Gonzalo Rodriguez-Pereyra’s contribution to The Puzzle of Existence is the last of a series of contributions on the question whether there might have been nothing. Rodriguez-Pereyra defends a version of the subtraction argument for metaphysical nihilism. That is, he argues (roughly) that for any concrete being and any possible world at which that being exists, the world obtained by subtracting that being from that world is likewise possible, and that it follows from this that there is an empty possible world. (The empty world is to be obtained by subtracting all of the concrete beings from some possible world with only finitely many such beings.)
This argument has already been defended (including by Rodriguez-Pereyra himself) in a number of places in the literature. The main aim of this new article is to defend the argument against the claim that it begs the question. The charge, which Rodriguez-Pereyra attributes to Alexander Paseau, is that, however the technical details work out (and there is a lot of concern about the technical details in this paper), the subtraction premise, in its general form, cannot be motivated in a way that is independent of metaphysical nihilism: insofar as we find it plausible that subtraction always results in a possible scenario, this must be because we find it plausible that there is an empty possible world.
The basic structure of Rodriguez-Pereyra’s response to this objection is as follows. A reasonable person who is unsure about metaphysical nihilism might well find subtraction plausible in a universe with an arbitrarily large finite population. That is, one might think that if a universe with exactly 67 concrete, contingent entities is possible, then so is a world which contains exactly 66 of those 67 entities, and nothing else. Furthermore, absent an independent argument against metaphysical nihilism, there is no good reason for supposing that the case of a world with only one entity is different from the case of a world with some arbitrary finite number of entities. Hence, unless there is some positive reason for thinking that the one-object world is a special case, we should accept metaphysical nihilism (i.e., the possibility that no concrete contingent beings exist).
This line of argument is, I take it, the core of the paper. It seems convincing to me, as far as it goes. That is, I think the argument might take a neutral, rational thinker who has certain prior beliefs/intuitions from a state of equippolence to a position of regarding nihilism as the default option, pending consideration of any further arguments anti-nihilists might offer. This is a pretty modest standard of success, but if we set the standards for success much higher than this then – let’s face it – there won’t be very many successful arguments in philosophy!
Anyway, my main worry is about something else. At the beginning of the paper, Rodriguez-Pereyra considers another line of objection to the argument, one I think is perhaps more important. This is the idea that it might be the case that, necessarily, if there are any concrete objects, there are infinitely many. Why might one think this? Well, Rodriguez-Pereyra can think of two reasons: first, one might think that, since space is (necessarily) infinitely divisible, it is necessary that every concrete object have infinitely many parts. Second, one might hold that sets whose ur-elements are concrete are themselves concrete, so that the existence of one concrete object generates infinitely many concrete sets.
Rodriguez-Pereyra’s strategy is to solve this problem by stipulation. He defines a concrete* object as one which is “(a) concrete, (b) non-set-constituted, and (c) a maximal occupant of a connected spatiotemporal region” (198). Condition (c) is a bit confusing. One might think that a maximal occupant of a connected spatiotemporal region is an object that takes up the whole region so as not to leave room for anything else that’s not a part of it, or something like that. This is not how Rodriguez-Pereyra defines this term. Rather, a maximal occupant of a connected spatiotemporal region is an object which exactly occupies a connected spatiotemporal region and is not a proper part of any object which occupies a connected spatiotemporal region. In other words, if such an object is a part of some larger whole, then that larger whole is a scattered (spatiotemporally disconnected) object. The argument then proceeds by subtracting concrete* objects with their parts.
Now here’s where I want to take issue. In order for the argument to work, Rodriguez-Pereyra now needs “a possible world with a finite domain of concrete* objects and in which every concrete object is a (proper or improper) part of a concrete* object” (200). Rodriguez-Pereyra thinks everyone will agree that there is such a world because concrete spatiotemporal objects which are not parts of concrete* objects are quite exotic (see 200n6), and Rodriguez-Pereyra says that he will “uncontroversially assume that it is a necessary condition of any object being concrete that it is spatiotemporal” (199). Now, it is currently popular among analytic metaphysicians to suppose that all actual concrete objects are spatiotemporal. This is because many analytic metaphysicians endorse relatively naive versions of physicalism. (As will appear below, the versions of physicalism in question are naive about physics; some of them are quite philosophically sophisticated.) On the other hand, though, there certainly are analytic metaphysicians who believe in non-spatiotemporal concrete objects. But second, and perhaps more importantly, it is extremely controversial to hold that being spatiotemporal is a necessary condition for concreteness, because many, perhaps most, analytic metaphysicians believe in the possibility of non-spatiotemporal concrete objects.
