The Grim Reaper Paradox: An Argument for No-One

In his 2014 paper, ‘A New Kalam Argument: Revenge of the Grim Reaper’, Rob Koons presents what is surely the canonical version of the Grim Reaper Paradox (GRP). Here I want to outline a quick, but I think novel, objection to that argument. I’m still thinking it through, so welcome comments. It’s quite likely I’ve overlooked something, and someone will point that out.

Here is the thought. The argument has a premise that is objectionable to Humeans, and another premise that is objectionable to anti-Humeans. Since the Humean / anti-Humean distinction is dichotomous, the argument has premises that are acceptable to no-one.

There are lots of ways to set the argument up, and a lot relies on the precise details of the particular version that is being articulated. However, Koons rightly stresses a few core premises, and for our purposes we can merely think about two of them:

1. The possibility of an individual reaper
2. The patchwork principle

I think 1 is objectionable to a Humean, and 2 is objectionable to an anti-Humean. But what do I mean exactly by Humean and anti-Humean here? Broadly, I’m following Loewer (2012), who says:

Humeans claim that there is no fundamental necessity in nature connecting spatio-temporally non-overlapping events in non-overlapping portions of space–time. … In contrast, non-Humeans think that there is fundamental necessity in nature.

Loewer, 2012, p. 116

Humeans think that reality is just a bunch of ‘categorical’ (non-modal) matters of fact, which is often referred to as the ‘Humean mosaic’, whereas anti-Humeans think there are also ‘thick’ modal properties, like potentialities, or capacities, or dispositions, etc.

So why think that anti-Humeans would object to the patchwork principle? Well, the patchwork principle, and in particular Koon’s version of it, says that we can ‘cut and paste’ together non-overlapping regions of spacetime (providing they have compatible topological and metrical structures – we can’t cut and paste together slice of 11-dimensional spacetime with a slice of regular 4-dimensional spacetime, etc). In conventional cases, this principle is intuitive. As Lewis says, if a dragon is possible, and a unicorn is possible, both a dragon and a unicorn together is possible. But this conflicts with the notion of thick modal properties in the following way. Take a wine glass and its thick modal property of being fragile. This means that it has a disposition to smash in the right circumstances, such as being knocked off the table at a dinner party, etc. But the patchwork principle says we can paste in together a region of spacetime where the glass is knocked off the table with one where it lies unbroken on the floor. But if this is possible, it cannot also be that it would necessarily smash if knocked off the table. Thick modal properties therefore restrict what combinations of spacetime regions we can cut and paste together. Anti-Humeans might still like to use a restricted version of the patchwork principle when reasoning about modality, or they might just abandon it altogether. But they will reject the unrestricted version because it’s incompatible with thick modal properties. Thus, they will reject the premise that requires an unrestricted patchwork principle (like we find in Koons’ version of the argument).

Why do I say that Humeans should reject the possibility of individual reapers? Well, this is quite simple. They have thick modal properties. According to Koons, a reaper just is something that has “the power and disposition” (Koons, 2014, p. 257) to do the relevant action (e.g. killing Fred, etc) iff the relevant condition obtains (e.g. if none of the prior reapers has already killed Fred, etc). But powers and dispositions are most straightforwardly construed as thick modal properties. Koons himself rejects ‘neo-Humeanism’ later on in that paper, indicating he doesn’t have a Humean reading of powers and dispositions in mind here. But if reapers have thick modal properties, then this goes beyond what the Humean allows in her metaphysics. They are not simply categorical properties, but types of necessary relations between objects. Thus, Humeans would deny that any objects have properties like this, and thus also that reapers do.

In conclusion then, it seems to me that the GRP requires a Humean premise (the patchwork principle) and an anti-Humean premise (the thick modal properties of reapers). As such it is not acceptable to either Humeans or anti-Humeans, and so is an argument for no-one.

What sort of pushback might my argument above generate? Well, I can see two broad approaches. One could try to build the argument without using thick modal properties and thus avoid the Humean objection (making an GRP argument for Humeans). Or one could try to build the argument with a suitably restricted patchwork principle (making a GRP argument for anti-Humeans). If this is right, then we have split the argument in two, and one might have better fortunes than the other. Or they both can be shown to be absolutely fine. Or both might be shown to be problematic. In any case, it seems to me to be an interesting development in the dialectic.