The Inadequacy of a Proposed Paraconsistent Set Theory

Abstract

We show that a paraconsistent set theory proposed in Weber (2010), this journal, is strong enough to provide a quite classical non-primitive 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 that all sets are distinct from themselves. 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.