Ground and Paradox

Boris Kment (Princeton University )

Boris Kment (Princeton) will present "Ground and Paradox" at 11 in Arts West North Wing 556 on 16 August.

Abstract: This paper discusses a cluster of interrelated paradoxes, including those of set theory (e.g. Russell’s paradox), truth (e.g. the Liar), and the theory of properties (e.g. the paradox of heterologicality). I argue that an independently motivated theory of metaphysical grounding provides philosophically satisfying treatments of these paradoxes. It yields as corollaries a version of the iterative conception of set (which underlies the standard axiomatic set theory ZFC), and a solution to the property-theoretic paradoxes that rests on rejecting the law of excluded middle. The latter solution also applies to the paradoxes of truth, which can be subsumed under the property-theoretic ones. The treatment of the property-theoretic paradoxes has structural similarities to Kripke’s approach to the Liar and promises to resolve outstanding difficulties for this position, including revenge cases.