A Note on Freedom from Detachment in the Logic of Paradox
Jc Beall, Thomas Förster, Jeremy Seligman · Notre Dame Journal of Formal Logic · 2012
We shed light on an old problem by showing that the logic LP cannot define a binary connective ⊙ obeying detachment in the sense that every valuation satisfying φ and ( φ ⊙ ψ ) also satisfies ψ , except trivially. We derive this as a corollary of a more general result concerning variable sharing.