Numerals and Pragmatic Interpretations

In this paper I address the problems of defining the semantics of numerals and accounting for how pragmatic inferences are made. I basically assume that a numeral n simply means '${\lambda}P{\lambda}x[#(x)n\;&\;P(x)]$', as commonly assumed. Even when a numeral n has 'at least' interpretation, a sentence with the number does not entail a sentence with n replaced with n-1. But when a sentence with n-1 holds, it is possible that a sentence with n or a larger number holds too. This is not based on a semantic relation, but on pragmatic informativeness. In addition to pragmatic strength, the actual reading of a numeral is affected by some background knowledge of generalizations about the world, but the ordering of pragmatic strength among numbers always plays a role in determining unilateral interpretations. In such a case, we can assume that a set of numbers relevant in the context forms a scale. Forming a scale does not necessarily lead to a unilateral interpretation. The bilateral interpretation of a number is possible in the context where it is known whether or not alternative sentences with contextually salient alternative numbers are true.