The syntax-semantics mapping, as discussed in §2.2, is rigid: once we have determined its action on the atomic types of the syntactic source calculus, everything is fixed. This rigidity is problematic as soon as we have a class of syntactic expressions with a non-uniform contribution to meaning assembly.  Noun phrases are a case in point.  Mapping np to semantic type e is appropriate for proper nouns and definite descriptions whose denotations can be taken to be individuals.  But for quantifying expressions like ‘someone’, ‘no student’, an interpretation of type e is inadequate. The rigid syntax-semantics mapping thus forces one to assign these expressions a higher-order type in the syntax, for example s/(np\s), so as to obtain a semantic type with the right kind of denotation as the translation image, (e → t) → t. If one wants to avoid this semantically motivated complication of the syntax, one could set np′ = (e → t) → t. But now the effect will be that simple transitive verbs (np\s)/np, which one would like to treat as binary relations e → e → t by default, are associated with third-order interpretations instead.