The Logic of Subtractives or, Barely anyone tried almost as hard as me

Abstract

This dissertation is about the meaning and distribution of the modifiers "almost" and "barely." We advocate for an analysis in which they are, across their uses, modifiers of quantifiers, encoding set subtraction; "barely," but not "almost", additionally contributes negation. Both modifiers remove elements from the arguments of quantifiers that they modify, and require exhaustification for their licensing as modifiers. We start with subtractive modified quantificational determiners, like "almost every" and "barely any." We then push this analysis further, showing it very naturally extends to degree constructions like comparatives and equatives, and captures the facts better other options. This extension also provides an argument for the idea that all natural language scales are dense. Numeral constructions like "almost one hundred" and "barely one hundred" appear to complicate the idea that "almost" and "barely" are in complementary distribution, but we argue this shows us there's more than meets the eye in such constructions. We offer a theory of numeral constructions that captures the overlapping distribution. Finally, we suggest that subtractives are evidence in favor of a view of exhaustification in which the contribution of the latter is presuppositional, rather than truth conditional.