Documentation

Linglib.Phenomena.SocialMeaning.Studies.Eckert2008

@cite{eckert-2008} — Variation and the Indexical Field #

Overview #

@cite{eckert-2008} argues that the meanings of variables are not precise or fixed but rather constitute a field of potential meanings — an indexical field, a constellation of ideologically related meanings, any one of which can be activated in the situated use of the variable. The field is fluid, and each new activation has the potential to change the field by building on ideological connections.

Key theoretical contributions #

The indexical field: a variable's social meaning is not a fixed correspondence to a social category but a structured space of ideologically linked persona traits. Context selects which region of the field is activated.
Stances vs. qualities: variables directly index interactional stances (momentary positions). Habitual stances accrete into attributed qualities (stable character traits) through stance accretion (@cite{eckert-2008} citing Rauniomaa 2003).
Social types as field anchors: social types (School Teacher, Nerd Girl, Gay Diva) anchor regions of the indexical field, providing culturally available clusters of traits.

Formalization #

The central formal contribution is showing that Eckert's stance accretion is the same composition operation as @cite{ochs-1992}'s indirect indexicality, both instantiated as Phenomena.SocialMeaning.IndexicalField.composeIndex:

Ochs: SFP → Stance → GenderPole (form indexes stance indexes gender)
Eckert: /t/ variant → Stance → Quality (form indexes stance, habitual stance accretes into quality)

Both are matrix products through an intermediate domain. The study file exercises this parallel with concrete data from Figures 3 and 4.

Concrete data #

Figure 1 (Belten High): ordinal leadership data for 7 NCS variables × 4 social groups. The key finding: burnout girls lead ALL variables, demonstrating that gender effects are mediated through social orientation — a generalization of @cite{ochs-1992}'s mediation thesis.
Figure 3 ((ING)): sign-valued indexical field for the velar/apical variants, based on @cite{campbell-kibler-2007}'s experimental data.
Figure 4 (/t/ release): stance accretion chain decomposed via composeIndex, with social type anchoring in quality space.

Connections #

Phenomena.SocialMeaning.IndexicalField.composeIndex: the shared composition operation
Phenomena.SocialMeaning.IndexicalField.IndexicalField: Eckert's concept, formalized as infrastructure in Core
Ochs1992: predecessor — composeIndex was introduced to formalize Ochs's indirect indexicality; Eckert generalizes it to stance accretion
Theories.Sociolinguistics.EckertMontague: the Eckert-Montague lift operationalizes the mapping from indexical field to compatible personae, connecting to @cite{burnett-2019}'s social meaning games

inductive Eckert2008.TraitKind :

Whether a trait is a momentary interactional stance or a stable attributed quality. @cite{eckert-2008} emphasizes the fluidity of this distinction: "anger and cynicism become part of one's identity ... through stance accretion."

stance : TraitKind
Momentary interactional positioning (gray in Figure 4).
quality : TraitKind
Stable attributed character trait (black in Figure 4).

Instances For

@[implicit_reducible]

instance Eckert2008.instDecidableEqTraitKind :

DecidableEq TraitKind

Equations

Eckert2008.instDecidableEqTraitKind x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Eckert2008.instReprTraitKind :

Equations

Eckert2008.instReprTraitKind = { reprPrec := Eckert2008.instReprTraitKind.repr }

def Eckert2008.instReprTraitKind.repr :

TraitKind → ℕ → Std.Format

Equations

One or more equations did not get rendered due to their size.

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inductive Eckert2008.INGDimension :

Bipolar social dimensions of (ING) meaning, from @cite{campbell-kibler-2007}'s matched guise experiments. Each dimension has a positive pole (indexed by velar) and a negative pole (indexed by apical).

education : INGDimension
formality : INGDimension
effort : INGDimension
articulateness : INGDimension

Instances For

@[implicit_reducible]

instance Eckert2008.instDecidableEqINGDimension :

DecidableEq INGDimension

Equations

Eckert2008.instDecidableEqINGDimension x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Eckert2008.instReprINGDimension :

Repr INGDimension

Equations

Eckert2008.instReprINGDimension = { reprPrec := Eckert2008.instReprINGDimension.repr }

def Eckert2008.instReprINGDimension.repr :

INGDimension → ℕ → Std.Format

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One or more equations did not get rendered due to their size.

