In this talk I will discuss the adequacy of prominent relations of theory equivalence as relations of theoretical synonymy.

A relation of theoretical synonymy should characterize the equivalence of formal theories with respect to their meaning or content. In logic and philosophy of science, the relation of definitional equivalence or its generalization, bi-interpretability, are predominantly used for this purpose. I will consider examples of theories that are bi-interpretable and argue that they should not be understood as synonymous. To do this, I will introduce five general principles of theoretical synonymy that seem intuitively plausible but are not satisfied by definitional equivalence or bi-interpretability. This gives rise to questioning the adequacy of bi-interpretability as a relation of theoretical synonymy.

Finally, I will briefly outline what interesting strengthenings of bi-interpretability might look like.