Interpretations of Numerals and Structured Contexts

Abstract

It has been assumed that the interpretation of a numeral n is determined as part of a scalar implicature, but there is a lot of evidence against it. First, numerals do not form a semantic scale but a pragmatic scale. Second, sometimes a numeral n is interpreted as ‘at least n’ or ‘at most n’, but the meaning of at least/most is not part of the meaning of a numeral. The meaning of a numeral is determined contextually. The basic principle is that we should make a statement as informative as possible. In making a statement informative, we consider two scales: one is the basic scalarity of largeness between numerals and the scalarity of likelihood. The two scales apply to two different regions with respect to a quantifier. The informativeness from the basic scalarity requires the numeral mentioned to be the maximal number of elements involved when each member in the quantifier domain is considered. And the alternative sentences with the numeral replaced with an alternative numeral are ordered by the informativeness from the unlikelihood scalarity, making the number mentioned a limit value among the maximal numbers of the elements involved in the meaning of the quantifier. The limit number n is taken to be ‘at least n’ or ‘at most n’. If no overt quantifier is involved, a universal quantifier over epistemic alternatives is provided by the support conditions of the sentence.