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@[implicit_reducible]

instance Eckert2008.instInhabitedINGDimension :

Inhabited INGDimension

Equations

Eckert2008.instInhabitedINGDimension = { default := Eckert2008.instInhabitedINGDimension.default }

def Eckert2008.instInhabitedINGDimension.default :

Equations

Eckert2008.instInhabitedINGDimension.default = Eckert2008.INGDimension.education

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@[implicit_reducible]

instance Eckert2008.instFintypeINGDimension :

Fintype INGDimension

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One or more equations did not get rendered due to their size.

def Eckert2008.ingField :

Phenomena.SocialMeaning.IndexicalField.IndexicalField Phenomena.SocialMeaning.ING.INGVariant INGDimension

The (ING) indexical field (Figure 3, based on @cite{campbell-kibler-2007}).

Sign-valued: +1 means the variant indexes toward the positive pole of the dimension, −1 indexes toward the negative pole. The velar variant indexes the positive pole (educated, formal, effortful, articulate) on all dimensions; the apical variant indexes the negative pole (uneducated, relaxed, easygoing, inarticulate).

@cite{eckert-2008} notes that context modulates interpretation: the velar variant can be heard as articulate or pretentious depending on presupposed indexicality. This context-dependent activation is operationalized computationally in @cite{burnett-2019}'s RSA model via context-specific priors.

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theorem Eckert2008.ing_anticorrelation (d : INGDimension) :

ingField.association Phenomena.SocialMeaning.ING.INGVariant.velar d = -ingField.association Phenomena.SocialMeaning.ING.INGVariant.apical d

Perfect anti-correlation: the two (ING) variants are mirror images on every dimension. Whatever the velar variant indexes toward, the apical variant indexes away from, and vice versa.

theorem Eckert2008.ing_velar_all_positive (d : INGDimension) :

ingField.indexes Phenomena.SocialMeaning.ING.INGVariant.velar d

The velar variant indexes the positive pole on all dimensions.

theorem Eckert2008.ing_contrasts_all (d : INGDimension) :

ingField.contrasts Phenomena.SocialMeaning.ING.INGVariant.velar Phenomena.SocialMeaning.ING.INGVariant.apical d

The two variants contrast on every dimension — (ING) is a maximally contrastive binary variable.

inductive Eckert2008.TReleaseVariant :

/t/ release variants. Released /t/ (hyperarticulated stop release) is the socially meaningful variant; unreleased is unmarked.

released : TReleaseVariant
unreleased : TReleaseVariant

Instances For

@[implicit_reducible]

instance Eckert2008.instDecidableEqTReleaseVariant :

DecidableEq TReleaseVariant

Equations

Eckert2008.instDecidableEqTReleaseVariant x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Eckert2008.instReprTReleaseVariant.repr :

TReleaseVariant → ℕ → Std.Format

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One or more equations did not get rendered due to their size.

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@[implicit_reducible]

instance Eckert2008.instReprTReleaseVariant :

Repr TReleaseVariant

Equations

Eckert2008.instReprTReleaseVariant = { reprPrec := Eckert2008.instReprTReleaseVariant.repr }

@[implicit_reducible]

instance Eckert2008.instInhabitedTReleaseVariant :

Inhabited TReleaseVariant

Equations

Eckert2008.instInhabitedTReleaseVariant = { default := Eckert2008.instInhabitedTReleaseVariant.default }

def Eckert2008.instInhabitedTReleaseVariant.default :

TReleaseVariant

Equations

Eckert2008.instInhabitedTReleaseVariant.default = Eckert2008.TReleaseVariant.released

