Abstract

In a recent paper, Barrett & Halvorson (2016) define a notion of equiva- lence for first-order theories, which they call “Morita Equivalence.” To argue that Morita equivalence is a reasonable measure of “theoretical equivalence,” they make use of the claim that Morita extensions “say no more” than the theories they are extending. The goal of this paper is to challenge this central claim by raising objections to their argument for it and by showing why there is good reason to think that the claim itself is false. In light of these criticisms, this paper develops a natural way for the advocate of Morita equivalence to respond. However, this response makes her criterion equivalent to mutual faithful interpretability, an already well-known and philosophically contentious barometer of theoretical equivalence.