The Degree Functions of Negative Adjectives

This paper provides a new account of positive versus negative antonyms. The data includes well known linguistic generalizations regarding negative adjectives, such as their incompatibility with measure-phrases (cf., two meters tall/ *short) and ratio-phrases (twice as tall/ #short), as well as the impossibility of truly cross-polar comparisons (*Dan is taller than Sam is short). These generalizations admit a variety of exceptions, e.g., positive adjectives that do not license measure phrases (cf., #two degrees warm/ cold), and rarely also negative adjectives that do (cf., two hours late/ early). Furthermore, new corpus data is presented, regarding the use of twice with positive and negative adjectives. The analysis the paper presents supposes that grammar associates gradable adjectives with measure functions – mapping of entities to a set of degrees, isomorphic to the real numbers (Kennedy 1999). On this analysis, negative adjectives map entities to values that are linearly reversed and linearly transformed in comparison with their values in the positive antonyms. As shown, the generalizations, as well as their exceptions, directly follow. Negative polarity is explained in terms of function-reversal, and non-licensing of measure-phrases is explained in terms of transformation by an unspecified value.