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 Kripkeā€™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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