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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.
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.
This paper aims to bring theoretical linguistics and cognition-general theories of learning into closer contact. I argue that linguists' notions of rich UGs are well-founded, but that cognition-general learning approaches are viable as well and that the two can and should co-exist and support each other. Specifically, I use the observation that any theory of UG provides a learning criterion -- the total memory space used to store a grammar and its encoding of the input -- that supports learning according to the principle of Minimum Description-Length. This mapping from UGs to learners maintains a minimal ontological commitment: the learner for a particular UG uses only what is already required to account for linguistic competence in adults. I suggest that such learners should be our null hypothesis regarding the child's learning mechanism, and that furthermore, the mapping from theories of UG to learners provides a framework for comparing theories of UG.
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