Question

Could the two Schonfinkeled functions be suitable denotations for the English verbs "adore" and "assign (to)" respectively? If yes, why? If not, why not?

Answer

The Schonfinkeled characteristic functions are a suitable denotations for the verbs "adore" and "assign (to)" because they were Schonfinkeled from right to left, mirroring the corresponding relations that are customarily specified so that "the grammatical object argument of a predicate corresponds to the right component of each pair in the relation, and the subject to the left one," as Heim and Kratzer put it.1 In turn, the argument relations revealed by the Schonfinkeled functions correspond to the Fregean denotations of 2-place predicates, as Heim and Kratzer point out, "since the object is closest to the predicate in hierarchical terms, it must provide the argument for the function denoted by the predicate."2 The right-to-left Schonfinkelization reflects the left-branching syntactic structure of English sentences.

Thus, when n-place predicates are interpreted as relations, they are related to Fregean denotations, which are for sentences the actual truth values, for proper names the individuals, and for VP nodes the functions. Even though Schonfinkelization reduces the 2-place (or 3-place) functions to 1-place functions, the Schonfinkeled functions for 2-place predicates such as "adores" provide a suitable denotation for their functions by mapping a function from individuals to functions from individuals to truth values.

However, in the case of "assigns to," the right to left Schonfinkeled functions show the denotations only for "assigns y to z," which is the typical English argument structure, but not for "assigns to z y," which is also a possible argument structure in English.

Also, if the functions for either "adores" or "assigns to" had been Schonfinkeled from left to right instead of right to left, they would not have been suitable denotations for the two verbs.