Lewis 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 (1986: 50–69).1 Egan has argued that the fact that some properties have some of their (second-order) 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...

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