Cross-Linguistic Typology of Nominal Plurality (WALS Chapters 33--36) #

@cite{corbett-2000} @cite{dryer-haspelmath-2013} @cite{haspelmath-2013}

Typological data on how languages encode plurality, drawn from four WALS chapters by Dryer, Haspelmath, Daniel, and Moravcsik. The data covers four dimensions of plural morphology and syntax:

Coding of Nominal Plurality (Ch 33, Dryer): How languages mark plural on nouns --- suffix, prefix, stem change, tone, reduplication, plural word, clitic, mixed morphological, or no marking at all. Suffixing dominates (495/957 languages), followed by plural words (150) and plural prefixes (118).
Occurrence of Nominal Plurality (Ch 34, Haspelmath): When plural marking is used. The crucial dimension is the interaction of animacy and obligatoriness: plural marking may be obligatory on all nouns, restricted to human nouns, or absent entirely. An implicational hierarchy governs this: if a language marks plural on inanimate nouns, it also marks plural on human nouns (never the reverse).
Plurality in Independent Personal Pronouns (Ch 35, Daniel): How pronouns encode number. The dominant pattern (114/260) is person-number stems (e.g. English I/we), where number is fused into the lexical root. Affix-based number on pronouns is rarer and may use either pronominal or nominal affixes.
The Associative Plural (Ch 36, Daniel & Moravcsik): "Tanaka and associates" constructions. 200/237 sampled languages have some form of associative plural. In nearly half (104), the associative marker is the same morpheme used for additive (ordinary) plurals.

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inductive Phenomena.Plurals.Typology.PluralCoding :

Type

How a language morphologically codes plurality on nouns (WALS Ch 33).

The nine categories distinguish morphological strategies (prefix, suffix, stem change, tone, reduplication, mixed) from phrasal strategies (plural word, clitic) and from the absence of any plural marking.

prefix : PluralCoding
suffix : PluralCoding
stemChange : PluralCoding
tone : PluralCoding
reduplication : PluralCoding
mixedMorphological : PluralCoding
pluralWord : PluralCoding
pluralClitic : PluralCoding
noPlural : PluralCoding

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instance Phenomena.Plurals.Typology.instDecidableEqPluralCoding :

DecidableEq PluralCoding

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Phenomena.Plurals.Typology.instDecidableEqPluralCoding x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

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instance Phenomena.Plurals.Typology.instBEqPluralCoding :

BEq PluralCoding

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Phenomena.Plurals.Typology.instBEqPluralCoding = { beq := Phenomena.Plurals.Typology.instBEqPluralCoding.beq }

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def Phenomena.Plurals.Typology.instBEqPluralCoding.beq :

PluralCoding → PluralCoding → Bool

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Phenomena.Plurals.Typology.instBEqPluralCoding.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.Plurals.Typology.instReprPluralCoding :

Repr PluralCoding

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Phenomena.Plurals.Typology.instReprPluralCoding = { reprPrec := Phenomena.Plurals.Typology.instReprPluralCoding.repr }

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def Phenomena.Plurals.Typology.instReprPluralCoding.repr :

PluralCoding → Nat → Std.Format

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structure Phenomena.Plurals.Typology.PluralCodingDistribution :

Type

WALS Chapter 33 distribution: language counts per plural coding strategy. Total: 957 languages.

prefixCount : Nat
suffixCount : Nat
stemChange : Nat
tone : Nat
reduplication : Nat
mixedMorphological : Nat
pluralWord : Nat
pluralClitic : Nat
noPlural : Nat

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instance Phenomena.Plurals.Typology.instReprPluralCodingDistribution :

Repr PluralCodingDistribution

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Phenomena.Plurals.Typology.instReprPluralCodingDistribution = { reprPrec := Phenomena.Plurals.Typology.instReprPluralCodingDistribution.repr }

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def Phenomena.Plurals.Typology.instReprPluralCodingDistribution.repr :

PluralCodingDistribution → Nat → Std.Format

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def Phenomena.Plurals.Typology.PluralCodingDistribution.total (d : PluralCodingDistribution) :

Nat

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d.total = d.prefixCount + d.suffixCount + d.stemChange + d.tone + d.reduplication + d.mixedMorphological + d.pluralWord + d.pluralClitic + d.noPlural

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def Phenomena.Plurals.Typology.ch33Distribution :

PluralCodingDistribution

Actual WALS Ch 33 counts.

