Possible Worlds as Truthmakers: Concrete or Abstract?

There are two main ways in which possible worlds are construed as ontological models of reality: concrete or abstract models. Menzel lists a third,‘combinatorialism’ (2017: §2.3), but I ignore it here, because it isn’t clear to me that all versions of it are ontologically serious, and because any problems found with the concrete and/or abstract constructs will threaten combinatorialism as well.

What Menzel calls ‘concretisin’—i.e. modal realism—construes possible worlds as concretely existing worlds existing in parity with the world we inhabit but not sharing our spatio-temporal boundary. Some opponents of CTCs argue that this is the only ontologically serious (but absurd) view of possible worlds (Martin 2000; Heil 2003). Indeed, even proponents of CTCs admit that hardly anybody accepts modal realism (e.g. Weatherson 2014).

The problem I have with concretism is that, even if we accept the reality of a plurality of concretely existing worlds—despite misgivings about empirically inaccessible worlds—then the viability of CTCs will vary depending on the ontology of a given particular world, and will at best only appear to be viable if it is assumed that all worlds are contingent in accordance with neo-Humean metaphysics. If a world is governed by primitive natural laws that are not reducible to patterns in the distribution of facts but make things happen in determinate ways, or is a world in which the causal powers of particulars make things happenin determinate ways, then other worlds are irrelevant to what happens in those worlds. It does not matter whether the laws are contingent in the sense that there could be other laws at other worlds. That comparison is irrelevant to decide if the facts in this world could have been distributed differently in this world.

What I am arguing here contradicts the received view. For instance, Collins, Hall, & Paul believe that the counterfactual account of causation is available also to non-Humeans:

Can facts about the laws themselves be reduced to the totality of categorical facts? Some—notably, Lewis (e.g., 1986b)—will say‘yes,’ others ‘no.’ We wish merely to note that with respect to the aims of the essays in this volume, almost nothing hangs on this dispute. (For example, Lewis’s account of causation could be adopted wholesale by one who disagreed with him about whether the laws themselves reduce to categorical facts.)

(Collins, Hall, & Paul 2004: 12)

Like Tim Maudlin (2004), I disagree with this claim. For someone like Maudlin who thinks that laws are sui generis primitives that secure that nature evolves in certain patterns, then other possible worlds are ontologically irrelevant. Maudlin has no reason at all to adopt Lewis’ account of causation. Possible worlds in his conceptual scheme represent at best possible ways the world could evolve within the boundaries allowed by the laws, i.e. possible worlds are determined by the world, and not vice versa. Indeed, all ontologies that include a commitment to substantial lawful or causal connections that govern what happens have thereby grounded counterfactual dependence on those substantial connections, in which case other possible worlds become redundant, or merely consequential. Whoever thinks that the laws of a world do not supervene on the contingent matters of facts of that world, but instead connect these matters of fact in determinate ways, has no reason to appeal to similarities between possible worlds as the basis for either causal or counterfactual claims. In such worlds ‘C caused E' is not true in virtue of similarities between closest possible worlds, but in virtue of a lawful connection between Cs and Es in the world in question. My conclusion is that it is not clear at all whether anyone other than neo-Humeans will find any reason to adopt Lewis’ account of causation. Indeed, it is not even clear that neo-Humeans can make use of CTCs (see Section 9.6).

It bears mentioning that Marcus Arvan offers an analogous argument when criticising the Lewis-Stalnaker analysis of counterfactuals for not being able to handle the possibility that possible worlds are computer simulations. In his view, the primitive causal features of ‘necessitarian’ simulations/worlds make other worlds irrelevant (2016: §2.3). In fact, he argues that the same goes for neo-Humean simulations (2016: §2.2).

According to what Menzel calls ‘abstractionism’, possible worlds are ‘abstract entities of a certain sort: They are states or conditions, of varying detail and complexity, that a concrete world could be in — they are ways that things, as a whole, could be’ (2017: §2.2.). Now, a prerequisite to make this work as an ontological theory, these abstract entities must be the truthmakers of the counterfactuals whose truth-conditions are meant to give the meaning of causal claims. They must be considered to be some kind of contrary-to-fact truthmakers, or contrary-to-fact ‘facts’ that make our beliefs true. It is not enough that they represent truthconditions, since they would then just be the conceptual consequences of a certain theory; consequences that would be just as much in need of truthmakers as the original claims we are considering.

I find that an ontology of abstract truthmakers threatens to make concrete reality irrelevant for the truth of our claims about concrete reality (see also Joshua Mozersky’s criticism of ersatz presentism (2015: 44)). If counterfactuals are made true in terms of abstract truthmakers, and causal claims are true derivatively of the truth of counterfactuals, then it seems that no causal claim of the kind ‘C caused E’ is ever made true by concretely occurring instances of causation but solely by some kind of abstract reality. To be sure, it may be true that the events C and E occur merely in virtue of their concrete occurrence, but that does not make true ‘C caused E’, since this is true only in virtue of the abstract contrary-to-fact truthmaker that ‘if C hadn’t occurred, E would not have occurred’. And, observe, in particular, that on this account the abstract truthmaker is not grounded in any concrete truthmaker, because there is no concrete state of affairs manifesting what wouldn’t have happened if something else hadn’t happened. The contrary-to-fact truthmaker that the bottle would not have shattered had not Suzy thrown the rock must exist as abstractum whether or not Suzy actually throws a rock, or else we would have to conclude, contrary to abstractionism, that the actual goings-on in concrete reality ground the abstract entities, which would undermine the fundamentality of the contrary-to-fact truthmakers. In sum, it appears to be a consequence of abstractionism that the claims whose meaning we are supposed to elucidate in terms of the truth-conditions of counterfactuals, never are claims about concrete reality but only about an abstract reality whose instantiation is contingent. I think this would come as a surprise to most competent speakers of English, which further undermines the claim that CTCs offer a plausible account of the ordinary concept of causation.

Does anything of the above show that abstractionism is false? No, it just shows that to accept it comes at an intellectual cost that is rarely brought out; a cost that is relevant for making an educated evaluation of the appeal of CTCs. In fact, most of what I have said could be interpreted merely as taking sides with some form of concretism (see below). However, it still seems to me that within the domain of abstractionism we see the same problems being repeated. First, that CTCs based on abstract possible worlds are implausible as an account of the ordinary concept of causation for the same reasons given above; we ordinarily accept counter-factuals on the basis of our causal knowledge, not the other way around. Second, that even in abstract ontologies where there are substantial connections, those connections will ground the counterfactual dependence between antecedent and consequent in counterfactual worlds, and then comparative similarity between worlds in an abstract plurality of worlds becomes irrelevant. Again, only a small subset of abstractionist ontologies will suit CTCs, and those assumed to be contingent will be open to the same objections I develop in Section 9.6.

In sum, abstractionism threatens to make concrete reality irrelevant for the truth of our causal and counterfactual claims, and abstractionism and concretism alike seem to imply that CTCs could at best be applied to that subset of worlds that are neo-Humean, i.e. where laws/substantial connections supervene on the distribution of local matters of fact. However, I worry there are not enough constraints on the manner in which such worlds can differ—whether concrete or abstract—to provide the structure required to ground counterfactual dependency on comparative similarity.