Križ (2016): Homogeneity, Non-Maximality, and All — Plural Instantiation #

@cite{kriz-2015} @cite{kriz-2016} @cite{fine-1975}

Homogeneity, Non-Maximality, and All. Journal of Semantics 33(3): 493-539.

This file is the plural instantiation of the general homogeneity substrate in Theories.Semantics.Homogeneity.Basic. It connects @cite{kriz-2016}'s plural-definite analysis (atoms as specification points; all as gap remover) to the substrate operators (removeGap, addressesIssue, usable, communicatedContent).

@cite{lasersohn-1999} (the "townspeople asleep" original observation), @cite{brisson-1998} (non-maximality terminology + but/although exception diagnostics), @cite{schwarz-2013} (processing evidence that maximal is the default reading), @cite{malamud-2012} (decision-theoretic precursor with issue partitions, criticised in Appendix A.3 of the paper), @cite{spector-2013} (embedded-plural projection), @cite{kriz-chemla-2015} (companion experimental data), @cite{magri-2014} (alternative gap-derivation via double EXH), @cite{cobreros-etal-2012} (Tolerant/Classical/Strict trivalence; Appendix A.2), @cite{gajewski-2005} (homogeneity-as-presupposition view, rejected in §4.4), @cite{roberts-1996} (QUD-stack tradition the §4.5 caveat distinguishes from).

Core Contributions #

Non-maximal readings of plural definites ("The professors smiled" true even if Smith didn't) arise from the interaction of two independent components:

Homogeneity (semantic): plural predication yields a three-valued truth value — true (all satisfy), false (none satisfy), or gap (some but not all).
Weakened Quality (pragmatic): the maxim of quality is weakened to "say only what is true enough for current purposes," where "current purposes" are formalized as an issue (partition of possible worlds).

The semantic effect of all is to remove the extension gap, making positive and negative extensions complementary. This prevents non-maximal readings because the pragmatic mechanism (Sufficient Truth + Addressing) has no gap to exploit.

§4.4 caveat — homogeneity is NOT a presupposition #

@cite{kriz-2016} §4.4 argues against the @cite{gajewski-2005} (and Schwarzschild 1994, Löbner 2000) view that the homogeneity gap is a presupposition. Križ's arguments include local accommodation behaviour and projection from conditional antecedents differing from standard presupposition behaviour. This file adopts the trivalent-but-not-presuppositional reading: gap-worlds are "between" true and false, not undefined-in-the-presupposition sense.

§4.5 caveat — current issue ≠ immediate-last QUD #

The variable name QUD W here is a substrate convenience and is NOT the @cite{roberts-1996} QUD-stack notion. @cite{kriz-2016} §4.5 is explicit (eq. 39, 40 examples) that identifying the current issue with the immediate-last question on the stack makes wrong predictions. Križ instead treats the current issue as referring to overarching goals of participants, underdetermined by linguistic material and not directly manipulable. The coarseQ/fineQ partitions in our finite model are pedagogical constructions; they are NOT meant as a commitment to the manipulable-QUD theory the paper rejects.

§4.6 puzzle — numerals block non-maximality #

@cite{kriz-2016} §4.6 flags as an unsolved puzzle that "the ten professors smiled" cannot get non-maximal readings, even though "the professors smiled" can. The paper offers only speculation. Križ also notes (43a-b) that French patterns differently. We do not address this puzzle here.

Contents #

barePluralTV, allPluralTV: plural-specific instantiations
Theorems linking gap-removal to all semantics
A 5-world finite model demonstrating end-to-end predictions (including §4.2 angry-Smith vs. neutral-Smith distinction)
§5/§6 bridges to data records in Plurals.NonMaximality and Plurals.Homogeneity
§7 connection back to the supervaluation framework

Finite Model #

A concrete 5-world model demonstrates end-to-end predictions: "the professors smiled" is usable at a gap-world (smithNeutral) under a coarse issue but not under a fine one, AND not at a gap-world (smithAngry) where Smith's anger is issue-relevant — capturing @cite{kriz-2016} §4.2's distinctive prediction. Adding "all" blocks non-maximal use entirely.

World	Smith	Jones	Lee	Bare plural	All
allSmiled	✓	✓	✓	TRUE	true
smithNeutral	✗	✓	✓	GAP	false
onlyLeeSmiled	✗	✗	✓	GAP	false
noneSmiled	✗	✗	✗	FALSE	false