@cite{beltrama-solt-burnett-2023} #

Context, precision, and social perception: A sociopragmatic study. Language in Society 52(5): 805–835. doi:10.1017/S0047404522000240

Two experiments (Exp 1: N=72 within-subjects; Exp 2: N=400 between-subjects) examining how numeral precision affects social perception across three PCA-derived evaluation dimensions and four communicative scenarios.

Core contributions #

Three-way variant contrast: Distinguishes precise ("forty-nine"), underspecified ("fifty"), and explicitly approximate ("about fifty") — extending prior work that only compared sharp vs. round numbers.
Core indexical ordering (robust across both experiments):
- Competence/Status: precise ≥ underspecified > approximate
- Warmth/Solidarity: approximate ≥ underspecified > precise
- Anti-Solidarity: precise > underspecified ≈ approximate
Underspecified as diagnostic (§General Discussion, p. 827–828): bare round numbers don't uniformly pattern with either endpoint. On competence, underspecified hugs precise; on anti-solidarity, it hugs approximate; on warmth, it is genuinely intermediate. This reveals precision and approximation as independent indexical loci.
Context modulation: high-precision-demand scenarios (For-the-record, Persuasion) amplify competence contrasts; low-demand scenarios (Bonding, Stranger) amplify warmth/solidarity contrasts.

Fragment connections #

Stimuli use numerals 49 (precise) and 50 (round), with "about" as the tolerance modifier:

Core.Roundness.roundnessScore: 49 → 0, 50 → 4
Semantics.Numerals.Precision.inferPrecisionMode: 49 →.exact, 50 →.approximate
Fragments.English.NumeralModifiers.about: tolerance modifier

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inductive BeltramaSoltBurnett2022.Variant :

Type

The three precision variants for numeral use (BSB2022 §3).

Extends the two-way distinction (exact/approximate) in @cite{beltrama-schwarz-2024} by factoring out bare round numerals as a third, diagnostically crucial category.

precise : Variant
underspecified : Variant
approximate : Variant

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@[implicit_reducible]

instance BeltramaSoltBurnett2022.instDecidableEqVariant :

DecidableEq Variant

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BeltramaSoltBurnett2022.instDecidableEqVariant x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

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def BeltramaSoltBurnett2022.instReprVariant.repr :

Variant → ℕ → Std.Format

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@[implicit_reducible]

instance BeltramaSoltBurnett2022.instReprVariant :

Repr Variant

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BeltramaSoltBurnett2022.instReprVariant = { reprPrec := BeltramaSoltBurnett2022.instReprVariant.repr }

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def BeltramaSoltBurnett2022.stimPrecise :

ℕ

The precise stimulus numeral (sharp, non-round).

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BeltramaSoltBurnett2022.stimPrecise = 49

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def BeltramaSoltBurnett2022.stimRound :

ℕ

The round stimulus numeral (used bare or with "about").

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BeltramaSoltBurnett2022.stimRound = 50

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theorem BeltramaSoltBurnett2022.stim_precise_not_round :

Core.Roundness.roundnessScore stimPrecise = 0

49 has zero roundness — no imprecise reading is possible.

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theorem BeltramaSoltBurnett2022.stim_round_is_round :

Core.Roundness.roundnessScore stimRound = 4

50 has moderate roundness (score 4) — imprecise readings available.

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theorem BeltramaSoltBurnett2022.precise_stim_is_exact :

Semantics.Numerals.Precision.inferPrecisionMode stimPrecise = Semantics.Numerals.Precision.PrecisionMode.exact

49 → exact precision mode (roundnessScore 0 < 2).

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theorem BeltramaSoltBurnett2022.round_stim_is_approximate :

Semantics.Numerals.Precision.inferPrecisionMode stimRound = Semantics.Numerals.Precision.PrecisionMode.approximate

50 → approximate precision mode (roundnessScore 4 ≥ 2).

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theorem BeltramaSoltBurnett2022.about_is_tolerance_modifier :

Fragments.English.NumeralModifiers.about.modType = Fragments.English.NumeralModifiers.ModifierType.tolerance ∧ Fragments.English.NumeralModifiers.about.conveysShape = true ∧ Fragments.English.NumeralModifiers.about.pragFunction = Fragments.English.NumeralModifiers.PragmaticFunction.peakedSignal

The Fragment entry "about" is a tolerance modifier that forces an approximate reading and conveys a peaked distribution shape.

