Abstract
David Lewis claims that his theory of modality successfully reduces modal items to nonmodal items. This essay will clarify this claim and argue that it is true. This is largely an exercise within ‘Ludovician Polycosmology’: I hope to show that a certain intuitive resistance to the reduction and a set of related objections misunderstand the nature of the Ludovician project. But these results are of broad interest since they show that would-be reductionists have more formidable argumentative resources than is often thought. Lewis’s reduction depends on a set of methodological commitments each of which is fairly plausible or at least currently popular, and none of which is particular to modality. The choice of which of these commitments to reject I leave to the discerning antireductionist. The essay proceeds as follows: §1 discusses reduction generally and one or two relevant puzzles; §2 discusses Lewis’s reduction in particular; the longest section, §3 replies to four objections.
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Notes
Not all asymmetric reduction relations are dependence relations. Every contingent fact supervenes asymmetrically on every necessary fact, but intuitively the fact that Susan Rumplebottom won the 2009 Gloucestershire Cheese Rolling competition does not depend on Goldbach’s conjecture.
In which four shipwrecked seamen were tried for cannibalising their cabin boy.
Perhaps you disagree with the specifics of these examples; perhaps you even reject all preserving reductions. That’s fine: my intention here is just to clarify eliminating reductions by the comparison.
By states of affairs I simply mean objects instantiating properties. There is an issue about the extent to which Lewis was really a truthmaker theorist; see the contributions by Lewis and Rosen to Lillehammer and Rodriguez-Pereyra (2003). But there is no doubt that he thought that ‘truth supervened on (and was distinct from) being,’ and that makes him enough of a truthmaker theorist for my purposes.
For instance Peter Railton talks of ‘a synthetic identification of the property of moral value with a complex nonmoral property’ (in his ‘Reply to David Wiggins,’ 1993, p. 317).
For more on this prima facie puzzle, see Carl Hempel (2001), Reduction: Ontological and Linguistic Facets.
From Stalnaker’s 2009 Hempel lecture: ‘If an account of modality were to meet [the reductive] condition, that would be a sure sign that it was on the wrong track.’ Cf. also the literature in philosophy of mind concerning the ‘explanatory gap’ (e.g. Levine 1998).
Lewis takes the heroic course and rejects the second premise, arguing that since von Neumann’s analysis is better adapted to the higher infinities it is the better analysis overall, and since it is the better analysis it is the true analysis. This is a minority view.
Quine’s Ontological Reduction and the World of Numbers worry about the Lowenheim-Skolem theorem is similar.
There is a open question about how many of the Lewis’s building blocks for his version of modal realism are an essential part of something that can still be called Ludovician Modal Realism. Surely not all of them are; perhaps even his commitment to sets is not. For simplicity I will stick with a view which I take to be as close as possible to Lewis’s 1986 and 1993.
A fuller presentation would need choice and replacement; these are not necessary for our purposes.
Definition. x is large iff there are some things such that (1) no two of them overlap, (2) their fusion is the whole of Reality, and (3) each of them contains exactly one atom that is part of x and at most one other atom. Otherwise x is small.
Dan Nolan (1996) has argued that this qualification is unnecessary. It has been suggested to me that David Lewis was persuaded by Nolan’s argument. I won’t pursue the debate further. See Efird and Stoneham (2008) and Darby and Watson (2010) for some fussing over the details of the principle of recombination; this is not relevant to our concerns here.
Although in his defense, I think he intended to echo the Treatise: ‘any thing may produce any thing’ (Hume, 1.3.15.1).
There is a worry here, namely that if we do not have a clear enough conceptio nof our reduction base that will undermine the intuitive rationale for the reduction itself (cf. Carl Hempel’s ‘Reduction: Ontological and Linguistic Facets’). However it seems to me that the worries here all concern non-central cases—but of course the vaguenes of dusk fails to undermine the day/night distinction.
Or rather, facts about certain properties being essential. Such facts may not be modal. But we can do without them anyway, so there’s no need to worry about this.
“A syllogism is language [logos] in which, certain things being asserted, something else follows of necessity from their being so.” Aristotle, Prior Analytics, 24b14.
Put aside for now the question whether the Principle of Recombination should be qualified with an upper mathematical bound.
