How Tall Is Tall? Compositionality, Statistics, and Gradable Adjectives

What is tall? Like many words, tall is fundamentally compositional in meaning — whether an item is tall depends on the statistical properties of the set of items it is being compared to. Despite preliminary evidence to this effect, no mathematical models of how tall operates in a given context have ever been empirically evaluated. We compare a number of statistical models to adults and children in judging which items are tall in various contexts, including both threshold-based and categorization-based models. We find that non-parametric statistical models of gradable adjectives best describes the judgments of people across a wide variety of contexts.