The Inadequacy of a Proposed Paraconsistent Set Theory

Abstract

We show that a paraconsistent set theory proposed in Weber (2010) is strong enough to provide a quite classical nonprimitive notion of identity, so that the relation is an equivalence relation and also obeys full substitutivity: a = b → (F(a) → F(b)). With this as background it is shown that the proposed theory also proves ∀x(x ≠ x). While not by itself showing that the proposed system is trivial in the sense of proving all statements, it is argued that this outcome makes the system inadequate.