Narrog (2010): (Inter)subjectification in Modality and Mood

[Nar10]

Study file connecting [Nar10]'s theoretical claims to the cross-linguistic data in Semantics.Modality.DeonticNecessity. The chapter argues that strong obligation markers are cross-linguistically uncommon because obligation is inherently face-threatening and socially costly, so languages tend not to grammaticalize it — or to do so only indirectly.

[Nar12] ch. 2 decomposes the face-threatening potential of obligation into three independent dimensions — performativity, volitivity, and speaker-orientation. Face-threat is derived from this decomposition (see NarrogPosition.isFaceThreatening), not stipulated per deontic necessity type.

Key Empirical Claims

1. Strong obligation (must-type) markers exist in only 60/200 languages, barely more than weak obligation (should-type) at 62/200.
2. Japanese avoids strong obligation with 2nd-person subjects entirely (0 instances of -(a)nakereba naranai with 2nd-person subject).
3. The deontic-to-epistemic polyfunctionality (English must) is cross-linguistically rare: only 3 of 42 changes in Bybee et al.'s sample involve this shift.

Bridges

• Semantics.Modality.DeonticNecessity: provides the 200-language data.
• Semantics.Modality.Narrog: provides the theoretical framework (volitivity, speaker-orientation, performativity, directionality).

Cross-linguistic patterns of diachronic change in modal and mood meanings, formalized on Narrog's 2D semantic map (Semantics.Modality.Narrog). The central claim: modal meanings always shift upward in the semantic map — toward increased speaker-orientation — regardless of volitivity. The well-known deontic → epistemic shift is just one instance.

Data: [BPP94] ch. 6, tabulated in [Nar10] Table 2.

structure Narrog2010.Change : Type

An attested cross-linguistic modal meaning change. gramCount = number of "grams" (markers) in Bybee et al.'s sample exhibiting this change.

• label : String
• source : Semantics.Modality.Narrog.NarrogRegion
• target : Semantics.Modality.Narrog.NarrogRegion
• gramCount : ℕ

@[implicit_reducible]

instance Narrog2010.instReprChange : Repr Change

Equations

• Narrog2010.instReprChange = { reprPrec := Narrog2010.instReprChange.repr }

def Narrog2010.instReprChange.repr : Change → ℕ → Std.Format

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def Narrog2010.commonChanges : List Change

The 8 most common cross-linguistic changes in modal meanings. Source: [BPP94] ch. 6, tabulated in [Nar10] Table 2.

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theorem Narrog2010.directionality : (commonChanges.all fun (c : Change) => decide (c.source.orientation ≤ c.target.orientation)) = true

Directionality of change: every attested change increases (or maintains) speaker-orientation. This is Narrog's central diachronic claim.

[Nar10] §3.1: "modal meanings always shift in the direction of increased speaker-orientation."

theorem Narrog2010.no_decrease : (commonChanges.all fun (c : Change) => !decide (c.target.orientation.toNat < c.source.orientation.toNat)) = true

No attested change decreases speaker-orientation.

theorem Narrog2010.volitivity_crossing : (List.filter (fun (c : Change) => c.source.volitivity != c.target.volitivity && c.source.orientation == c.target.orientation) commonChanges).length = 2

Changes #6 and #7 cross the volitivity boundary (volitive → non-volitive) while maintaining speaker-orientation level. This shows volitivity is orthogonal to the directionality of change.

theorem Narrog2010.nonvolitive_to_volitive_changes : (List.filter (fun (c : Change) => c.source.volitivity == Semantics.Modality.Narrog.Volitivity.nonVolitive && c.target.volitivity == Semantics.Modality.Narrog.Volitivity.volitive) commonChanges).length = 3

Changes #1, #2, #3 go from non-volitive to volitive: the "unexpected" direction per [Nar10] p. 397. These are the three most frequent cross-linguistic changes (13, 9, 5 grams respectively).

theorem Narrog2010.directionality_via_subjectivity : (commonChanges.all fun (c : Change) => decide (c.source.orientation.toSubjectivityLevel ≤ c.target.orientation.toSubjectivityLevel)) = true

End-to-end: the speaker-orientation → subjectivity bridge preserves the directionality claim. Every attested change that increases speaker-orientation also increases (or maintains) subjectivity level.

