Metaphysical theories of modality: Properties, relations and possibilities
Many theories assimilate the idioms of modality to those of quantification; they hold that so-and-so is possible iff there is a "world" at which it is true that so-and-so. "Modal realism" identifies worlds with certain concrete particulars, and truth at a world with what is true of it. Rival "ersatz" theories identify worlds with certain abstract entities and identify what is true at them with what they represent.
David Lewis argues that pre-theoretic modal intuitions are best explained by modal realism. I try to make a case for ersatzism.
First, I argue that modal realism is flawed on the grounds that it entails the impossibility of certain intuitively possible spatiotemporal structures; it fails to explain fully even those intuitions with which it is compatible; and it renders the origin of modal knowledge mysterious.
Next, I argue that objections to ersatzism are not conclusive.
Lewis objects that even a generic version of ersatzism requires an unnameable and maybe unintelligible primitive relation. I suggest that the problems with naming are perfectly general; they have nothing to do with metaphysical theories of modality in particular. And I suggest a solution taken from Lewis himself. I also argue that any purported unintelligibility is due to illegitimately assimilating the relation to spatiotemporal relations.
Finally, I consider some difficulties with a version of ersatzism that aims to reduce modality to impure set-theory. One concerns the accommodation of intuitions about properties that are not, but might have been, instantiated. Another concerns accommodation of intuitions about relations of exclusion and entailment among properties. I suggest that these difficulties are due to faulty assumptions about the nature of properties rather than any fundamental flaws in this ersatz approach. So I propose an account of properties that when incorporated into ersatzism circumvents these difficulties and allows it to claim the advantages of modal realism without its drawbacks. Unlike traditional accounts, this takes the essence of a property to consist in its role in imposing a certain classificational structure on the particulars that instantiate it, rather than in any unique and irreducible "quiddity".