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def BeltramaSoltBurnett2022.classifyVariant (n : ℕ) (hasToleranceModifier : Bool) :

Variant

Classify a numeral into a variant based on roundness and modifier presence.

End-to-end derivation chain: Fragment modifier type + Core.Roundness score → Variant.

Non-round (score < 2): .precise regardless of modifier
Round + no modifier: .underspecified (imprecision available, not forced)
Round + tolerance modifier: .approximate (imprecision forced)

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theorem BeltramaSoltBurnett2022.classify_49 :

classifyVariant stimPrecise false = Variant.precise

"forty-nine minutes" → precise variant.

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theorem BeltramaSoltBurnett2022.classify_50_bare :

classifyVariant stimRound false = Variant.underspecified

"fifty minutes" (bare) → underspecified variant.

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theorem BeltramaSoltBurnett2022.classify_50_about :

classifyVariant stimRound true = Variant.approximate

"about fifty minutes" → approximate variant.

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def BeltramaSoltBurnett2022.exp1Mean :

Variant → Sociolinguistics.SCM.SocialDimension → ℚ

Experiment 1 (within-subjects, N=72) cell means. PCA factor scores mapped to SocialDimension: Status → .competence, Solidarity → .warmth, Anti-Solidarity → .antiSolidarity.

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def BeltramaSoltBurnett2022.exp2Mean :

Variant → Sociolinguistics.SCM.SocialDimension → ℚ

Experiment 2 (between-subjects, N=400) cell means.

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theorem BeltramaSoltBurnett2022.competence_precise_gt_approx :

exp1Mean Variant.precise Sociolinguistics.SCM.SocialDimension.competence > exp1Mean Variant.approximate Sociolinguistics.SCM.SocialDimension.competence ∧ exp2Mean Variant.precise Sociolinguistics.SCM.SocialDimension.competence > exp2Mean Variant.approximate Sociolinguistics.SCM.SocialDimension.competence

Competence: precise > approximate (both experiments).

Speakers using sharp numbers are perceived as more articulate, intelligent, confident, and trustworthy than those using explicitly approximate numbers. Exp 1: 5.01 > 4.84; Exp 2: 5.16 > 4.90.

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theorem BeltramaSoltBurnett2022.warmth_approx_gt_precise :

exp1Mean Variant.approximate Sociolinguistics.SCM.SocialDimension.warmth > exp1Mean Variant.precise Sociolinguistics.SCM.SocialDimension.warmth ∧ exp2Mean Variant.approximate Sociolinguistics.SCM.SocialDimension.warmth > exp2Mean Variant.precise Sociolinguistics.SCM.SocialDimension.warmth

Warmth: approximate > precise (both experiments).

Speakers using "about fifty" are perceived as friendlier, cooler, more laid-back, and more likeable than those using "forty-nine." Exp 1: 4.58 > 4.37; Exp 2: 4.84 > 4.15.

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theorem BeltramaSoltBurnett2022.antiSol_precise_gt_approx :

exp1Mean Variant.precise Sociolinguistics.SCM.SocialDimension.antiSolidarity > exp1Mean Variant.approximate Sociolinguistics.SCM.SocialDimension.antiSolidarity ∧ exp2Mean Variant.precise Sociolinguistics.SCM.SocialDimension.antiSolidarity > exp2Mean Variant.approximate Sociolinguistics.SCM.SocialDimension.antiSolidarity

Anti-Solidarity: precise > approximate (both experiments).

Speakers using sharp numbers are perceived as more pedantic and uptight. Exp 1: 4.37 > 4.10; Exp 2: 3.85 > 3.49.

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theorem BeltramaSoltBurnett2022.sign_alignment :

Sign alignment: competence and anti-solidarity share sign direction (both favor precise), while warmth reverses (favors approximate).

This is the core sign structure of the precision indexical field. It is consistent with the precisionField associations in @cite{beltrama-schwarz-2024}, where .exact →.competence = +1, .exact →.warmth = −1, and .exact →.antiSolidarity = +1.

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def BeltramaSoltBurnett2022.bsbField :

Phenomena.SocialMeaning.IndexicalField.IndexicalField Variant Sociolinguistics.SCM.SocialDimension

The three-way indexical field for numeral precision (BSB2022).

Association values are idealized signs (±1) matching the empirical ordering from §5. The underspecified variant gets 0 (neutral) — the diagnostic theorem (§7) shows its empirical position varies by dimension.

The precise/approximate cells have the same signs as @cite{beltrama-schwarz-2024}'s precisionField on all three social dimensions.