Survey data on deontic necessity from a genealogically diverse sample of 200 languages ([Nar10] appendix; [Nar12] Table 6.6).

• Table 3 / Table 6.5: Area-level counts of NEC (obligation) and POT (ability/situational possibility) markers, split by 6 geographic areas.
• Table 4 / Table 6.6: Aggregate counts of deontic necessity type (strong, weak, neutral, indeterminate) — the finest-grained published data; per-language type assignments are not available.

The Table 4 total (60 + 62 + 22 + 32 = 176) exceeds 131 (languages with any NEC marker) because 44 languages have markers of multiple types ([Nar10] fn. 17).

inductive Narrog2010.DeonticNecessityType : Type

How a language grammaticalizes deontic necessity. From [Nar10] Table 4 / [Nar12] Table 6.6.

• strong : DeonticNecessityType
• weak : DeonticNecessityType
• neutral : DeonticNecessityType
• indeterminate : DeonticNecessityType

@[implicit_reducible]

instance Narrog2010.instDecidableEqDeonticNecessityType : DecidableEq DeonticNecessityType

Equations

• Narrog2010.instDecidableEqDeonticNecessityType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Narrog2010.instReprDeonticNecessityType.repr : DeonticNecessityType → ℕ → Std.Format

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@[implicit_reducible]

instance Narrog2010.instReprDeonticNecessityType : Repr DeonticNecessityType

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• Narrog2010.instReprDeonticNecessityType = { reprPrec := Narrog2010.instReprDeonticNecessityType.repr }

def Narrog2010.deonticNecessityCounts : List (DeonticNecessityType × ℕ)

Language counts by deontic necessity type.

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def Narrog2010.sampleSize : ℕ

The sample size: 200 genealogically diverse languages.

Equations

• Narrog2010.sampleSize = 200

inductive Narrog2010.Area : Type

Geographic area classification used in the sample.

• africa : Area
• americas : Area
• australia : Area
• eurasia : Area
• pacific : Area
• southSoutheastAsia : Area

@[implicit_reducible]

instance Narrog2010.instDecidableEqArea : DecidableEq Area

Equations

• Narrog2010.instDecidableEqArea x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Narrog2010.instReprArea : Repr Area

Equations

• Narrog2010.instReprArea = { reprPrec := Narrog2010.instReprArea.repr }

def Narrog2010.instReprArea.repr : Area → ℕ → Std.Format

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• Narrog2010.instReprArea.repr Narrog2010.Area.africa prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Narrog2010.Area.africa")).group prec✝
• Narrog2010.instReprArea.repr Narrog2010.Area.americas prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Narrog2010.Area.americas")).group prec✝
• Narrog2010.instReprArea.repr Narrog2010.Area.australia prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Narrog2010.Area.australia")).group prec✝
• Narrog2010.instReprArea.repr Narrog2010.Area.eurasia prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Narrog2010.Area.eurasia")).group prec✝
• Narrog2010.instReprArea.repr Narrog2010.Area.pacific prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Narrog2010.Area.pacific")).group prec✝

structure Narrog2010.AreaModalPresence : Type

Per-area counts of obligation (NEC) and ability/possibility (POT) marking. Source: [Nar10] Table 3 / [Nar12] Table 6.5.

• area : Area
• bothNecPot : ℕ
• onlyNec : ℕ
• onlyPot : ℕ
• neither : ℕ

@[implicit_reducible]

instance Narrog2010.instReprAreaModalPresence : Repr AreaModalPresence

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• Narrog2010.instReprAreaModalPresence = { reprPrec := Narrog2010.instReprAreaModalPresence.repr }

def Narrog2010.instReprAreaModalPresence.repr : AreaModalPresence → ℕ → Std.Format

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def Narrog2010.instBEqAreaModalPresence.beq : AreaModalPresence → AreaModalPresence → Bool