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inductive Phenomena.Plurals.Typology.PluralOccurrence :

Type

When plural marking occurs on full nouns (WALS Ch 34).

The six values cross two dimensions: animacy scope (none / human-only / all) and obligatoriness (optional / obligatory). An implicational hierarchy holds: if inanimate nouns are marked, human nouns are too (never the reverse).

noNominalPlural : PluralOccurrence
humanOnlyOptional : PluralOccurrence
humanOnlyObligatory : PluralOccurrence
allNounsAlwaysOptional : PluralOccurrence
allNounsOptionalInanimates : PluralOccurrence
allNounsAlwaysObligatory : PluralOccurrence

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instance Phenomena.Plurals.Typology.instDecidableEqPluralOccurrence :

DecidableEq PluralOccurrence

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Phenomena.Plurals.Typology.instDecidableEqPluralOccurrence x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

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def Phenomena.Plurals.Typology.instBEqPluralOccurrence.beq :

PluralOccurrence → PluralOccurrence → Bool

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Phenomena.Plurals.Typology.instBEqPluralOccurrence.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.Plurals.Typology.instBEqPluralOccurrence :

BEq PluralOccurrence

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Phenomena.Plurals.Typology.instBEqPluralOccurrence = { beq := Phenomena.Plurals.Typology.instBEqPluralOccurrence.beq }

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instance Phenomena.Plurals.Typology.instReprPluralOccurrence :

Repr PluralOccurrence

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Phenomena.Plurals.Typology.instReprPluralOccurrence = { reprPrec := Phenomena.Plurals.Typology.instReprPluralOccurrence.repr }

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def Phenomena.Plurals.Typology.instReprPluralOccurrence.repr :

PluralOccurrence → Nat → Std.Format

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structure Phenomena.Plurals.Typology.PluralOccurrenceDistribution :

Type

WALS Chapter 34 distribution: language counts per occurrence type. Total: 290 languages.

noNominalPlural : Nat
humanOnlyOptional : Nat
humanOnlyObligatory : Nat
allNounsAlwaysOptional : Nat
allNounsOptionalInanimates : Nat
allNounsAlwaysObligatory : Nat

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instance Phenomena.Plurals.Typology.instReprPluralOccurrenceDistribution :

Repr PluralOccurrenceDistribution

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Phenomena.Plurals.Typology.instReprPluralOccurrenceDistribution = { reprPrec := Phenomena.Plurals.Typology.instReprPluralOccurrenceDistribution.repr }

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def Phenomena.Plurals.Typology.instReprPluralOccurrenceDistribution.repr :

PluralOccurrenceDistribution → Nat → Std.Format

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def Phenomena.Plurals.Typology.PluralOccurrenceDistribution.total (d : PluralOccurrenceDistribution) :

Nat

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d.total = d.noNominalPlural + d.humanOnlyOptional + d.humanOnlyObligatory + d.allNounsAlwaysOptional + d.allNounsOptionalInanimates + d.allNounsAlwaysObligatory

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def Phenomena.Plurals.Typology.ch34Distribution :

PluralOccurrenceDistribution

Actual WALS Ch 34 counts.

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inductive Phenomena.Plurals.Typology.PronounPlurality :

Type

How independent personal pronouns encode number (WALS Ch 35).

