Harbour (2016): Impossible Persons — the partition calculus #

[Har16a]

Person categories are derived, not primitive: they are the cells of a partition of the π-lattice induced by two features, ±author and ±participant. Crucially — and this is the thesis of [Har16a] (Ch. 4.2.3, Ch. 9) — the features denote operations on person lattices, not predicates: their values are actions ⊕ (disjoint addition) and ⊖ (joint subtraction), "not truth functors, which would reduce the features to first-order predicates, but actions by and on the person lattices."

The operators themselves (⊕/⊖/lexComp/nePowerset) are reusable substrate in Syntax.Minimalist.Phi.Lattice; this file builds the partition construction on top and checks the empirical results, which come out by construction rather than being stipulated:

the ontology is the speaker i, hearer u, and others o; referents are sets of these (Finset Ω), and the three feature lattices are powerset sublattices ℒau ⊆ ℒpt ⊆ ℒπ (the egocentric chain, [Har16a] p. 74);
a feature acts on a collection: +F(G) = G ⊕ ℒF (pairwise join, (17)) and −F(G) = G ⊖ ℒF (strip ℒF's maximum, (19));
cells are made disjoint by Lexical Complementarity ((31): a cell properly containing a sibling is confined to the difference) and the ∅-winnowing of the variable head φ (§4.4); and
composition is noncommutative (Ch. 4.2.3), so the order of the two features yields the standard tripartition (participant outermost: the two −participant cells coincide) or the quadripartition (author outermost: inclusive/exclusive split).

Main declarations #

refine / cellsOf — Lexical Complementarity over a sibling family + ∅-winnowing, the partition construction over Phi.Lattice's ⊕/⊖/act operators.
Examples — the concrete three-element ontology {i, u, o} = Fin 3, where the partition cells live and the derived theorems are decide-checked.
signOf — Harbour's ±author/±participant signs for a Cysouw Category (theory-laden; cf. the neutral Person.Category.toFeatures).

Main results (all derived, none stipulated) #

inclusive_ne_exclusive, exclusive_excludes_addressee, inclusive_has_both — inclusive (+author +participant) and exclusive (+author −participant) come out disjoint, with the exclusive genuinely −participant. This is exactly the distinction a Boolean-membership encoding (the foil [Har16a] argues against) collapses.
quad_covers / quad_disjoint — the cells cover ℒπ and are pairwise disjoint.
tri_card / quad_card — composition order gives 3 vs 4 cells (noncommutativity).
five_partitions — the two-feature inventory's five parameter settings yield five distinct partitions ([Har16a] Table 4.1).
inclusive_has_no_singleton — the inclusive holds no singleton, so the singular realizes only three persons (no four-way singular).

The number side ([Har14a]; [Har16a] Ch. 6) is the Phi.Recursion/Corbett2000 bridge.

Harbour (2016): Impossible Persons — the partition calculus #

Main declarations #

Main results (all derived, none stipulated) #

The partition construction (over Phi.Lattice's operators) #

The three-element ontology {i, u, o} and the derived results #

Quadripartition — author composes outermost ([Har16a] §4.3.5) #

Standard tripartition — participant composes outermost ([Har16a] §4.3.4) #

The five partitions ([Har16a] Table 4.1) #

No four-way singular person ([Har16a] Ch. 4) #

The phi kernel: a shared form, not a shared denotation ([Har16a] Ch. 9) #

Bridge to Cyclic Agree ([BR09]) #

Bridge to Corbett (2000): attested number systems are generable ([Har14a]) #

Harbour's sign decomposition of the Cysouw categories ([Har16a] Table 4.3) #

Application: the Tamil clusivity contrast through the Pronoun API #

The partition construction (over `Phi.Lattice`'s operators) #

The three-element ontology `{i, u, o}` and the derived results #