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theorem BeltramaSoltBurnett2022.opposite_directions (d : Sociolinguistics.SCM.SocialDimension) :

bsbField.association Variant.precise d = -bsbField.association Variant.approximate d

Precise and approximate have algebraically opposite associations on every dimension — the same anti-symmetry as @cite{beltrama-schwarz-2024}'s opposite_directions.

Underspecified diagnostic (BSB2022's deepest contribution, p. 827–828).

On each dimension, the underspecified variant does not sit uniformly between precise and approximate. Its proximity to each endpoint varies by dimension, revealing precision and approximation as independent indexical loci.

The interpretation (p. 827): when underspecified clusters with precise and away from approximate, the contrast is approximation-driven (it is approximation that downgrades the trait). When underspecified clusters with approximate and away from precise, the contrast is precision-driven (it is precision that upgrades the trait).

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On competence, underspecified is closer to precise than to approximate. The contrast is approximation-driven: it is "about" that downgrades Status, not sharp numbers that upgrade it. Exp 1: |5.01−4.96| = 0.05 < |4.96−4.84| = 0.12. Exp 2: |5.16−5.06| = 0.10 < |5.06−4.90| = 0.16.

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On anti-solidarity, underspecified is closer to approximate than to precise. The contrast is precision-driven: it is sharp numbers that make you seem pedantic, not "about" that makes you seem relaxed. Exp 1: |4.19−4.10| = 0.09 < |4.37−4.19| = 0.18. Exp 2: |3.59−3.49| = 0.10 < |3.85−3.59| = 0.26.

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On warmth, underspecified is genuinely intermediate: it falls strictly between precise and approximate in both experiments. Both precision and approximation contribute independently to the Solidarity contrast, pulling underspecified in opposite directions.

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Diagnostic asymmetry: the dimension on which underspecified is closest to each endpoint differs. On competence, the cluster gap (precise to underspecified) is smaller than the outlier gap; on anti-solidarity, the reverse. This crossover is what makes underspecified diagnostic.

Formalized as: the ratio of within-cluster to between-cluster gap reverses between competence and anti-solidarity.

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inductive BeltramaSoltBurnett2022.Scenario :

Type

Communicative scenario (BSB2022 §3.1).

forTheRecord : Scenario
persuasion : Scenario
stranger : Scenario
bonding : Scenario

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@[implicit_reducible]

instance BeltramaSoltBurnett2022.instDecidableEqScenario :

DecidableEq Scenario

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BeltramaSoltBurnett2022.instDecidableEqScenario x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

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def BeltramaSoltBurnett2022.instReprScenario.repr :

Scenario → ℕ → Std.Format

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@[implicit_reducible]

instance BeltramaSoltBurnett2022.instReprScenario :

Repr Scenario

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BeltramaSoltBurnett2022.instReprScenario = { reprPrec := BeltramaSoltBurnett2022.instReprScenario.repr }

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inductive BeltramaSoltBurnett2022.PrecisionDemand :

Type

Precision demand level of a communicative scenario.

high : PrecisionDemand
low : PrecisionDemand

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@[implicit_reducible]

instance BeltramaSoltBurnett2022.instDecidableEqPrecisionDemand :

DecidableEq PrecisionDemand

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BeltramaSoltBurnett2022.instDecidableEqPrecisionDemand x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

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@[implicit_reducible]

instance BeltramaSoltBurnett2022.instReprPrecisionDemand :

Repr PrecisionDemand

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BeltramaSoltBurnett2022.instReprPrecisionDemand = { reprPrec := BeltramaSoltBurnett2022.instReprPrecisionDemand.repr }

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def BeltramaSoltBurnett2022.instReprPrecisionDemand.repr :

PrecisionDemand → ℕ → Std.Format

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def BeltramaSoltBurnett2022.Scenario.precisionDemand :

Scenario → PrecisionDemand

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def BeltramaSoltBurnett2022.exp1CompetenceByScenario :

Scenario → Variant → ℚ

Exp 1 scenario-specific means on competence (Status). For-the-record vs Bonding, precise vs approximate.

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theorem BeltramaSoltBurnett2022.competence_enhanced_in_high_demand :

exp1CompetenceByScenario Scenario.forTheRecord Variant.precise - exp1CompetenceByScenario Scenario.forTheRecord Variant.approximate > exp1CompetenceByScenario Scenario.bonding Variant.precise - exp1CompetenceByScenario Scenario.bonding Variant.approximate

Context amplifies competence contrast in high-demand scenarios.

