Abstract

We show that finitely axiomatized first-order theories that involve some criterion of identity for entities of a category C can be reformulated as conjunctions of a non-triviality statement and a criterion of identity for entities of category C again. From this, we draw two conclusions: First, criteria of identity can be very strong deductively. Second, although the criteria of identity that are constructed in the proof of the theorem are not good ones intuitively, it is difficult to say what exactly is wrong with them once the modern metaphysical view of identity criteria is presupposed.