Cross-Polar Nomalies

Generally, explanations for the anomaly of these examples are based on the intuition that degrees of ‘tallness’ and degrees of ‘shortness’ are of a different nature and hence cannot be compared. Note that this is not obvious, since pre-theoretically one may think that tallness and shortness are different words for the same measurement, roughly: vertical spacial extension (or simply: height). Kennedy (2001) (following Rullmann 1995, Seuren 1978, 1984, von Stechow 1984: a.o.) provides a very elegant implementation of this idea: An A+ like tall relates an individual to a positive length, an Alike short to a negative one, where a positive length is an interval (a set of degrees) that starts just above 0 and extends up to an object’s height (length/width/richness. . . ), whereas a negative length is an interval that starts just above an object’s height (length/width/richness . . . ) and goes up to ∞. Whatever the semantics of (mo)re, it cannot compare a positive with a negative length (in this technical sense), hence the anomaly of (1). On the other hand, since, say, tallness and shortness ‘live’ on the same scale and are logically related to an object’s height, the usual entailment patterns (A is taller than B iff B is shorter than A etc.) follow under any reasonable semantics for relational measure constructions.