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@[implicit_reducible]

instance Eckert2008.instFintypeTReleaseVariant :

Fintype TReleaseVariant

Equations

Eckert2008.instFintypeTReleaseVariant = { elems := {Eckert2008.TReleaseVariant.released, Eckert2008.TReleaseVariant.unreleased}, complete := Eckert2008.instFintypeTReleaseVariant._proof_1 }

inductive Eckert2008.TReleaseStance :

Stances directly indexed by released /t/ (gray labels in Figure 4). These are momentary interactional positions: emphasis, anger, exasperation, annoyance — a gradient of emotional intensity.

emphatic : TReleaseStance
angry : TReleaseStance
exasperated : TReleaseStance
annoyed : TReleaseStance

Instances For

@[implicit_reducible]

instance Eckert2008.instDecidableEqTReleaseStance :

DecidableEq TReleaseStance

Equations

Eckert2008.instDecidableEqTReleaseStance x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Eckert2008.instReprTReleaseStance.repr :

TReleaseStance → ℕ → Std.Format

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@[implicit_reducible]

instance Eckert2008.instReprTReleaseStance :

Repr TReleaseStance

Equations

Eckert2008.instReprTReleaseStance = { reprPrec := Eckert2008.instReprTReleaseStance.repr }

@[implicit_reducible]

instance Eckert2008.instInhabitedTReleaseStance :

Inhabited TReleaseStance

Equations

Eckert2008.instInhabitedTReleaseStance = { default := Eckert2008.instInhabitedTReleaseStance.default }

def Eckert2008.instInhabitedTReleaseStance.default :

Equations

Eckert2008.instInhabitedTReleaseStance.default = Eckert2008.TReleaseStance.emphatic

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@[implicit_reducible]

instance Eckert2008.instFintypeTReleaseStance :

Fintype TReleaseStance

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One or more equations did not get rendered due to their size.

def Eckert2008.TReleaseStance.all :

List TReleaseStance

Equations

Eckert2008.TReleaseStance.all = [Eckert2008.TReleaseStance.emphatic, Eckert2008.TReleaseStance.angry, Eckert2008.TReleaseStance.exasperated, Eckert2008.TReleaseStance.annoyed]

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inductive Eckert2008.TReleaseQuality :

Qualities indirectly indexed through stance accretion (black labels in Figure 4). These are stable attributed character traits that emerge from habitual use of the stances above.

educated : TReleaseQuality
articulate : TReleaseQuality
formal : TReleaseQuality
elegant : TReleaseQuality
polite : TReleaseQuality
effortful : TReleaseQuality
prissy : TReleaseQuality
clear : TReleaseQuality
careful : TReleaseQuality

Instances For

@[implicit_reducible]

instance Eckert2008.instDecidableEqTReleaseQuality :

DecidableEq TReleaseQuality

Equations

Eckert2008.instDecidableEqTReleaseQuality x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Eckert2008.instReprTReleaseQuality.repr :

TReleaseQuality → ℕ → Std.Format

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One or more equations did not get rendered due to their size.

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@[implicit_reducible]

instance Eckert2008.instReprTReleaseQuality :

Repr TReleaseQuality

Equations

Eckert2008.instReprTReleaseQuality = { reprPrec := Eckert2008.instReprTReleaseQuality.repr }

def Eckert2008.instInhabitedTReleaseQuality.default :

TReleaseQuality

Equations

Eckert2008.instInhabitedTReleaseQuality.default = Eckert2008.TReleaseQuality.educated

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@[implicit_reducible]

instance Eckert2008.instInhabitedTReleaseQuality :

Inhabited TReleaseQuality

Equations

Eckert2008.instInhabitedTReleaseQuality = { default := Eckert2008.instInhabitedTReleaseQuality.default }

@[implicit_reducible]

instance Eckert2008.instFintypeTReleaseQuality :

Fintype TReleaseQuality

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def Eckert2008.variantStanceAssoc :

TReleaseVariant → TReleaseStance → ℚ

Level 1: released /t/ directly indexes stances.

