Grounding a Pragmatic Theory of Vagueness on Experimental Data: Semi-Orders and Weber’s Law

[This article appeared as a chapter in 'Vagueness and Rationality in Language Use and Cognition' published by Springer International Publishing in 2019] One of the traditional pragmatic approaches to vagueness suggests that there needs to be a significant gap between individuals or objects that can be described using a vague adjective like 'tall' and those that cannot. In contrast, intuitively, an explicit comparative like 'taller' does not require fulfillment of the gap requirement. Our starting point for this paper is the consideration that people cannot make precise measures under time pressure and their ability to discriminate approximate heights (or other values) obeys Weber’s law. We formulate and experimentally test three hypotheses relating to the difference between positive and comparative forms of the vague adjectives, gap requirement, and Weber’s law. In two experiments, participants judged appropriateness of usage of positive and comparative forms of vague adjectives in a sentence-picture verification task. Consequently, we review formal analysis of vagueness using weak orders and semi-orders and suggest adjustments based on the experimental results and properties of Weber’s law.