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• Narrog2010.instBEqAreaModalPresence.beq x✝¹ x✝ = false

@[implicit_reducible]

instance Narrog2010.instBEqAreaModalPresence : BEq AreaModalPresence

Equations

• Narrog2010.instBEqAreaModalPresence = { beq := Narrog2010.instBEqAreaModalPresence.beq }

def Narrog2010.AreaModalPresence.total (a : AreaModalPresence) : ℕ

Equations

• a.total = a.bothNecPot + a.onlyNec + a.onlyPot + a.neither

def Narrog2010.areaData : List AreaModalPresence

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

def Narrog2010.countOf (t : DeonticNecessityType) : ℕ

Count of a specific deontic necessity type.

Equations

• Narrog2010.countOf t = match List.find? (fun (x : Narrog2010.DeonticNecessityType × ℕ) => x.1 == t) Narrog2010.deonticNecessityCounts with | some (fst, n) => n | none => 0

def Narrog2010.areaSampleTotal : ℕ

Total languages across all areas.

Equations

• Narrog2010.areaSampleTotal = List.foldl (fun (x1 : ℕ) (x2 : Narrog2010.AreaModalPresence) => x1 + x2.total) 0 Narrog2010.areaData

def Narrog2010.languagesWithNec : ℕ

Total languages with any NEC marker (both + onlyNec).

Equations

• Narrog2010.languagesWithNec = List.foldl (fun (acc : ℕ) (a : Narrog2010.AreaModalPresence) => acc + a.bothNecPot + a.onlyNec) 0 Narrog2010.areaData

def Narrog2010.languagesWithPot : ℕ

Total languages with any POT marker (both + onlyPot).

Equations

• Narrog2010.languagesWithPot = List.foldl (fun (acc : ℕ) (a : Narrog2010.AreaModalPresence) => acc + a.bothNecPot + a.onlyPot) 0 Narrog2010.areaData

theorem Narrog2010.area_totals_sum_to_200 : areaSampleTotal = sampleSize

Area totals sum to the sample size.

theorem Narrog2010.nec_count : languagesWithNec = 131

Languages with any NEC marker: 121 + 10 = 131.

theorem Narrog2010.pot_count : languagesWithPot = 156

Languages with any POT marker: 121 + 35 = 156. (Paper says 157 = 121 + 35 + 1; the discrepancy is in the original.)

theorem Narrog2010.strong_count : countOf DeonticNecessityType.strong = 60

theorem Narrog2010.weak_count : countOf DeonticNecessityType.weak = 62

theorem Narrog2010.neutral_count : countOf DeonticNecessityType.neutral = 22

theorem Narrog2010.indeterminate_count : countOf DeonticNecessityType.indeterminate = 32

theorem Narrog2010.pot_more_common_than_nec : languagesWithPot > languagesWithNec

POT markers are more common than NEC markers cross-linguistically. [Nar10] p. 406: 156 vs 131.

def Narrog2010.toNarrogPosition : DeonticNecessityType → Semantics.Modality.Narrog.NarrogPosition

Map deontic necessity type to its position in Narrog's 3D space.

Strong obligation is performative + volitive + speaker-oriented: the speaker creates the obligation by uttering it. Weak obligation is descriptive: the speaker reports an existing norm. This difference explains the cross-linguistic asymmetry in grammaticalization.

Equations

• Narrog2010.toNarrogPosition Narrog2010.DeonticNecessityType.strong = Semantics.Modality.Narrog.strongObligation
• Narrog2010.toNarrogPosition Narrog2010.DeonticNecessityType.weak = Semantics.Modality.Narrog.weakObligation
• Narrog2010.toNarrogPosition Narrog2010.DeonticNecessityType.neutral = Semantics.Modality.Narrog.weakObligation
• Narrog2010.toNarrogPosition Narrog2010.DeonticNecessityType.indeterminate = Semantics.Modality.Narrog.dynamicAbility

theorem Narrog2010.strong_face_threatening : (toNarrogPosition DeonticNecessityType.strong).isFaceThreatening = true

Strong obligation is face-threatening (derived from 3D position).

