 To analyze the inconsistency in more detail, consider an extensional model of concepts, in which the material equivalence of concepts \(F\) and \(G\) serves as both necessary and sufficient conditions for the identity of \(F\) and \(G\), i.e., in which \(F = G \equiv \forall x(Fx \equiv Gx)\).  So, given this understanding, if it is not the case that \(F\) and \(G\) are materially equivalent, then \(F\) and \(G\) are distinct concepts; and if \(F\) and \(G\) are distinct concepts, then they are not materially equivalent.