Abstract
David Lewis’s arguments against magical ersatzism are notoriously puzzling. Untangling different strands in those arguments is useful for bringing out what he thought was wrong with not just one style of theory about possible worlds, but with much of the contemporary metaphysics of abstract objects. After setting out what I take Lewis’s arguments to be and how best to resist them, I consider the application of those arguments to general theories of properties and relations. The constraints Lewis motivates turn out to yield an argument for concretism about possible individuals that is quite different from the better-known Lewisian arguments for that position. The discussion also touches on the puzzling question of whether things are the way they are because of the properties they have, or are the properties and relations the way they are because of the things that have them.
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Notes
Because swimming elephants are in the way? Perhaps the simile has now stretched too far.
Lewis’s argument has since been relied on by others: see for example Hawley (2010, pp. 123–124), who appears to agree with Lewis that a “magical” theory of structural universals would be unacceptable, or at least “uncomfortable”, for some of the reasons Lewis offers.
Translating Lewis’s ersatzist into talking about propositions is the strategy pursued by van Inwagen in describing the view in van Inwagen (1986).
For discussion of Lewis’s attitude to quantitative parsimony and objections to it, see Nolan (1997).
Zaragoza (2007) also makes the point that a magical ersatzer need not be worried by this.
Zaragoza suggests that “Lewis can very plausibly claim that there is a general presumption in favour of stronger combinatorial principles”, and objects that since Lewis postulates his own limitations on recombination, the question of who has the stronger principles here is debatable (Zaragoza 2007, pp. 397–400). While my question of which principles here are “simple, general and apparently motivated” is not quite the question of mere strength, a similar debate to the one Zaragoza discusses can be had between the Lewisian and the magical ersatzer about my question as well.
I am convinced that these further options, and other options such as taking selection to be internal but in virtue of the internal structure of non-simple elements, will not help the magical ersatzer unless one or other of the main horns of Lewis’s argument can be blunted. Jubien (1991) argues that a way of taking selection to be extrinsic can meet Lewis’s objections, as can a way of taking it to be intrinsic but due to internal structure of the elements. I disagree, but space prevents a full discussion here.
Lewis appears to be keen to adopt the negation of the view he attributes to the magical erstazer. How could he do this if the view was unintelligible?
An ersatzer could replace her claims about necessary connections between different features of the concrete cosmos and different elements being selected with claims about which element would be selected, given different specifications of the concrete world. While a counterfactual construal of the theory of selection may have some other advantages (e.g. a smoother generalisation to a theory of selection of impossible worlds) it is unlikely to assuage Lewis’s concerns about brute modal connections between distinct existences, so I will stick with discussing magical ersatzers who formulate their theories in terms of necessary connections between the nature of the concrete cosmos and what the cosmos bears the selection relation to.
Denby (2006, pp. 168–170) in effect offers this alternative on behalf of the magical ersatzer as his “vagueness” alternative.
For a different interpretation of what Lewis’s view of naturalness and eligibility amounted to, see Schwarz (2014).
Denby (2006, pp. 167–168) makes the point that using naturalness to explain how we are able to refer specifically to selection is a move available to the magical ersatzer.
I gloss over three technicalities in particular. One is that Lewis is explicit that the account of properties in the text is one among several which are acceptable specifications of our expression “property” (Lewis 1986b, pp. 55–57). The other is that Lewis believed that some properties, and perhaps many interesting ones, would be proper classes (Lewis 2002, p. 8). The third is that properties and relations do not quite correspond to our usual one- or two-place predicates, because of the temporal dimension: temporal worms can be red at one time and not-red at another, and so we do not want them in or not in a set like “the set of all and only red things” simpliciter (Lewis 1986b, pp. 202–204).
One might think that there should be “linguistic” or “pictorial” alternatives to magical theories of properties and relations, by analogy with the options Lewis offers ersatzers about possible worlds. I doubt that there are “linguistic” ones, in part because I suspect that in the end “linguistic” options need to help themselves to theories of meaning and interpretation that under scrutiny will turn out to be relevantly like magical ones, and so are a limited alternative. This leaves open the intriguing possibility that a “pictorial” approach to properties and relations is possible, where properties and relations are Instantiated in virtue of their similarity to their instances. This would be a surprising resurrection of Plato’s suggestion that Forms are connected to the everyday world through mimesis.
Thanks to Jason Turner, Katherine Hawley, Kris McDaniel, Carrie Jenkins, L.A. Paul, and audiences at the David Lewis Society meeting in Seattle in 2012, and the University of Sydney in 2013, for helpful feedback.
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Nolan, D. It’s a kind of magic: Lewis, magic and properties. Synthese 197, 4717–4741 (2020). https://doi.org/10.1007/s11229-014-0565-4
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DOI: https://doi.org/10.1007/s11229-014-0565-4