See: Remarks on Truth-Grounding and the Liar
A short paper that uniquely identifies the syntactic cause for Alethic Paradox
, provides an algorithm to do so, and demonstrates a class of philosophical solutions satisfactory for that. It also provides a consistency proof for axiom scheme Kripke-Feferman
that satisfies the four intuitions about Alethic Paradox (which have all been argued for - any theory should explain how these intuitions arose in the first place) as well as the empirical observation that most people never apply T-Schema to the Liar Sentence (providing experimental evidence in favor of my proposal).