Negation and modality in unilateral truthmaker semantics

Abstract

Fine (J Philos Logic 46(6):625–674, 2017) develops a unilateral and a bilateral truthmaker semantics for propositional logic. The unilateral approach trades off the primitive exact falsification relation of the bilateral approach for a primitive exclusion relation between states, thereby raising the question if exclusion serves any purpose other than to avoid exact falsification. We argue that exclusion is motivated independently of its use in avoiding exact falsification, namely as a foundation for the reconstruction of modal notions such as possibility and necessity. This reconstruction in turn motivates what we call emergent exclusion: an atomic state can exclude a sum of atomic states collectively without excluding any of these atomic states individually. Emergent exclusion is banned in Fine (2017a) in order to maintain exact equivalence in de Morgan’s law \(\lnot (P \wedge Q) \Leftrightarrow \lnot P \vee \lnot Q\); we argue that the two sides of this law are not exactly equivalent and discuss a variety of state spaces that feature emergent exclusion. This paper aims to be accessible to linguists without prior exposure to truthmaker semantics. We highlight points of contact with natural language semantics, such as event semantics and algebraic semantics of plurals and conjunction.