Proof-Theoretic Harmony and the Strength of Rules

According to inferentialists the meaning of logical vocabulary is given by the rules of inference governing its use. In response to a challenge posed by Arthur Prior, inferentialists have typically argued that not all sets of rules can define a connective. The project of determining which sets of rules are acceptable definitions has come to be known as the project of finding a criterion of proof-theoretic harmony. One of the best-known proposals is Neil Tennant’s. His criterion of harmony relies on the notions of the strength of a proposition and the strength of a rule. In this note, I argue that Tennant’s appeal to the notion of the strength of a rule gives rise to problems that make his account unsustainable. I also argue that the sort of consideration that gets Tennant into trouble applies, more generally, to other so-called ‘local’ accounts of harmony, and casts doubts on the idea that we can uniquely determine the harmonious counterpart of a given set of rules.