Rigidity for Predicates and Overgeneralization

What is it for a predicate to be rigid? The following seems to be a plausible straightforward proposal. Inasmuch as rigidity for singular terms concerns sameness of signification across possible worlds, so does rigidity for predicates: a predicate is rigid iff it signifies the same property across the different possible worlds (and is flexible otherwise). This I call the simple proposal about rigidity for predicates. It is arguably suggested by Kripke himself in N&N, and seems to be tacitly assumed in discussions in philosophy of mind, philosophy of science, or metaethics.

However, it has received a number of criticisms in the recent literature. Among them: that it is unduly committed to the view that predicates signify entities like properties (the signification problem), and that it would trivialize the notion, by covering any predicate whatsoever (the trivialization problem).

I have written a paper defending the simple proposal from another objection. Although the objection is not usually formulated sharply, nor clearly distinguished from the trivialization concern, the idea behind it seems to be that the proposal would overgeneralize, by covering predicates for artifactual, social, or evaluative properties, such as ‘is a knife,’ ‘is a bachelor,’ or ‘is funny.’ And this despite the fact about the (relative) “unnaturalness” of the properties signified. Hence I label it the over-generalization problem. Recent proponents of this objection include Schwartz 2002 and Haukioja 2006.

My paper has been conditionally accepted in Synthèse, and I plan to write the final version in the next days. All comments, suggestions, and objections more than welcome ;-{)}!!