Consider a different sort of worry, suggested to me by Jack Spencer. I have argued that Modal Realism satisfies the material adequacy constraint without appeal to primitive modality on the basis of two premises: (1) realism: modal claims obtain independently of modal beliefs; (2) a methodological commitment to simplicity, systematicity and conservatism. In virtue of the second we are entitled to believe that Modal Realism meets the material adequacy constraint, in virtue of the first this is not objectionably circular. The ersatzist has her own material adequacy constraint. From among the possible ersatz items she must select all and only those which represent possible states of affairs. Can she make this selection by appealing to the same two premises as Lewis and thereby also avoid primitive modality?
Lewis distinguishes three types of ersatzist views, according to their manner of representing possibilities: linguistic ersatzism posits linguistic items which represent in virtue of stipulated meanings; pictorial ersatzism posits pictures or models which represent by isomorphism; magical ersatzism posits items in whose nature it is to represent possibilities.
According to linguistic ersatzism: Possibly p iff according to some ersatz sentence p. An ersatz sentence, for our purposes, is a long conjunction of claims specifying precisely how the world that it represents would be like if it were actualised. All ersatz sentences actually exist; all represent their worlds as actualised; but only that sentence which represents the actual world is actualised. The problem with linguistic ersatzism concerns the representation relation. First let’s distinguish explicit claims from implicit claims. Implicit claims are those which are implied by explicit claims. But this implication relation is modal. So let us suppose instead that ersatz sentences are maximally specific so that all representation claims are explicit. In order to get the necessary descriptive power, precision and context-independence the syntax had better not be from any natural language; let it be mathematical. This makes vivid the fact that the meanings of the sentences are stipulated. Ersatz sentences represent this and not that possibility partly in virtue of a contribution from ourselves, and hence, unavoidably, partly in virtue of our modal beliefs. This violates the realist premise. It follows that the linguistic ersatzist cannot avail herself of the Modal Realist escape from primitivity.
Pictorial ersatzism has a different problem: it is descriptively adequate only if it collapses into linguistic ersatzism or Modal Realism. Lewis does a nice job of showing this (pp. 168–173). According to magical ersatzism, ersatz items are intrinsically such as to represent what they represent. The magical ersatzist must posit some class of sui generis abstract objects with these intrinsic representational powers, and from among them, he must grant special status to those which represent genuine possibilities. Both ostensibly require modal primitives. However the magical ersatzist does not violate the realist premise or the methodological premise. So if these premises under certain conditions entitle Lewis to eschew primitivity, they can do the same for the magical ersatzist. So I concede that the methodological strategy in the main text enables the magical ersatzist to avoid a certain appeal to primitive modality. There are other problems with this view, and other appeals to primitive modality, which unfortunately I do not have space to discuss.
Thanks to Carla Merino for this suggestion.
Upon learning about the existence of all these worlds why should we not thereby take ourselves to have discovered that actuality is larger than we thought? Indeed, the natural next thought is that possibility concerns the different ways this larger actuality, that is, the whole set of worlds, might have been. These two thoughts go beyond this paper. In short, the answers are: (1) No, we distinguish actuality and existence and tell a story about tacitly restricted quantifiers; (2) No, there is no sense in claiming that possibly all the possibilities might not have been actual. See also John Divers’s (2002) response to the advanced modalizing worry.
The epigraph for his book quotes Lucretius: ‘If you take a little trouble, you will attain to a thorough understanding of these truths. For one thing will be illuminated by another, and eyeless night will not rob you of your road till you have looked into the heart of nature’s darkest mysteries. So surely will facts throw light upon facts.’ (From his On the Nature of the Universe).
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Acknowledgments
For helpful discussions and feedback, many thanks to John Burgess, Meghan Flaherty, Gilbert Harman, Boris Kment, John Mackay, Carla Merino, Ryan Robinson, Gideon Rosen, Jack Spencer, Nick Stang, and Jack Woods.
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Maguire, B. Defending David Lewis’s modal reduction. Philos Stud 166, 129–147 (2013). https://doi.org/10.1007/s11098-012-0024-3
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DOI: https://doi.org/10.1007/s11098-012-0024-3