Degrees and segments

Abstract

I make two related proposals, one about directed scale segments and the other about the nature of degrees. Bale (2007Bale ( , 2011 argued that degrees should be analyzed as sets of individuals and that degree arguments are created in the syntax from relational predicates. Schwarz (2010) showed that Bale's construction runs into problems when the relational predicate is complex, consisting of an LF constituent that contains more than just a gradable adjective. I modify Bale's proposal so that it overcomes Schwarz's objection. But first I propose a semantics for comparatives based on quantification over directed scale segments, triples consisting of two degrees and a measure function. The modification of Bale's proposal depends upon this. Segments are of independent interest as they permit a conjunctive semantics for extended adjectival phrases, the way events do for verb phrases. Potential benefits of 'degree-conjunctivism' are explored.

Interpreting Degree Semantics

“…Beginning with degrees themselves, a first distinction found in the literature is between whether degrees should be understood to be primitive (i.e., not reducible to abstractions based on other objects; the default assumption) or as labels for equivalence classes of objects (as in Cresswell, 1976), possible objects (Schwarzschild, 2013), or of states (Anderson and Morzycki, 2015), etc. Appeal to degrees simpliciter, or to aspects of their nature, has important consequences for the data coverage of a degree-based theory.…”