The key typological variable is whether number is expressed in the stem, an affix, or both, and whether the affix is shared with nouns.

noIndependentPronouns : PronounPlurality
numberIndifferent : PronounPlurality
personNumberAffixes : PronounPlurality
personNumberStem : PronounPlurality
pnStemPronominalAffix : PronounPlurality
pnStemNominalAffix : PronounPlurality
personStemPronominalAffix : PronounPlurality
personStemNominalAffix : PronounPlurality

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instance Phenomena.Plurals.Typology.instDecidableEqPronounPlurality :

DecidableEq PronounPlurality

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Phenomena.Plurals.Typology.instDecidableEqPronounPlurality x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

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instance Phenomena.Plurals.Typology.instBEqPronounPlurality :

BEq PronounPlurality

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Phenomena.Plurals.Typology.instBEqPronounPlurality = { beq := Phenomena.Plurals.Typology.instBEqPronounPlurality.beq }

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def Phenomena.Plurals.Typology.instBEqPronounPlurality.beq :

PronounPlurality → PronounPlurality → Bool

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Phenomena.Plurals.Typology.instBEqPronounPlurality.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.Plurals.Typology.instReprPronounPlurality :

Repr PronounPlurality

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Phenomena.Plurals.Typology.instReprPronounPlurality = { reprPrec := Phenomena.Plurals.Typology.instReprPronounPlurality.repr }

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def Phenomena.Plurals.Typology.instReprPronounPlurality.repr :

PronounPlurality → Nat → Std.Format

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structure Phenomena.Plurals.Typology.PronounPluralityDistribution :

Type

WALS Chapter 35 distribution: language counts per pronoun plurality type. Total: 260 languages.

noIndependentPronouns : Nat
numberIndifferent : Nat
personNumberAffixes : Nat
personNumberStem : Nat
pnStemPronominalAffix : Nat
pnStemNominalAffix : Nat
personStemPronominalAffix : Nat
personStemNominalAffix : Nat

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instance Phenomena.Plurals.Typology.instReprPronounPluralityDistribution :

Repr PronounPluralityDistribution

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Phenomena.Plurals.Typology.instReprPronounPluralityDistribution = { reprPrec := Phenomena.Plurals.Typology.instReprPronounPluralityDistribution.repr }

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def Phenomena.Plurals.Typology.instReprPronounPluralityDistribution.repr :

PronounPluralityDistribution → Nat → Std.Format

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def Phenomena.Plurals.Typology.PronounPluralityDistribution.total (d : PronounPluralityDistribution) :

Nat

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def Phenomena.Plurals.Typology.ch35Distribution :

PronounPluralityDistribution

Actual WALS Ch 35 counts.

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inductive Phenomena.Plurals.Typology.AssociativePlural :

Type

Type of associative plural marking (WALS Ch 36).

Associative plurals are "X and associates" constructions (e.g. Japanese Tanaka-tachi 'Tanaka and his group'). The typological split is between languages where the associative marker overlaps with the additive (ordinary) plural marker vs. languages with a dedicated associative form.

sameAsAdditive : AssociativePlural
uniqueAffixal : AssociativePlural
uniquePeriphrastic : AssociativePlural
absent : AssociativePlural

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instance Phenomena.Plurals.Typology.instDecidableEqAssociativePlural :

DecidableEq AssociativePlural

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Phenomena.Plurals.Typology.instDecidableEqAssociativePlural x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

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instance Phenomena.Plurals.Typology.instBEqAssociativePlural :

BEq AssociativePlural

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Phenomena.Plurals.Typology.instBEqAssociativePlural = { beq := Phenomena.Plurals.Typology.instBEqAssociativePlural.beq }

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def Phenomena.Plurals.Typology.instBEqAssociativePlural.beq :

AssociativePlural → AssociativePlural → Bool

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Phenomena.Plurals.Typology.instBEqAssociativePlural.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.Plurals.Typology.instReprAssociativePlural :

Repr AssociativePlural

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Phenomena.Plurals.Typology.instReprAssociativePlural = { reprPrec := Phenomena.Plurals.Typology.instReprAssociativePlural.repr }

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def Phenomena.Plurals.Typology.instReprAssociativePlural.repr :

AssociativePlural → Nat → Std.Format

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structure Phenomena.Plurals.Typology.AssociativePluralDistribution :