theorem Narrog2010.weak_not_face_threatening : (toNarrogPosition DeonticNecessityType.weak).isFaceThreatening = false

Weak obligation is NOT face-threatening (descriptive, not performative).

theorem Narrog2010.face_threat_from_performativity : (toNarrogPosition DeonticNecessityType.strong).performativity ≠ (toNarrogPosition DeonticNecessityType.weak).performativity ∧ (toNarrogPosition DeonticNecessityType.strong).toRegion = (toNarrogPosition DeonticNecessityType.weak).toRegion

The face-threat asymmetry between strong and weak obligation is structurally explained: they differ only in performativity.

theorem Narrog2010.strong_obligation_minority : countOf DeonticNecessityType.strong < sampleSize / 2

Strong obligation is a minority pattern: only 60/200 languages.

theorem Narrog2010.weak_ge_strong : countOf DeonticNecessityType.weak ≥ countOf DeonticNecessityType.strong

Weak obligation (should-type) is at least as common as strong (must-type).

theorem Narrog2010.deontic_epistemic_shift_uncommon : (List.filter (fun (c : Change) => c.source.volitivity == Semantics.Modality.Narrog.Volitivity.volitive && c.target.volitivity == Semantics.Modality.Narrog.Volitivity.nonVolitive) commonChanges).length = 2

The deontic → epistemic shift is uncommon cross-linguistically.

Of the 8 most common modal changes (Bybee et al. 1994), only changes #6 and #7 go from volitive (deontic) to non-volitive (epistemic), and these are among the least frequent (3 and 2 grams respectively).

structure Narrog2010.PersonDistribution : Type

Person distribution for Japanese strong necessity -(a)nakereba naranai.

[Nar10] Table 5 (Chiang 2007: 72): of 115 tokens, 0 have a 2nd-person subject. This avoidance reflects the face-threatening nature of strong obligation directed at the addressee.

• construction : String
• firstPerson : ℕ
• secondPerson : ℕ
• thirdPerson : ℕ

@[implicit_reducible]

instance Narrog2010.instReprPersonDistribution : Repr PersonDistribution

Equations

• Narrog2010.instReprPersonDistribution = { reprPrec := Narrog2010.instReprPersonDistribution.repr }

def Narrog2010.instReprPersonDistribution.repr : PersonDistribution → ℕ → Std.Format

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

def Narrog2010.japaneseStrongNecessity : PersonDistribution

Equations

• Narrog2010.japaneseStrongNecessity = { construction := "-(a)nakereba naranai", firstPerson := 52, secondPerson := 0, thirdPerson := 63 }

def Narrog2010.japaneseAbbreviated : PersonDistribution

Equations

• Narrog2010.japaneseAbbreviated = { construction := "-(a)nakya/naktya", firstPerson := 35, secondPerson := 13, thirdPerson := 4 }

theorem Narrog2010.strong_avoids_second_person : japaneseStrongNecessity.secondPerson = 0

Strong necessity completely avoids 2nd-person subjects.

theorem Narrog2010.abbreviated_allows_second_person : japaneseAbbreviated.secondPerson > 0

The abbreviated form allows 2nd-person (mitigated by omitting the negative consequent).

theorem Narrog2010.strong_total : japaneseStrongNecessity.firstPerson + japaneseStrongNecessity.secondPerson + japaneseStrongNecessity.thirdPerson = 115

Total tokens for strong necessity.

theorem Narrog2010.abbreviated_total : japaneseAbbreviated.firstPerson + japaneseAbbreviated.secondPerson + japaneseAbbreviated.thirdPerson = 52

Total tokens for abbreviated form.

theorem Narrog2010.face_threat_predicts_avoidance : (toNarrogPosition DeonticNecessityType.strong).isFaceThreatening = true ∧ japaneseStrongNecessity.secondPerson = 0

The 2nd-person avoidance pattern is predicted by face-threat: strong necessity (face-threatening) avoids 2nd-person, while the abbreviated form (mitigated → less face-threatening) allows it.

This connects the pragmatic dimension (face-threat from performativity) to the distributional observation (person restrictions).