Exhaustification in the semantics of cause and because

We show that a single operation can account for three seemingly distinct properties of the semantics of cause and because. The properties are, firstly, their comparative nature: interpreting cause and because involves comparing what would happen in the presence of the cause (a positive condition) with what would happen in the absence of the cause (a negative condition). Secondly, there is an asymmetry in logical strength between the two conditions: the positive condition involves a universal modal while the negative condition involves an existential modal. Thirdly, the positive and negative conditions have the same modal base, i.e. are interpreted while assuming the same set of background facts. Despite their apparent dissimilarity, we show that these three properties are predicted by a single operation: exhaustification. The comparative nature of cause and because follows from the comparative nature of exhausatification, which compares a sentence with its alternatives. The asymmetry in strength arises because exhaustification negates alternatives: given the duality between universal and existential quantification, negation flips a necessity modal into a possibility modal, producing the observed strength asymmetry. Finally, the positive and negative condition have the same modal base since, rather cause and because having two modals in their semantics—one for the positive condition and one for the negative condition—their semantics contains a single modal which is copied by exhaustification. We conclude by showing that this exhaustification operator violates Economy constraints, suggesting that it is not subject to licensing conditions but part of lexical semantics of cause and because.