David Lewis + Kit Fine = Weirdness

David Lewis thinks that properties are just sets of possible individuals. SEP: “Lewis argues that for any set of actual and possible objects (fundamental or not), there is a property, namely the property an object has just in case it is a member of the given set.”

Kit Fine thinks that essence is an asymmetrical relationship. Specifically, it is an asymmetrical relationship between a set and its constituent(s). Although Socrates is essential to the singleton set {Socrates}, the set is not essential to Socrates. “It is no part of the essence of Socrates to belong to the singleton.” (“Essence and Modality“)

Suppose you accept both. Then no individual has any property essentially. After all, a property is a set, and it is not part of the essence of any individual to belong to any set. Moreover, every property has its bearers essentially. After all, constituents of a set are essential to that set. On the face of it, that is pretty weird.

Ways to get out: (1) Most obviously, don’t put Lewis and Fine together. (2) Clarify what Fine says, so that the essence relationships hold for some sets but not others. (3) Clarify what Lewis says, so properties aren’t just sets, but in some sense correspond to them. Both (2) and (3) look ad hoc to me, so perhaps the weirdness can count as an incompatibility result between Lewis and Fine?

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3 Responses to David Lewis + Kit Fine = Weirdness

  1. Jon S says:

    I suspect you have overgeneralized what Fine says. To have a property essentially, if you take up the Lewisian analysis, is (trivially) to belong to that set which is the property essentially. In the article you cite, Fine wants to exploit the intuition that an object’s belonging to its singleton set is not part of what makes the object what it is, in order to drive a wedge between essence and necessity. But–and admittedly it’s been a few years since I’ve read that article–I don’t think he tries to press the more general claim that no object belongs to any set essentially. Neither does he need such a claim. The resolution, then, ought to be something like (2). But that isn’t ad hoc just because it means getting clear about Fine’s actual view.

  2. Shen-yi Liao says:

    So, which objects (do you think Fine thinks) belong to a set essentially and which objects don’t? What is the cut-off?

  3. Jon S says:

    That seems like a question that doesn’t need to be answered precisely for there to be a distinction between essential and non-essential properties. Presupposing the existence of possibilia and the Lewisian analysis of properties, we can certainly give examples. Following Fine, none of the members of a singleton belong to it essentially. (This would create a problem if Fine believed in essential haecceities, in addition to the existence of possibilia and the Lewisian analysis of properties, but I suspect he’d be pretty happy rejecting at least one of those options.) Assuming that species-membership is essential, all of the members of a set that includes precisely those actual and possible objects of a certain species belong to that set essentially, etc. But this is all just to say that objects to a set essentially iff they bear the corresponding property essentially–which is trivial, given the Lewisian analysis of properties. To answer your question, then, one must first say what it is for a property to be essential. Fine has an answer to that in the paper you cite, but since it’s more or less definitional, I doubt you’ll be happy with it. At any rate, the addition of Lewis here causes no additional problems that I can see.

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