Title: Truthmaker semantics for containment and nonsense

Abstract: Conceptivism is the doctrine according to which a proposition cannot entail another proposition if the latter contains a concept which is not already contained in the former: entailment does not introduce any additional conceptual content. This doctrine motivates so-called containment logics, namely logics where a formula B cannot be deduced from a formula A if B contains a propositional variable which is not already contained in A. Interestingly, most containment logics can be described as the result of filtering another logic by this syntactic condition. For instance, A follows from B in Parry’s logic PAI if and only if A classically follows from B and all the propositional variables of B occur in A. Routley uses this fact to discredit containment logics as syntactic artefacts lacking any semantic depth. In this talk, I investigate the semantic properties of containment logics to rebut Routley’s critique. I look at two recent strategies to semantically characterise containment logics without syntactic filters: Berto (2019)’s two-component semantics, where entailment contains a condition of topical inclusion, and logics of nonsense (e.g., Ferguson (2015)), which include a truth-value representing meaninglessness. Both are somewhat unsatisfactory and call for a more general approach. I argue that the framework of truthmaker semantics (e.g., Fine (2017)) can be used to that end. I develop sound and complete truthmaker semantics for logics of nonsense and adapt them to model containment logics. The truthmaker understanding of containment logics provides a purely semantic foundation for them, thus refuting Routley’s claim that they are syntactic artefacts.