Comparative Similarity and Supervenience

It has been objected that my comparison between worlds with respect to a single matter of fact is out of place, because comparisons between worlds are rarely so simple. Lewis emphasises that the ‘respects of similarity and difference that enter into the overall similarity of worlds are many and varied’ and in particular that ‘similarities in matters of particular fact trade off against similarities of law’ (Lewis 1973impossible, then the objection holds good.

I detect two ways in which it is argued that laws contribute to overall similarity independently of the distribution of facts. The first relates to an early definition of ‘nomic dependence’ offered by Lewis, in which he claims that the set F of true propositions of particular fact does not imply on its own every material conditional, but that we need in addition a set of law-propositions L:

The family Cp C„ ... of propositions depends nomically on the family Ap A„ ... iff there are a nonempty set L of true law-propositions and a set F of true propositions of particular fact such that L and F jointly imply (but F alone does not imply) all the material conditionals Aj D

Cp A, D C,, ... between the corresponding propositions in the two families.

(Lewis 1973«: 563)

The suggestion here is that F and L contribute independently of each other to the set of material conditionals true in a given world. I find that this conflicts with Lewis’ understanding of the laws as supervening on the distribution of particular fact, which is the standard sense often paraphrased as ‘there cannot be an A-difference without a B-difference’ (McLaughlin & Bennett 2018). Indeed, Lewis says quite explicitly that: ‘we have an arrangement of qualities. And that is all. There is no difference without difference in the arrangement of qualities. All else supervenes on that’ (Lewis 1986a: ix). This makes laws epiphenomenal consequences of the distribution of qualities, and thus we should be able to infer all the material conditionals from F alone, i.e. from the set of true propositions of fact. There is a one-to-one correspondence between the local matters of fact—on which the truth of the law-propositions in L supervene—and the true propositions in F, in which case F alone surely implies all the material conditionals and the law-propositions in L. After all, the regularities in a world are not there because of the laws in that world, the laws are there because the regularities are there; that is what is meant by the laws supervening on the facts. Basically, when all worlds reduce to a mosaic of local matters of fact there really is only one respect of similarity and difference: distribution of local matters of fact.

The second way in which it is argued that even if laws supervene on the facts they can still contribute individually to similarity between worlds is by analogy to other kinds of supervening phenomena. So, for instance, that even if the moral supervenes upon the physical, there could be a big overall difference between worlds that were physically very alike, since a tiny physical difference can make a big moral difference. The argument here is that a tiny difference in base properties can make a big difference in higher-order properties. Two responses come to the fore. First, I am finding it difficult to construe an example where a tiny physical difference gives a big moral difference, except those that translate into examples of tiny physical differences leading to big physical differences on which big moral differences supervene. A tiny nudge in the ice-hockey rink may not amount to much morally, but on the edge of a cliff it may have serious moral implications. However, there is a moral difference only if the nudge leads in one case but not the other to a physical fall and physical death or injury. The big supervening moral difference then reduces to a big physical difference. Second, for CTCs to work it is not enough to show that there can be tiny base differences that give big higher-order differences. They must show that any tiny difference in the distribution of base qualities that contradicts any given counterfactual must make such a big difference with respect to overall similarity that there will always be a comparatively closer world where the tiny differences in base qualities do not contradict the counterfactual. It is the latter claim that I am challenging.

Although I have nowhere come across anyone arguing this, one could consider whether the distinction made between strong and weak super-venience could support the case of CTCs. However, as McLaughlin & Bennett point out (2018: §4.3.4) when the domain of base properties is restricted to intrinsic properties—as is the case with neo-Humean worlds—then weak and strong supervenience coincides. And yes, there is talk of supervenience relations of varying modal force, but the variation is between nomological and logical necessity (McLaughlin & Bennett 2018: §3.1). None of these distinctions will support the idea that in a neo-Humean reality laws can vary somehow independently of the facts.

Is there still a sense of ‘supervene’ that could be used to make sense of overall comparative similarity and consequently motivate the intelligibility of CTCs? I am happy to leave that open. My aim is only to show that on closer inspection there is nothing particularly clear about the notion of counterfactual dependence to make CTCs look more appealing or promising than causal accounts of counterfactuals (or to simply give up counterfactuals), and to show that the scope of ontologies for which CTCs are apt, or relevant, is considerably smaller than popularly believed.

It bears mentioning that I am not the first to question the intelligibility of the concept of comparative overall similarity. Michael Morreau argues that ‘there can be no combining of the various similarities and differences of things into useful comparisons of overall similarity’ (Morreau 2010: 469). However, while I question that there can be but one kind of similarity/difference, Morreau argues that even if worlds could differ in many different respects, there is no useful way to combine these different respects into one measure of overall comparative similarity.


Above I have tried to undermine the appeal and promise of CTCs, initially by appeal to relatively simple considerations that I think have been overlooked. For instance, that nobody accepts counterfactual claims about phenomena whose causal connection they don’t think they understand, and that this understanding agrees with a longstanding philosophical tradition according to which counterfactual dependence is grounded in necessary causal connections. These considerations do not prove that CTCs are completely untenable but should show that their intuitive appeal has been exaggerated and that they have yet to address fairly basic objections.

The thrust of my argument is that, contrary to popular belief, CTCs are not equally appealing to everyone regardless of their ontological commitments. In particular, I argue that an ontology of possible worlds is irrelevant for everyone who is committed to substantial connections of some form. Indeed, philosophers who deny both neo-Humean contingency and necessary connections do not thereby automatically turn to CTCs but instead simply accept that counterfactuals are strictly speaking false. Finally, I have argued that CTCs should not even be appealing to the proponents of neo-Humean metaphysics. Or, to be more precise, I have argued that if reality is contingent in the way neo-Humeans claim it is, there is nothing to constrain reality in the way required to reinstate counterfactual dependency in terms of comparative similarity. Neo-Humeans, in giving up substantial connections, should give up counterfactual dependence.

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