Exp 1, Status: In For-the-record (high demand), precise is rated 0.39 points above approximate. In Bonding (low demand), the gap vanishes (−0.02). The Status advantage of precision is contextually relevant only when descriptive accuracy matters (BSB2022 p. 830).

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theorem BeltramaSoltBurnett2022.competence_neutralized_in_bonding :

exp1CompetenceByScenario Scenario.bonding Variant.approximate ≥ exp1CompetenceByScenario Scenario.bonding Variant.precise

In Bonding, the competence contrast is neutralized: approximate ≥ precise.

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def BeltramaSoltBurnett2022.exp2WarmthByScenario :

Scenario → Variant → ℚ

Exp 2 scenario-specific means on warmth (Solidarity). Stranger vs For-the-record, precise vs underspecified (the significant interaction from Table 4 row 9 re-leveled, p. 823).

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theorem BeltramaSoltBurnett2022.warmth_enhanced_in_low_demand :

exp2WarmthByScenario Scenario.stranger Variant.underspecified - exp2WarmthByScenario Scenario.stranger Variant.precise > exp2WarmthByScenario Scenario.forTheRecord Variant.underspecified - exp2WarmthByScenario Scenario.forTheRecord Variant.precise

Context amplifies warmth contrast in low-demand scenarios.

Exp 2, Solidarity: In Stranger (low demand), underspecified is rated 0.44 points above precise. In For-the-record (high demand), the gap vanishes (0.01). When precision is communicatively irrelevant, the Solidarity penalty of sharp numbers becomes salient (BSB2022 p. 826).

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Bidirectional context modulation: high-demand contexts amplify competence contrasts while suppressing warmth contrasts, and vice versa.

This crossover interaction between precision demand and social dimension composes Scenario.precisionDemand with the dimension-specific indexical field: which region of the field is activated depends on the communicative situation.

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theorem BeltramaSoltBurnett2022.non_round_collapses (n : ℕ) (h : Core.Roundness.roundnessScore n < 2) :

classifyVariant n true = Variant.precise ∧ classifyVariant n false = Variant.precise

Non-round numerals collapse the three-way distinction to a single variant: .precise. There is nothing for social perception to modulate.

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theorem BeltramaSoltBurnett2022.round_supports_contrast (n : ℕ) (h : Core.Roundness.roundnessScore n ≥ 2) :

classifyVariant n false = Variant.underspecified ∧ classifyVariant n true = Variant.approximate

Round numerals support the full three-way contrast: bare → underspecified, modified → approximate.

The BSB2022 indexical field (bsbField) can be lifted to a grounded field over the SCM property space via fromIndexicalField, connecting the empirical sign-valued associations to the persona-theoretic infrastructure used by @cite{burnett-2019}'s Social Meaning Games.

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def BeltramaSoltBurnett2022.bsbGroundedField :

Sociolinguistics.EckertMontague.GroundedField Variant Sociolinguistics.SCM.scmSpace

The BSB2022 indexical field converted to a grounded field over the SCM property space.

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BeltramaSoltBurnett2022.bsbGroundedField = Sociolinguistics.EckertMontague.fromIndexicalField BeltramaSoltBurnett2022.bsbField

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theorem BeltramaSoltBurnett2022.precise_scmProperties :

bsbGroundedField.indexedProperties Variant.precise = {Sociolinguistics.SCM.SCMProperty.competent, Sociolinguistics.SCM.SCMProperty.cold, Sociolinguistics.SCM.SCMProperty.antiSolidary}

Precise indexes {competent, cold, antiSolidary}: positive association with competence and anti-solidarity, negative with warmth.

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theorem BeltramaSoltBurnett2022.approximate_scmProperties :

bsbGroundedField.indexedProperties Variant.approximate = {Sociolinguistics.SCM.SCMProperty.incompetent, Sociolinguistics.SCM.SCMProperty.warm, Sociolinguistics.SCM.SCMProperty.solidary}

Approximate indexes {incompetent, warm, solidary}: the complement.

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theorem BeltramaSoltBurnett2022.underspecified_indexes_nothing :

bsbGroundedField.indexedProperties Variant.underspecified = ∅

Underspecified indexes nothing: zero association on all dimensions → no indexed social properties. Under the EM lift, this makes underspecified compatible with all personae — consistent with its diagnostic role as a neutral baseline (§7).

Documentation

Linglib.Phenomena.Imprecision.Studies.BeltramaSoltBurnett2022

@cite{beltrama-solt-burnett-2023} #

Core contributions #

Fragment connections #