Connectedness as a constraint on exhaustification

Abstract

“Scalar implicatures” is a phrase used to refer to some inferences arising from the competition between alternatives: typically, “Mary read some of the books” ends up conveying that Mary did not read all books, because one could have said “Mary read all books”. The so-called grammatical theory argues that these inferences obtain from the application of a covert operator $exh$, which not only has the capability to negate alternative sentences, but also the capability to be embedded within sentences under other linguistic operators, i.e. $exh$ has the potential to add to the meaning of expressions (not necessarily full sentences), the negation of their alternatives. This view typically seeks support from the existence of readings that could not be explained without the extra-capability of $exh$ to occur in embedded positions. However, if some embedded positions seem to be accessible to $exh$, not all conceivable positions that $exh$ could occupy yield sensible results. In short: the $exh$ approach is powerful, maybe too powerful. Various approaches based on logical strength and monotonicity have been proposed to justify on principled grounds the limited distribution of $exh$; these approaches are mostly based on a comparison between possible parses, and considerations of monotonicity (e.g., the Strongest Meaning Hypothesis). We propose a new constraint based instead on “connectedness”, ruling out parses because of inherent problems their outcome may raise. Connectedness is a sister notion of monotonicity, which has been recruited to explain certain lexical restrictions on nouns, adjectives and more recently quantifiers; we propose here that connectedness could play a similar role at the level of propositional meanings.