Paucity, abundance, and the theory of number

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.