Paucity, abundance, and the theory of number

Abstract

Approximative numbers, like paucal and greater plural, can be characterized in terms of a feature, [±additive], concerned with additive closure. The two parameters affecting this feature (whether it is active and whether + and − values may cooccur) also affect the two features that generate nonapproximative numbers. All three features are shown to be derivative of concepts in the literature on aspect and telicity, to have a straightforwardly compositional semantics, and to eschew ad hoc stipulations on cooccurrence (such as geometries and filters). Thus, what is proposed is a general theory of number, free of extrinsic stipulations. Empirically, the theory yields a characterization of all numbers attested crosslinguistically, a combinatorial explanation of Greenberg-style implications affecting their cooccurrence, a natural account of morphological compositionality, and insight into their diachronic sources and trajectories.

The morphosemantics of Spanish indefinites

“…My proposal follows Bennett (1974), Chierchia (1998), Farkas and de Swart (2010), Harbour (2014), among others, in the idea that the morphological plural feature is semantically interpreted as plural. On the other hand, Krifka (1989), Lasersohn (1998, 2011), Sauerland (2003, Sauerland et al (2005), Spector (2007), and others, propose that that feature is not semantically plural (because it is not interpreted at all, or because morphologically marked plural nouns denote sets that contain both atomic and non-atomic individuals, or because they have a naïve semantics).…”

“…Natural languages make use of number categories that are encoded on pronouns or nouns, including singular, dual, trial, minimal, augmented, unit augmented, paucal, greater paucal, greater plural, global plural, or plural (see Corbett 2000 andHarbour 2014 for definitions and illustrations). Paucal and greater paucal occur in the pronoun system of, for example, Sursurunga, an Oceanic language of New Ireland (Corbett 2000: 26-30;Hutchinsson 1986).…”

“…Indeed, there are Greenberg-style typological generalizations in this area: there is no trial without dual, no greater paucal without (lesser) paucal, no dual without singular, etc. See Harbour (2014) (i) is odd for me and the speakers I've consulted-algunos requires a number greater than two. Given that algunos expresses an imprecise number, however, some data disagreement is predicted.…”

“…If atoms were excluded, the complement of Q _ would not be join-complete. Complement completeness also excludes other unwanted cuts (see Harbour 2014 …”

“…I propose that plural morphology in algunos contributes the semantics of Harbour's (2014) [+additive] feature, and that alg-contributes [−additive] in both algún and algunos. I claim that all that the analysis requires is to import into the DP domain part of the technology already introduced by Harbour for number in the NP domain.…”