Type

WALS Chapter 36 distribution: language counts per associative plural type. Total: 237 languages.

sameAsAdditive : Nat
uniqueAffixal : Nat
uniquePeriphrastic : Nat
absent : Nat

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def Phenomena.Plurals.Typology.instReprAssociativePluralDistribution.repr :

AssociativePluralDistribution → Nat → Std.Format

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instance Phenomena.Plurals.Typology.instReprAssociativePluralDistribution :

Repr AssociativePluralDistribution

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Phenomena.Plurals.Typology.instReprAssociativePluralDistribution = { reprPrec := Phenomena.Plurals.Typology.instReprAssociativePluralDistribution.repr }

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def Phenomena.Plurals.Typology.AssociativePluralDistribution.total (d : AssociativePluralDistribution) :

Nat

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d.total = d.sameAsAdditive + d.uniqueAffixal + d.uniquePeriphrastic + d.absent

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def Phenomena.Plurals.Typology.ch36Distribution :

AssociativePluralDistribution

Actual WALS Ch 36 counts.

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Phenomena.Plurals.Typology.ch36Distribution = { sameAsAdditive := 104, uniqueAffixal := 48, uniquePeriphrastic := 48, absent := 37 }

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structure Phenomena.Plurals.Typology.PluralityProfile :

Type

A language's plurality profile across all four WALS dimensions.

language : String
iso : String
ISO 639-3 code
coding : PluralCoding
Ch 33: How plurality is coded on nouns
occurrence : PluralOccurrence
Ch 34: When plural marking occurs
pronounPlurality : PronounPlurality
Ch 35: Pronoun plurality type
associativePlural : AssociativePlural
Ch 36: Associative plural

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instance Phenomena.Plurals.Typology.instReprPluralityProfile :

Repr PluralityProfile

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Phenomena.Plurals.Typology.instReprPluralityProfile = { reprPrec := Phenomena.Plurals.Typology.instReprPluralityProfile.repr }

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def Phenomena.Plurals.Typology.instReprPluralityProfile.repr :

PluralityProfile → Nat → Std.Format

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def Phenomena.Plurals.Typology.instBEqPluralityProfile.beq :

PluralityProfile → PluralityProfile → Bool

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Phenomena.Plurals.Typology.instBEqPluralityProfile.beq x✝¹ x✝ = false

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instance Phenomena.Plurals.Typology.instBEqPluralityProfile :

BEq PluralityProfile

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Phenomena.Plurals.Typology.instBEqPluralityProfile = { beq := Phenomena.Plurals.Typology.instBEqPluralityProfile.beq }

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instance Phenomena.Plurals.Typology.instDecidableEqPluralityProfile :

DecidableEq PluralityProfile

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Phenomena.Plurals.Typology.instDecidableEqPluralityProfile = Phenomena.Plurals.Typology.instDecidableEqPluralityProfile.decEq

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def Phenomena.Plurals.Typology.instDecidableEqPluralityProfile.decEq (x✝ x✝¹ : PluralityProfile) :

Decidable (x✝ = x✝¹)

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def Phenomena.Plurals.Typology.english :

PluralityProfile

English: suffix plural (-s), obligatory on all nouns, person-number stems in pronouns (I/we, you/you), no productive associative plural.

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def Phenomena.Plurals.Typology.mandarin :

PluralityProfile

Mandarin Chinese: no morphological plural on nouns (bare nouns are number- neutral), person stem + nominal plural affix -men on pronouns (wo/wo-men 'I/we'), associative plural uses same -men marker.

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def Phenomena.Plurals.Typology.japanese :

PluralityProfile

Japanese: no morphological plural on common nouns, plural on all nouns is always optional (suffix -tachi limited, and optional), person-number stems in pronouns, unique periphrastic associative plural (-tachi on proper names: Tanaka-tachi).

