Grimm (2018): Grammatical Number and the Scale of Individuation #

Grimm orders the individuation types of nominal descriptions on a scale, substances below granular aggregates below collective aggregates below individuals (IndividuationType), and argues that a language's grammatical number categories partition the scale by an order-preserving map (section 3.4). No category then spans two disconnected segments of the scale (ordConnected_fiber_of_monotone), and this is all that order preservation asks: a classification whose classes are contiguous is monotone for an order on its classes (exists_linearOrder_monotone_iff). The impossible system of Table 21 fails under every ordering of its classes (bad_not_monotone). The systems of Table 20 and section 4.1, Dagaare with a class per type, the tripartite Welsh, Turkana, Maltese, and Miraña, binary English, and Yudja with number on humans alone, are monotone classifications (welsh_monotone and its siblings). Markedness follows the scale: the zero-coded value of a class is single reference for individuals and multiple reference for aggregates, with no contrast at the bottom (welsh_default_monotone and its siblings), and Dagaare's inverse marking is one coded value read in the two directions. Animacy refines the picture (section 4.2): on the product of the scale with the animacy hierarchy, the collective/singulative class ascends from below, the inverse of Smith-Stark's plural marking, and the regions of Maltese, Welsh, and Turkana nest (collective_regions_nest).

Implementation notes #

The individuation types are primitive, as in the paper: equivalence classes of nominal descriptions by individuation properties, which the paper ranks by perceptibility of minimal units, spatial separation, consistency of shape, and interaction, and which section 4.3 extends to function for artifacts. Grimm's dissertation derives the middle of the scale from the strength of the connection relation under which aggregate nouns' referents cluster (Mereology.IsCluster). Each language's countability classes are an enumeration ordered by scale position, and the classification of the four individuation types is the language's row of Table 20, 23, or 24. Turkana and Maltese share Welsh's partition and differ in agreement and animacy reach, Yudja shares English's and differs in restricting the contrast to humans; the classification does not record these. The animacy tiers of Fig. 3, inanimates below Haspelmath's lower and higher animates below humans, are ranks of the library's AnimacyHierarchy; the full animacy–individuation lattice, an Aissen product, and the connected region constraint (28) over it are not formalized.

Grimm (2018): Grammatical Number and the Scale of Individuation #

Implementation notes #

References #

The scale of individuation, section 3.2 #

The order-preservation thesis, section 3.4 #

The number systems, Tables 20, 23, and 24 #

The impossible system, Table 21 #

Coding and markedness, sections 3.4 and 4.4 #

Countability and animacy, section 4.2 #