Semantic conditions for moderate inferentialists – solutions to the categoricity problem

Abstract Moderate inferentialists defend the thesis that inferences determine the truth-conditional meanings of the logical operators. An important technical and philosophical challenge to this position is the so-called categoricity problem . This is the problem that logics can be soundly interpreted by non-standard models which undermines the idea that inferences lead, unambiguously, to model-theoretic meanings. Several strategies to solve this issue can be found in the literature. One approach consists in strengthening the proof-systems in such a way that the logics in question cannot be soundly interpreted by the non-standard models. Another restricts the class of admissible models of a logic by inferentialistically acceptable principles to rule out non-standard models. This paper discusses attempts in line with this latter solution strategy to the categoricity problem. Our goal is to investigate restrictions on models that are both inferentialistically well-motivated and applicable to a wide variety of logical systems. This is not an easy task, since several inferentialistically unobjectionable restrictions do not generalize beyond particular logical systems, whereas other general and successful principles lack inferentialistically acceptable motivations. This paper proposes a taxonomy of several classes of principles and investigates their scope and chances of success in the context of the project of the moderate inferentialist about logical meanings.