The emphatic stance is the strongest direct association; the others form a gradient of decreasing emotional intensity. Unreleased /t/ is unmarked (zero association with all stances).

Equations

Instances For

def Eckert2008.stanceQualityAssoc :

TReleaseStance → TReleaseQuality → ℚ

Level 2: habitual stances accrete into perceived qualities.

Numerical values are modeling choices reflecting qualitative descriptions in @cite{eckert-2008}, not values from the paper. The emphatic stance is the broadest mediator, contributing to articulateness, clarity, education, effort, and weakly to formality traits. The exasperated stance mediates prissiness (the Gay Diva pathway in @cite{podesva-2007}). Angry mediates perceived effort. Annoyed is too transient to accrete.

Equations

Instances For

def Eckert2008.composedQuality (v : TReleaseVariant) (q : TReleaseQuality) :

ℚ

The composed variant → quality association via stance accretion. This IS the @cite{ochs-1992} parallel: the same composeIndex operation that mediates form → stance → gender in Japanese SFPs here mediates form → stance → quality for /t/ release.

composedQuality(v, q) = Σ_s variantStance(v, s) × stanceQuality(s, q)

Equations

Eckert2008.composedQuality v q = Phenomena.SocialMeaning.IndexicalField.composeIndex Eckert2008.variantStanceAssoc Eckert2008.stanceQualityAssoc Eckert2008.TReleaseStance.all v q

Instances For

theorem Eckert2008.all_qualities_positive (q : TReleaseQuality) :

composedQuality TReleaseVariant.released q > 0

All qualities have positive composed association with released /t/. Parallel to @cite{ochs-1992}'s all_nonexclusive: indirect indexicality through non-negative mediators preserves positivity.

theorem Eckert2008.unreleased_zero (q : TReleaseQuality) :

composedQuality TReleaseVariant.unreleased q = 0

Unreleased /t/ has zero association with all qualities — the unmarked variant carries no social meaning through this pathway.

theorem Eckert2008.quality_ranking :

composedQuality TReleaseVariant.released TReleaseQuality.effortful > composedQuality TReleaseVariant.released TReleaseQuality.articulate ∧ composedQuality TReleaseVariant.released TReleaseQuality.articulate = composedQuality TReleaseVariant.released TReleaseQuality.clear ∧ composedQuality TReleaseVariant.released TReleaseQuality.articulate > composedQuality TReleaseVariant.released TReleaseQuality.educated ∧ composedQuality TReleaseVariant.released TReleaseQuality.educated > composedQuality TReleaseVariant.released TReleaseQuality.prissy ∧ composedQuality TReleaseVariant.released TReleaseQuality.prissy = composedQuality TReleaseVariant.released TReleaseQuality.careful ∧ composedQuality TReleaseVariant.released TReleaseQuality.prissy > composedQuality TReleaseVariant.released TReleaseQuality.formal ∧ composedQuality TReleaseVariant.released TReleaseQuality.formal = composedQuality TReleaseVariant.released TReleaseQuality.elegant ∧ composedQuality TReleaseVariant.released TReleaseQuality.formal = composedQuality TReleaseVariant.released TReleaseQuality.polite

Quality ranking by composed association strength: effortful (9/8) > articulate = clear (3/4) > educated (1/2)

prissy = careful (3/8) > formal = elegant = polite (1/4).

Effortful is strongest because it is mediated through three stances (emphatic, angry, exasperated). Articulateness and clarity tie as the primary emphatic accretions. The formality cluster (formal, elegant, polite) is weakest — a secondary association.