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def Phenomena.Plurals.Typology.turkish :

PluralityProfile

Turkish: suffix plural (-ler, -lar with vowel harmony), obligatory on all nouns (except after numerals), person stem + nominal plural affix on pronouns (ben vs biz, sen vs siz, but -ler suffix also used), associative plural uses same -ler marker (Ali-ler 'Ali and associates').

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def Phenomena.Plurals.Typology.finnish :

PluralityProfile

Finnish: suffix plural (-t nominative, -i- oblique), obligatory on all nouns, person-number stem + pronominal affix in pronouns (mina/me), no productive associative plural.

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def Phenomena.Plurals.Typology.arabic :

PluralityProfile

Arabic (Standard): mixed morphological plural --- both suffixation (-aat, -uun) and "broken" stem-internal changes are productive, neither is clearly primary. Obligatory on all nouns. Person-number stem in pronouns (ana/nahnu). Associative plural same as additive.

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def Phenomena.Plurals.Typology.hungarian :

PluralityProfile

Hungarian: suffix plural (-k), obligatory on all nouns, person-number stem + nominal plural affix on pronouns (en vs mi, with -k also on nouns), unique affixal associative plural (-ek: Pal-ek 'Paul and associates', distinct from additive -k or -ak).

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def Phenomena.Plurals.Typology.swahili :

PluralityProfile

Swahili: plural marked by noun class prefixes (wa-, vi-, mi-, ma-), obligatory on all nouns, person-number stems in pronouns (mimi/sisi), no productive associative plural.

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def Phenomena.Plurals.Typology.indonesian :

PluralityProfile

Indonesian: complete reduplication (rumah-rumah 'houses'), plural marking optional on all nouns. Person-number stems in pronouns (saya/kami). No productive associative plural.

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def Phenomena.Plurals.Typology.hindi :

PluralityProfile

Hindi: suffix plural (-e, -en, -iya), obligatory on all nouns, person-number stems in pronouns (mai vs ham), associative plural uses same plural marker (Sharma-log 'Sharma and family').

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def Phenomena.Plurals.Typology.korean :

PluralityProfile

Korean: suffix plural (-tul), optional on all nouns (number-neutral bare forms are common), person-number stems in pronouns (na/uri), associative plural uses same -tul marker.

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def Phenomena.Plurals.Typology.tagalog :

PluralityProfile

Tagalog: plural word (mga, prenominal), optional on all nouns, person-number stems in pronouns (ako/kami/tayo), unique periphrastic associative plural (sina: sina Pedro 'Pedro and associates').

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def Phenomena.Plurals.Typology.russian :

PluralityProfile

Russian: suffix plural (-y, -i, -a), obligatory on all nouns, person-number stem + nominal plural affix in pronouns (ja vs m-y), no productive associative plural.

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def Phenomena.Plurals.Typology.zulu :

PluralityProfile

Zulu (Bantu): prefix plural (class prefixes: umu-ntu/aba-ntu), obligatory on all nouns, person-number stems in pronouns, associative plural uses same prefix system (o-Faku 'Faku and company').

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def Phenomena.Plurals.Typology.hawaiian :

PluralityProfile

Hawaiian: plural word (mau, prenominal), optional on all nouns, person-number stems in pronouns, associative plural absent.

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def Phenomena.Plurals.Typology.lezgian :

PluralityProfile

Lezgian (Daghestanian): suffix plural (-ar, -er), obligatory on all nouns (but absent with numerals), person-number stems in pronouns, associative plural uses same suffix.

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def Phenomena.Plurals.Typology.allLanguages :

List PluralityProfile

All language profiles in our sample.

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Suffixing is the dominant plural marking strategy (WALS Ch 33). Plural suffixes (495) outnumber every other single strategy.

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theorem Phenomena.Plurals.Typology.suffixing_is_majority :

ch33Distribution.suffixCount * 2 > ch33Distribution.total

Over half of all sampled languages use plural suffixes.

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Obligatory marking on all nouns is the most common occurrence pattern (WALS Ch 34): 133 out of 290 languages.

