A Metainferential Hierarchy of Validity Curry Paradoxes (Brian Cross Porter)

The Logic and Metaphysics Workshop will meet on October 12th from 4:15-6:15 (NY time) via Zoom for a talk by Brian Cross Porter (CUNY).

Title: A Metainferential Hierarchy of Validity Curry Paradoxes

Abstract: The validity curry paradox is a paradox involving a validity predicate which does not use any of the logical connectives; triviality can be derived using only the structural rules of Cut and Contraction with intuitively plausible rules for the validity predicate. This has been used to argue that we should move to a substructural logic dropping Cut or Contraction. In this talk, I’ll present metainferential versions of the validity curry paradox. We can recreate the validity curry paradox at the metainferential level, the metametainferential level, the metametametainferential level, and so on ad infinitum. I argue that this hierarchy of metaninferential validity curry paradoxes poses a problem for the standard substructural solutions to the validity curry paradox.

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