The composed form–quality association factors through the stance domain. Parallel to Ochs1992.mediation_ze_masc: the mediation thesis made computationally explicit.

inductive Eckert2008.SocialType :

Social types that anchor regions of the /t/ release indexical field (boxes in Figure 4). Each type is a culturally available persona cluster — a bundle of qualities that provides an interpretive anchor for hearers.

british : SocialType
schoolTeacher : SocialType
nerdGirl : SocialType
gayDiva : SocialType

Instances For

@[implicit_reducible]

instance Eckert2008.instDecidableEqSocialType :

DecidableEq SocialType

Equations

Eckert2008.instDecidableEqSocialType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Eckert2008.instReprSocialType.repr :

SocialType → ℕ → Std.Format

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One or more equations did not get rendered due to their size.

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@[implicit_reducible]

instance Eckert2008.instReprSocialType :

Repr SocialType

Equations

Eckert2008.instReprSocialType = { reprPrec := Eckert2008.instReprSocialType.repr }

@[implicit_reducible]

instance Eckert2008.instInhabitedSocialType :

Inhabited SocialType

Equations

Eckert2008.instInhabitedSocialType = { default := Eckert2008.instInhabitedSocialType.default }

def Eckert2008.instInhabitedSocialType.default :

Equations

Eckert2008.instInhabitedSocialType.default = Eckert2008.SocialType.british

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@[implicit_reducible]

instance Eckert2008.instFintypeSocialType :

Fintype SocialType

Equations

One or more equations did not get rendered due to their size.

def Eckert2008.socialTypeQualities :

SocialType → TReleaseQuality → Bool

Which qualities each social type activates in the /t/ release field (spatial regions in Figure 4).

These are proto-personae in the sense of @cite{burnett-2019}'s social meaning games: quality bundles that the Eckert-Montague lift maps to compatible persona sets. Mappings are based on spatial proximity in Figure 4 and textual descriptions.

Equations

Instances For

theorem Eckert2008.all_types_include_articulate (st : SocialType) :

socialTypeQualities st TReleaseQuality.articulate = true

All social types include articulate — the most central quality in the /t/ release field. This reflects the ideological core of hyperarticulation as a semiotic resource.

theorem Eckert2008.educated_branching :

socialTypeQualities SocialType.british TReleaseQuality.educated = true ∧ socialTypeQualities SocialType.nerdGirl TReleaseQuality.educated = true ∧ socialTypeQualities SocialType.british TReleaseQuality.elegant = true ∧ socialTypeQualities SocialType.nerdGirl TReleaseQuality.elegant = false

British and Nerd Girl share educated but differ on formality — the field branches from education into refinement (British) vs. intellectual emphasis (Nerd Girl).

theorem Eckert2008.nerdGirl_subset_schoolTeacher (q : TReleaseQuality) :

socialTypeQualities SocialType.nerdGirl q = true → socialTypeQualities SocialType.schoolTeacher q = true

Nerd Girl's qualities are a subset of School Teacher's. This reflects the text: nerd girls' /t/ release "builds primarily on the social significance of clear speech, which in turn is associated with a school-teachery standard" (p.468).

theorem Eckert2008.prissy_unique_to_gayDiva :

socialTypeQualities SocialType.gayDiva TReleaseQuality.prissy = true ∧ socialTypeQualities SocialType.british TReleaseQuality.prissy = false ∧ socialTypeQualities SocialType.schoolTeacher TReleaseQuality.prissy = false ∧ socialTypeQualities SocialType.nerdGirl TReleaseQuality.prissy = false

Prissy is unique to Gay Diva among the four social types.

theorem Eckert2008.types_cover_all_qualities (q : TReleaseQuality) :

∃ (st : SocialType), socialTypeQualities st q = true

Every quality is activated by at least one social type — the four types collectively cover the full quality space.

inductive Eckert2008.BeltenGroup :

Social categories at Belten High School, Detroit (@cite{eckert-2008} Figure 1, based on Eckert 1989, 2000).

