On measurement and quantification: The case of most and more than half

The quantifiers most and more than half pose a challenge to formal semantic analysis. On the one hand, their meanings seem essentially the same, prompting accounts that treat them as logically equivalent. On the other hand, their behavior diverges in a number of interesting ways. This article draws attention to some previously unnoticed contrasts between the two and develops a novel semantic analysis of them, based on principles of measurement theory. Most and more than half have logical forms that are superficially equivalent (per Hackl 2009), but that place different requirements on the structure of the underlying measurement scale: more than half requires a ratio scale, while most can be interpreted relative to an ordinal scale or one with a semiordered structure. The latter scale type is motivated by findings from psychophysics and by psychological models of humans’ approximate numerical abilities. A corpus analysis is presented that confirms the predictions of the present account.