Abstract
Here is a puzzle, which I learned from Terence Parsons in his “True Contradictions” [8]. First Degree Entailment is a logic which allows for truth value gaps as well as truth value gluts. If you are agnostic between assigning paradoxical sentences gaps and gluts, then this looks no different, in effect, from assigning them a gap value? After all, on both views you end up with a theory that doesn’t commit you to the paradoxical sentence or its negation. How is the fde theory any different from the theory with gaps alone? In this paper, I will present a clear answer to this puzzle – an answer that explains how being agnostic between gaps and gluts is a genuinely different position than admitting gaps alone, by using the formal notion of a bi-theory, and showing that while such positions might agree on what is to be accepted, they differ on what is to be rejected.