School-oriented jocks and urban-oriented burnouts define a local opposition that cross-cuts gender, creating four social groups with distinct patterns of variation.

jockBoys : BeltenGroup
jockGirls : BeltenGroup
burnoutBoys : BeltenGroup
burnoutGirls : BeltenGroup

Instances For

@[implicit_reducible]

instance Eckert2008.instDecidableEqBeltenGroup :

DecidableEq BeltenGroup

Equations

Eckert2008.instDecidableEqBeltenGroup x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Eckert2008.instReprBeltenGroup.repr :

BeltenGroup → ℕ → Std.Format

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One or more equations did not get rendered due to their size.

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@[implicit_reducible]

instance Eckert2008.instReprBeltenGroup :

Repr BeltenGroup

Equations

Eckert2008.instReprBeltenGroup = { reprPrec := Eckert2008.instReprBeltenGroup.repr }

def Eckert2008.instInhabitedBeltenGroup.default :

Equations

Eckert2008.instInhabitedBeltenGroup.default = Eckert2008.BeltenGroup.jockBoys

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@[implicit_reducible]

instance Eckert2008.instInhabitedBeltenGroup :

Inhabited BeltenGroup

Equations

Eckert2008.instInhabitedBeltenGroup = { default := Eckert2008.instInhabitedBeltenGroup.default }

@[implicit_reducible]

instance Eckert2008.instFintypeBeltenGroup :

Fintype BeltenGroup

Equations

One or more equations did not get rendered due to their size.

inductive Eckert2008.NCSVariable :

Variables involved in the Northern Cities Shift at Belten High.

The NCS splits into chronological layers: older changes (vowel fronting, stabilized across the suburban area, led by girls) and newer changes (vowel backing, more advanced in the urban center, led by burnouts). Negative concord is a syntactic variable.

ae_raising : NCSVariable
a_fronting : NCSVariable
open_o_lowering : NCSVariable
wedge_backing : NCSVariable
ay_backing : NCSVariable
epsilon_backing : NCSVariable
negation : NCSVariable

Instances For

@[implicit_reducible]

instance Eckert2008.instDecidableEqNCSVariable :

DecidableEq NCSVariable

Equations

Eckert2008.instDecidableEqNCSVariable x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Eckert2008.instReprNCSVariable.repr :

NCSVariable → ℕ → Std.Format

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One or more equations did not get rendered due to their size.

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@[implicit_reducible]

instance Eckert2008.instReprNCSVariable :

Repr NCSVariable

Equations

Eckert2008.instReprNCSVariable = { reprPrec := Eckert2008.instReprNCSVariable.repr }

def Eckert2008.instInhabitedNCSVariable.default :

Equations

Eckert2008.instInhabitedNCSVariable.default = Eckert2008.NCSVariable.ae_raising

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@[implicit_reducible]

instance Eckert2008.instInhabitedNCSVariable :

Inhabited NCSVariable

Equations

Eckert2008.instInhabitedNCSVariable = { default := Eckert2008.instInhabitedNCSVariable.default }

@[implicit_reducible]

instance Eckert2008.instFintypeNCSVariable :

Fintype NCSVariable

Equations

One or more equations did not get rendered due to their size.

def Eckert2008.beltenLeadership :

BeltenGroup → NCSVariable → ℚ

Leadership ranking from Figure 1. 2 = leader (black in figure), 1 = runner-up (gray), 0 = neither.

Older NCS changes are led by girls (burnout girls lead, jock girls runner-up). Newer NCS changes are led by burnouts (burnout girls lead, burnout boys runner-up). Negation: burnout girls lead despite the overall male tendency for negative concord.

The key finding: burnout girls are leaders (= 2) across ALL variables — they embed the urban–suburban opposition linguistically, demonstrating that the gender effect is mediated through social orientation, not a direct gender → language mapping. This is @cite{ochs-1992}'s mediation thesis generalized to the ethnographic domain.

Equations

Instances For

theorem Eckert2008.burnoutGirls_lead_all (v : NCSVariable) :

beltenLeadership BeltenGroup.burnoutGirls v = 2

Universal leadership: burnout girls lead every NCS variable.