I can think of four reasons one might believe in the actual existence of non-spatiotemporal concrete beings. First, one might be a dualist about human persons and think that souls don’t count as spatiotemporal. Second, one might believe in one or more wholly immaterial persons, and one might think this person or these persons count as concrete. Third, one might think that some or all of the entities in fundamental physics are not actually spatiotemporal after all, but are nevertheless concrete. Fourth, one might be an idealist of some stripe or other (whether Berkeleian, Leibnizian, or Kantian) and deny that anything spatiotemporal could be ontologically fundamental, and therefore hold that there is some kind of non-spatiotemporal ‘ontological subbasement.’
Since it might be unclear to some people how option 3 goes, let me divide it into 5 sub-options (one could take more than one of these). These are just 5 things a philosopher informed about modern physics might say; I’m not necessarily endorsing them.
3a: because quantum particles are not extended and do not have precise locations, they don’t count as (what metaphysicians mean by) spatiotemporal.
3b: the wavefunctions of quantum mechanics are real concrete entities, but the mathematical spaces over which they are defined are not at all the same as physical space-time, so they should not be regarded as (literally) spatiotemporal (in the metaphysician’s sense). For instance, I’m told that the wavefunction for a two particle system is defined over a six-dimensional Hilbert space.
3c: Thinking of the particles as having vague locations is only one way of interpreting the wavefunction; on an alternative interpretation, one might think that quantum mechanics just tells us the probability of an observation event occurring in a given spacetime region. If this is right, then one might deny that the particles are located at all (only the observation events are located), and if they’re not located then they are certainly not spatiotemporal.
3d: if one of the ‘holographic’ theories in fundamental physics is true, then ordinary physical spacetime (the spacetime we move around in) isn’t even physically fundamental, so there must be more fundamental concrete stuff which is not located in our spacetime, and hence we might regard that stuff as (in some sense) non-spatiotemporal).
3e: the laws of nature are concrete non-spatiotemporal entities.
(These possibilities are the reasons why I said above that it was somewhat naive to think that physicalism entailed the non-existence of non-spatiotemporal concrete things. The entailment is at best non-obvious and at worst non-existent, but it is sometimes taken as practically definitional.)
These are examples of reasons you might believe in the actual existence of concrete non-spatiotemporal objects. But all we need for Rodriguez-Pereyra’s assumption to be false is the possibility of concrete non-spatiotemporal entities. Here, we are on even safer ground, for a great many philosophers are willing to admit the possibility of some or all of the concrete non-spatiotemporal entities mentioned above, even if they don’t think any of them are actual.
Where does this leave Rodriguez-Pereyra’s argument? Well, Rodriguez-Pereyra doesn’t actually need the premise that necessarily all concrete objects are spatiotemporal. What he needs is just the claim that there is a possible world at which there are finitely many concrete* objects and every concrete object is a part of a concrete* object. The proponents of most of the positions mentioned above will be willing to admit the existence of possible worlds at which all of the concrete objects are spatiotemporal. There are, however, two exceptions.
First, some philosophers believe in the necessary existence of an immaterial God whom they consider to be a concrete object. This is easily sidestepped by restricting the argument to contingent objects. Of course this weakens the conclusion to the claim that there is a possible world at which there are no contingent concrete objects, but that’s close enough.
The more problematic case is the case of those who think that all spatiotemporal objects are non-fundamental (case 4 and some variants of case 3). These philosophers might think that this is necessarily the case, that nothing that is literally spatiotemporal could possibly be fundamental. If this is right, then there is no possible world of the sort Rodriguez-Pereyra needs.
The obvious way to fix this would be to talk about taking away the concrete* objects along with, not only their parts, but also their ontological grounds. However, absent some kind of theory of the ontological grounding of such objects, this renders the subtraction principle quite doubtful. If the concrete* objects have unknown grounds, then why should we think the objects are independent of each other? They might, for instance, be grounded in the same fundamental reality.
Rodriguez-Pereyra’s argument relies on a picture of a world as a four-dimensional spacetime with filled and unfilled regions, and essentially nothing more to it. As a picture of the actual world, this is quite naive, but Rodriguez-Pereyra only needs it to be a picture of a class of possible worlds. The possibility of such worlds enjoys a certain amount of plausibility (they certainly seem conceivable, for instance). However, there are arguments to be made against such possibilities. Here, I have merely gestured at (and not endorsed) these arguments, but I want to point out that if any of them succeeds then Rodriguez-Pereyra’s defense of the subtraction argument fails.
(Cross-posted at blog.kennypearce.net.)