Properties, possibilia and contingent second-order predication

Analysis 69 (4):643-649 (2009)
Abstract
1. The problemLewis identifies the monadic property being F with the set of all actual and possible Fs; the dyadic relation R is identified with the set of actual and possible pairs of things that are related by R; and so on . 1 Egan has argued that the fact that some properties have some of their properties contingently leads to trouble: " Let @ be the actual world, in which being green is [someone's] favourite property, and let w be a world in which being green is [nobody's] favourite property. Since being green is somebody's favourite property in @, it must be a member of … being somebody's favourite property. Since being green is not anybody's favourite property in w, it must not be a member of being somebody's favourite property. Contradiction. " Egan suggests identifying properties with functions from worlds to extensions. However, as Lewis and others have complained, this has the drawback of turning monadic properties into relations . 2 In this article, we shall show that the Lewisian has the resources to block the above argument while simultaneously respecting the adicity of the relevant property and the contingency of the predication without changing his theory of properties. However, our analysis reveals a hidden ambiguity in the Lewisian conception of properties, and on either disambiguation the resulting account of properties seems inadequate.2. On ‘being someone's favourite property’The phrase ‘ being someone's favourite property’ is ambiguous. Given Lewis's ontology of possibilia, where the phrase picks out a monadic property it is not one that is possessed contingently; where it picks out a property that is possessed contingently it is not one that is monadic. But the argument works only if being someone's favourite property is both monadic and possessed contingently.Why should …
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