This is the central empirical finding of the Belten High study. The burned-out burnout girls led all other burnouts, male and female, in all NCS urban variables AND negative concord — despite the general population pattern of male-led negation.

theorem Eckert2008.jockBoys_not_universal :

∃ (v : NCSVariable), beltenLeadership BeltenGroup.jockBoys v < 2

No other group leads all variables — burnout girls' universal leadership is unique.

theorem Eckert2008.jockGirls_not_universal :

∃ (v : NCSVariable), beltenLeadership BeltenGroup.jockGirls v < 2

theorem Eckert2008.burnoutBoys_not_universal :

∃ (v : NCSVariable), beltenLeadership BeltenGroup.burnoutBoys v < 2

theorem Eckert2008.older_runner_up_is_jockGirls :

beltenLeadership BeltenGroup.jockGirls NCSVariable.ae_raising = 1 ∧ beltenLeadership BeltenGroup.jockGirls NCSVariable.a_fronting = 1 ∧ beltenLeadership BeltenGroup.jockGirls NCSVariable.open_o_lowering = 1

Gender × orientation interaction: older variables split by gender (jock girls are runners-up), newer variables split by social orientation (burnout boys are runners-up).

theorem Eckert2008.newer_runner_up_is_burnoutBoys :

beltenLeadership BeltenGroup.burnoutBoys NCSVariable.wedge_backing = 1 ∧ beltenLeadership BeltenGroup.burnoutBoys NCSVariable.ay_backing = 1 ∧ beltenLeadership BeltenGroup.burnoutBoys NCSVariable.epsilon_backing = 1

theorem Eckert2008.jockBoys_never_lead (v : NCSVariable) :

beltenLeadership BeltenGroup.jockBoys v = 0

Jock boys never lead or run up — they are the most linguistically conservative group, furthest from both the gender-led and orientation-led change fronts.

def Eckert2008.composedField :

Phenomena.SocialMeaning.IndexicalField.IndexicalField TReleaseVariant TReleaseQuality

The /t/ release composed association as an IndexicalField.

Parallel to Ochs1992.composedField: both lift composed association values to the IndexicalField type, connecting the study-specific composition back to the core infrastructure.

Equations

Eckert2008.composedField = { association := Eckert2008.composedQuality, order := Phenomena.SocialMeaning.IndexicalField.IndexicalOrder.second }

Instances For

theorem Eckert2008.composedField_released_indexes_articulate :

composedField.indexes TReleaseVariant.released TReleaseQuality.articulate

The composed field indexes released /t/ toward articulateness.

theorem Eckert2008.composedField_contrasts_all (q : TReleaseQuality) :

composedField.contrasts TReleaseVariant.released TReleaseVariant.unreleased q

Released and unreleased /t/ contrast on every quality — the composed field is maximally contrastive.

The (ING) indexical field (§2) lives over INGDimension — a domain-specific 4-axis space derived from @cite{campbell-kibler-2007}. To connect it to the Eckert-Montague lift (EckertMontague.emFieldMI), we project it to SocialDimension (the 3-axis SCM framework from @cite{fiske-cuddy-glick-2007}).

Dimension mapping rationale:

education → competence: education is a core competence indicator
formality → antiSolidarity: formal register indexes social distance (pedantic, uptight — the antiSolidarity pole in SCM/BSB2022)
effort → competence: effortful speech signals diligence/precision
articulateness → competence: articulateness is a competence signal

This maps 3 of 4 ING dimensions to competence and 1 to antiSolidarity, with warmth = 0. @cite{burnett-2019} makes a different choice: mapping formality to warmth (aloof ≈ cold) rather than antiSolidarity. Both are defensible — the present mapping follows BSB2022's PCA loadings where "pedantic/uptight" loaded on an independent factor from warmth.