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theorem Phenomena.Plurals.Typology.animacy_hierarchy_human_over_inanimate :

ch34Distribution.humanOnlyOptional + ch34Distribution.humanOnlyObligatory > 0

The animacy hierarchy for nominal plurality (Haspelmath, Ch 34): human nouns are more likely to have plural marking than inanimates. In the WALS sample, no language has plural only on inanimates --- the three logically possible "inanimate-only" types are unattested. This is captured here as: languages with human-only plural (59) outnumber any hypothetical inanimate-only count (0).

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Person-number stems dominate pronoun plurality (WALS Ch 35). 114/260 languages fuse person and number into an unanalysable stem (e.g. English I/we, Dogon mi/emme). This is the single largest category, larger than any other individual type.

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theorem Phenomena.Plurals.Typology.pronoun_number_near_universal :

ch35Distribution.noIndependentPronouns + ch35Distribution.numberIndifferent < 15 ∧ ch35Distribution.total - (ch35Distribution.noIndependentPronouns + ch35Distribution.numberIndifferent) > 240

Nearly all languages distinguish number in pronouns: only 10/260 languages lack number distinctions in independent personal pronouns (2 with no independent pronouns + 8 number-indifferent).

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theorem Phenomena.Plurals.Typology.associative_plural_widespread :

ch36Distribution.sameAsAdditive + ch36Distribution.uniqueAffixal + ch36Distribution.uniquePeriphrastic > ch36Distribution.absent * 5

Associative plurals are widespread: 200/237 sampled languages have some form of associative plural (only 37 lack them entirely).

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theorem Phenomena.Plurals.Typology.associative_often_overlaps_additive :

ch36Distribution.sameAsAdditive * 2 ≥ ch36Distribution.uniqueAffixal + ch36Distribution.uniquePeriphrastic

In nearly half of languages with associative plurals, the associative marker overlaps with the additive plural marker (104/200 languages with associative plurals).

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def Phenomena.Plurals.Typology.PluralityProfile.hasMorphologicalPlural (p : PluralityProfile) :

Bool

Does a language have morphological plural marking on nouns?

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def Phenomena.Plurals.Typology.PluralityProfile.hasObligatoryPlural (p : PluralityProfile) :

Bool

Does a language have obligatory plural marking on all nouns?

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def Phenomena.Plurals.Typology.PluralityProfile.pronounsDistinguishNumber (p : PluralityProfile) :

Bool

Does a language distinguish number in pronouns?

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theorem Phenomena.Plurals.Typology.pronouns_mark_number_even_without_nominal_plural :

have noNominal := List.filter (fun (p : PluralityProfile) => p.coding == PluralCoding.noPlural) allLanguages; (noNominal.all fun (x : PluralityProfile) => x.pronounsDistinguishNumber) = true

In our sample: every language that lacks nominal plural marking still distinguishes number in its pronouns.

This instantiates the hierarchy: pronouns > nouns for number marking.

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theorem Phenomena.Plurals.Typology.obligatory_implies_morphological :

have obligatory := List.filter (fun (x : PluralityProfile) => x.hasObligatoryPlural) allLanguages; (obligatory.all fun (x : PluralityProfile) => x.hasMorphologicalPlural) = true

In our sample: every language with obligatory plural on all nouns also has morphological (affixal) plural marking --- obligatory marking implies the language has developed a morphological strategy, not just a plural word or clitic.

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theorem Phenomena.Plurals.Typology.all_sample_pronouns_distinguish_number :

(allLanguages.all fun (x : PluralityProfile) => x.pronounsDistinguishNumber) = true

In our sample: all 16 languages distinguish number in pronouns. This is consistent with the near-universality seen in the full WALS sample (250/260).

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theorem Phenomena.Plurals.Typology.ch33_total :

Phenomena.Plurals.Typology.ch33✝.length = 1066

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theorem Phenomena.Plurals.Typology.ch34_total :

Phenomena.Plurals.Typology.ch34✝.length = 291

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theorem Phenomena.Plurals.Typology.ch35_total :