... he aruges that the numerals should be analyzed as predicates of the type <e, t>. Given an integer K and the numeral k to which K corresponds, the semantic of k is to check if the referred entity is of the size K. In other words, the logical formula of k is simply given by [[k]] = Lambda x: |x| = K. This formula never induces the implication as in (**). In order that a chain of decreasing numerals induce a suggestion of decrease, the numerals involved should be of the interpretation of 'at least k', which would be possible only if they are affected by the type change to quantifiers. Provided that a numeral k is combined with some noun N to be coerced to a quantifier, the semantics will be as Lambda P: For some x [P(x) and N(x) and |x| = K] of the type <<e, t>, t>, where the existential quantifier induces the interpretation of 'at least k'.

type과 lambda와 quantifier와.. 가슴이 설레지 않니?