The Weekly Newsletter of MIT Linguistics

LFRG 11/18 - Raj Singh & Ida Toivonen

Speaker: Raj Singh & Ida Toivonen (Carleton University)
Title: Distance distributivity and the semantics of indefinite noun phrases
Time: Wednesday, 11/18, 5:30-7 pm
Location: 32-D461

The sentences in (1) are equivalent ways of expressing the meaning that for each boy x, there is a ball y such that x kicked y:

(1a) Each boy kicked a ball
(1b) The boys each kicked a ball
(1c) The boys kicked a ball each

This meaning is transparently expressed in (1a) and (1b), but it is harder to see how to derive this compositionally in (1c) because the distributive marker “each” is far away from “the boys”, hence “distance distributivity”. Previous approaches have approached the problem by analyzing the “each” in (1c) — so-called binominal “each” — as a new kind of operator, either derived from another “each” through type-shifting or by lexical stipulation (see e.g., Zimmermann, 2002; Dotlacil, 2014; Champollion, 2014; Cable, 2014).

We present evidence within and across languages suggesting that this approach misses important empirical generalizations. For example, unlike (1a) and (1b), (1c) becomes ungrammatical if “a” is replaced by anything that’s not an existential quantifier (Safir & Stowell, 1988):

(3a) Each boy kicked {the/no/every/one} ball
(3b) The boys each kicked {the/no/every/one} ball
(3c) The boys kicked {*the/*no/*every/one} ball each

In fact, in some languages (e.g., East Cree, Hungarian), distance distributivity is marked simply by reduplicating the numeral: “the boys kicked one-one ball” (e.g., Farkas, 1997; Junker, 2000).

We also present new experimental evidence from English and Swedish suggesting that participants prefer NPs headed by numerals to NPs headed by the indefinite article as hosts for binominal “each”. That is, although both (4a) and (4b) are acceptable, (4a) is preferred to (4b):

(4a) The boys kicked one ball each
(4b) The boys kicked a ball each

The talk will overview these and other generalizations that come from our experimental data collection as well as from typological studies. We will suggest an approach to distance distributivity that introduces no new semantic operators. Instead, our proposal reuses semantic machinery that has been motivated independently, but has to make stipulations about how these meanings are or are not visible at the surface. Specifically, we will argue that (i) indefinite objects in English can receive an incorporation semantics even though there’s no overt evidence for this (building on Carlson, 2006), (ii) that on their non-incorporated interpretation indefinites denote General Skolem Functions (e.g., Kratzer, 1998; Chierchia, 2001; Winter, 2004; Schlenker, 2006; Steedman, 2012), and (iii) that binominal “each”, like other markers of distance distributivity across languages, is the overt realization of a bound variable inside the Skolem term denoted by the indefinite NP it appears adjacent to on the surface.