Ground and Paradox (Boris Kment)

The Logic and Metaphysics Workshop will meet on October 29th from 4:15-6:15 in room 6494 of the CUNY Graduate Center for a talk by Boris Kment (Princeton).

Title: Ground and Paradox

Abstract: This paper discusses a cluster of interrelated paradoxes, including the semantic and property-theoretic paradoxes (such as the paradox of heterologicality), as well as the set-theoretic paradoxes and the Russell-Myhill paradox. 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 and an analogous solution to Russell-Myhill. Moreover, it generates a paracomplete solution to the property-theoretic paradoxes. This solution also applies to the semantic paradoxes, 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 it promises to resolve the main outstanding difficulties for this position, such as revenge cases and the problem of adding a conditional with a sufficiently strong logic.

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