to the UP? Joe Schmidt has some interesting stuff on the UP/UPD and I'm thinking about looking into it more.
I’m not following this. ‘No causeless events’ is an implied condition of the setup. Without it, there is no paradox (as you explained). If you allow causeless events, you could imagine other weird stuff, e.g. an infinite number of GRs causelessly failing to do their duty, or Fred and all the GRs causelessly vanishing in a puff of smoke.
If you use the paradox to argue for causal finitism, you implicitly assume ‘no causeless events’ (at least, no relevant causeless events) and that the people you are trying to persuade accept it too. Otherwise, they will see no paradox. I think that UP objectors implicitly do accept it, but argue that no further metaphysical thesis is necessary.
I don't think "no causeless events" is an implied condition of the setup. Rather, I think it is paradoxical that (assuming CF is false) if you set up the Grim Reapers with alarm times where there is no first alarm time, then you _ensure_ (obviously not causally!) that a causeless event eventuates.
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