The sign structure is preserved: velar indexes the positive pole of all 4 dimensions, so it indexes competent + antiSolidary in SCM.

def Eckert2008.ingFieldSCM :

Phenomena.SocialMeaning.IndexicalField.IndexicalField Phenomena.SocialMeaning.ING.INGVariant Sociolinguistics.SCM.SocialDimension

The (ING) indexical field projected to SCM dimensions.

All three of education, effort, and articulateness collapse to competence (same sign for both variants), while formality projects to antiSolidarity. Warmth is zero — (ING) carries no warmth signal in this analysis.

Equations

One or more equations did not get rendered due to their size.

Instances For

theorem Eckert2008.ingFieldSCM_signs_match_ingField :

(∀ (d : Sociolinguistics.SCM.SocialDimension), ingFieldSCM.association Phenomena.SocialMeaning.ING.INGVariant.velar d ≥ 0) ∧ ∀ (d : Sociolinguistics.SCM.SocialDimension), ingFieldSCM.association Phenomena.SocialMeaning.ING.INGVariant.apical d ≤ 0

The SCM projection preserves the sign structure of the domain-specific field: velar is positive on all mapped dimensions, apical is negative.

def Eckert2008.ingGroundedField :

Sociolinguistics.EckertMontague.GroundedField Phenomena.SocialMeaning.ING.INGVariant Sociolinguistics.SCM.scmSpace

The (ING) field grounded in the SCM property space via fromIndexicalField. This is the same bridge used by @cite{beltrama-schwarz-2024} and @cite{beltrama-solt-burnett-2022} for round/precise number variants.

Equations

Eckert2008.ingGroundedField = Sociolinguistics.EckertMontague.fromIndexicalField Eckert2008.ingFieldSCM

Instances For

theorem Eckert2008.velar_scm_properties :

ingGroundedField.indexedProperties Phenomena.SocialMeaning.ING.INGVariant.velar = {Sociolinguistics.SCM.SCMProperty.competent, Sociolinguistics.SCM.SCMProperty.antiSolidary}

The velar variant indexes {competent, antiSolidary} in SCM: educated, formal, effortful, articulate → competent + socially distant.

theorem Eckert2008.apical_scm_properties :

ingGroundedField.indexedProperties Phenomena.SocialMeaning.ING.INGVariant.apical = {Sociolinguistics.SCM.SCMProperty.incompetent, Sociolinguistics.SCM.SCMProperty.solidary}

The apical variant indexes {incompetent, solidary} in SCM: uneducated, relaxed, easygoing, inarticulate → incompetent + solidary/approachable.

def Eckert2008.ingEM (v : Phenomena.SocialMeaning.ING.INGVariant) :

Finset (Finset Sociolinguistics.SCM.scmSpace.Property)

The Eckert-Montague lift applied to the ING grounded field. Returns the set of SCM personae compatible with each variant via intersection semantics (a persona is compatible iff it shares at least one property with the variant's Eckert field).

Equations

Eckert2008.ingEM v = Sociolinguistics.EckertMontague.emFieldMI Eckert2008.ingGroundedField v

Instances For

theorem Eckert2008.velar_em_count :

(ingEM Phenomena.SocialMeaning.ING.INGVariant.velar).card = 6

The velar variant is compatible with 6 of 8 SCM personae. Excluded: {incompetent, warm, solidary} and {incompetent, cold, solidary} — the two personae that have neither competent nor antiSolidary.

theorem Eckert2008.apical_em_count :

(ingEM Phenomena.SocialMeaning.ING.INGVariant.apical).card = 6

The apical variant is compatible with 6 of 8 SCM personae. Excluded: {competent, warm, antiSolidary} and {competent, cold, antiSolidary} — the two personae that have neither incompetent nor solidary.

theorem Eckert2008.velar_apical_em_differ :

ingEM Phenomena.SocialMeaning.ING.INGVariant.velar ≠ ingEM Phenomena.SocialMeaning.ING.INGVariant.apical

The two variants exclude different personae, confirming that the EM lift distinguishes them despite both being compatible with most of the persona space.