A New Semantics for Number

Abstract

Research on the semantics of number has been strongly influenced by the distri bution of overt number morphology in English. As is well know, number can be expressed on nouns and on verbs in English. In example (1), overt plural morphol ogy is present in both places.(1)The books- [PL] were-[pL] lying on the table.All research on plurality has assumed the the [pI]-feature on the noun is interpreted in some way. Bennett (1974) was the first to propose a semantics of number along these lines, and this assumption has been adopted by all subsequent research. Fur thermore most research has followed Bennett to assume that the [PI]-feature on the verb remains uninterpreted in English, and is a reflex of syntactic agreement with the subject. 1 A contemporary version of Bennett's proposal (e.g. Chierchia 1998b, Schwarzschild 1996) assigns to the singular noun book a set of individuals as its extension, while the extension of the plural noun books includes groups of these in dividuals (and, for Schwarzschild, atomic individuals, as well). These denotations are illustrated in (2): 2 (2) a.[book] = {a, b, c} b.[books] = {aEBbEBc, aEBb, aEBc, ... } However, in many languages, overt plural morphology is also found on the determiner as shown by the German example (3a) . Even in English plurality is also expressed on demonstrative determiners as in (3b). In this paper, I will argue that even German does not express morpholog ically the [PI]-feature that is interpreted. I propose that there is another syntactic head above the determiner, which I call the ¢-head, and that the only semantically contentful number features are contained in this head. Furthermore, I will argue that [PI] on nouns is not interpreted, but is a reflex of syntactic agreement with a ¢-head, just like [PI] on adjectives, verbs, and determiners. There have to be two agreement processes, one to establish agreement in the DP between N, A, D, and the ¢-head. The other one to establish agreement between the finite verb and a ¢P in the subject position.I first present my proposal in all detail, and then present two arguments

In support of representational economy: Agreement in heritage Spanish

“…Finding sensitivity to both singular and plural agreement errors, we concluded that number in the native baseline is a multi-valued feature (both singular and plural are specified feature values; cf. Sauerland 2003;Scontras 2013a;. Finding sensitivity only to agreement errors involving feminine adjectives, we concluded that gender is single-valued (feminine is the specified feature value, while masculine serves as the absence of gender specification, consistent with the classic analysis proposed by Harris 1991; see also Kramer 2015).…”

Dependent plural pronouns with Skolemized choice functions

“…Although we will not be committed to a particular view of the semantics of phi-features in this paper, it is worthwhile demonstrating this more concretely, adopting one particular analysis. Let us tentatively assume that pronominal phi-features are presupposition triggers (Heim 2008;Heim and Kratzer 1998;Sauerland 2003Sauerland , 2008aSchlenker 2003; but see Stokke 2010; Sudo 2013 for criticisms). For expository purposes, we assume that pronouns have internal structures as illustrated by (45) for 'her' with index i:…”

“…Disregarding the issue of semantically vacuous phi-features (see Heim 2008;Percus 2006;Sauerland 2003Sauerland , 2008aSpector 2007), the features in (45) can be given the following meanings.…”

“…4, when augmented with a semantics of pronominal phi-features, e.g. the presuppositional analysis (Heim 2008;Heim and Kratzer 1998;Sauerland 2003Sauerland , 2008aSchlenker 2003), these spell-out rules become redundant and can be totally dispensed with.…”

“…Thus the sentence does not necessarily imply that John and Bill like the same author. Some researchers take dependent plural pronouns as evidence for semantically inert number features, and put forward an analysis along the lines of Kratzer's (1998a) 'Minimal Pronoun Account' (Heim 2008;Kratzer 2009;Sauerland 2003). The Minimal Pronoun Account would explain (1a) as follows: the plural feature of they is just a morphosyntactic reflex of the binding relation with the matrix subject the first-years, and is copied from this binder at the PF component.…”