What Exactly Do Numbers Mean?

Abstract

Number words are generally used to refer to sets of an exact cardinal value, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics (two means EXACTLY TWO), many linguistic accounts propose that numbers have lower-bounded semantics (AT LEAST TWO), and that speakers restrict their reference through a pragmatic inference (scalar implicature). We address this debate through studies of children. First, we examine toddlers' offline comprehension of number words and find they interpret numbers exactly even in contexts where implicatures are cancelled. Next we consider arguments that patterns of numerical acquisition support lower-bounded semantics and find that these acquisition patterns are better explained by an exact account. Finally, we revisit data from online comprehension and demonstrate that five-year-old children access numerical upper bounds as rapidly as lower bounds, contrary to the hypothesis of lower-bounded semantics. We conclude that number words have exact meanings.