Department of Philosophy, University of Nevada Las Vegas
—We lay out a generalized version of the Russell-Myhill Paradox, which purports to show that the notion of proposition is incoherent because it generates a violation of Cantor's theorem (according to which the power set of any set must have more members than that set). We recast the paradox without appeal to the notion of truth (to bypass responses that appeal to deflationism about truth) or appeal to the contents of mental states (to bypass responses to Kaplan’s version of the paradox for possible-world semantics). We leverage the generalized paradox to present a dilemma: traditional and current theories of propositions favored by many appear to fall to the paradox, while theories that escape the dilemma suffer from otherwise persistent problems—the Benacerraf problems, the problem of the unity of the proposition, and an inability to explain representation, among others. We then sketch a branching way forward, one according to which we must either accept a non-representational account of propositions or reject the existence of propositions while accounting for proposition-talk.