On Pylkkänen's Semantics for Low Applicatives

Standard neo-Davidsonian approaches to the semantics of sentences like (1a) assign them representations like (1b), where the verb is analyzed as a unary predicate of events with its arguments and adjuncts related to it by means of binary thematic relations (Parsons 1991).

1. 1.

   1. a. John wrote Mary that letter for Bill.

   2. b. ∃e[writing(e) & Agent(e,John) & Theme(e,that_letter) & Goal(e,Mary) & Beneficiary(e,Bill) & Past(e)]

Such radical "separation," resulting in the arguments of a predicate being related to each other only through the event in which they commonly participate, has been argued to be necessary for a correct semantics of plurality and conjunction (Schein 1993, to appear, Pietroski 2005) and to yield an attractive account of focus (Herburger 2000).

Pylkkänen (2002, 2008) offers an alternative analysis in developing an account of what she terms "high" and "low" applicative constructions. In brief, high applicatives, counterpart to the for-PP in (1a), are analyzed in the neo-Davidsonian way: as expressing relations between events and individuals (λxλe[Beneficiary(e,x)]). However, low applicatives, counterpart to the indirect object (Mary) in (1a), receive a radically different treatment. In Pylkkänen's words, "Low applied arguments bear no semantic relation to the verb whatsoever: they bear only a transfer-of-possession relation to the direct object" (2008:14). (2b) displays the semantic analysis that Pylkkänen recommends for (2a) (ignoring irrelevant details).

1. 2.

   1. a. John wrote Mary that letter.

   2. b. ∃e[writing(e) & Agent(e,John) & Theme(e,that_letter) & to-the-possession-of(that_letter,Mary)]

As advertised, the referent of Mary is not related to the event quantification by means of any binary thematic relation such as Goal; rather, it is related directly to the referent of the theme argument by means of to-the-possession-of(x,y). This semantics figures importantly in Pylkkänen's account of the differences between high and low applicatives. High applicatives can combine at a relatively high point in the derivation since they only require access to the event variable of the verb. Low applicatives, by contrast, must combine earlier in the derivation, in the local vicinity of the direct object to which they are related.

Uncoupling the indirect object argument from the event structure of the verb has an important logical consequence that Pylkkänen apparently does not foresee. Consider the conjunction in (3a), where that letter refers to the same entity in both conjuncts. (3a) does not entail (3b). John's writing a letter, and that letter's coming into Mary's possession, does not entail that John wrote the letter to Mary. A standard neo-Davidsonian analysis blocks this unwanted inference, doing so in an intuitively natural way. The conjunction in (4a) does not entail (4b) since Mary is related (as Goal) to the giving event e′, and not to the writing event e, and there is no way of deducing the latter from the former.

1. 3.

   1. a. John wrote that letter and Bill gave Mary that letter.

   2. b. John wrote Mary that letter.

2. 4.

   1. a. ∃e[writing(e) & Agent(e,John) & Theme(e,that_letter)] & ∃e′[giving(e′) & Agent(e′,Bill) & Theme(e′,that_letter) & Goal(e′,Mary)]

   2. b. ∃e[writing(e) & Agent(e,John) & Theme(e,that_letter) & Goal(e,Mary)]

Consider now (5a–b), the analysis of (3a–b) under Pylkkänen's (2002, 2008) semantics for low applicatives.

1. 5.

   1. a. ∃e[writing(e) & Agent(e,John) & Theme(e,that_letter)] & ∃e′[giving(e′) & Agent(e′,Bill) & Theme(e′,that_letter) & to-the-possession-of(that_letter,Mary)]

   2. b. ∃e[writing(e) & Agent(e,John) & Theme(e,that_letter) & to-the-possession-of(that_letter,Mary)]

In fact, (5a) does entail (5b) under the elementary logical reasoning in (6).¹

1. 6.

   1. a. ∃e[writing(e) & Agent(e,John) & Theme(e,that_letter)] & ∃e′[giving(e′) & Agent(e′,Bill) & Theme(e′,that_letter) & to-the-possession-of(that_letter,Mary)]

   2. b. ∃e[writing(e) & Agent(e,John) & Theme(e,that_letter)] & ∃e′[giving(e′) & Agent(e′,Bill) & Theme(e′,that_letter)] & to-the-possession-of(that_letter,Mary)

   3. c. ∃e[writing(e) & Agent(e,John) & Theme(e,that_letter)] & to-the-possession-of...