Subject-Auxiliary Inversion: Empirical Data

@cite{radford-2009} @cite{adger-2003} @cite{sag-wasow-bender-2003} @cite{chomsky-1957} @cite{henry-1995} @cite{klima-1964} @cite{mccloskey-2006} @cite{westergaard-2009}

Theory-neutral data on subject-auxiliary inversion (SAI) in English and beyond.

The Phenomenon

In English, finite auxiliaries invert with the subject in matrix questions but not in embedded questions. This basic pattern interacts with negation, conditionals, exclamatives, and shows systematic dialectal variation.

Classic Data

The core SAI pattern has been a central case study in generative syntax since @cite{chomsky-1957}. Textbook presentations: @cite{radford-2009}, @cite{adger-2003}, @cite{sag-wasow-bender-2003}.

Boundary Cases

Several phenomena push beyond the textbook treatment:

• Negative inversion
• Conditional inversion
• Embedded inversion in non-standard varieties
• Do-support and verb movement
• Verb-specific acquisition of inversion

inductive Phenomena.WordOrder.SubjectAuxInversion.SAIContext : Type

The syntactic context in which SAI does or does not occur.

• matrixWh : SAIContext

  Matrix wh-question: "What can John eat?"

• matrixYN : SAIContext

  Matrix yes/no question: "Can John eat pizza?"

• embedded : SAIContext

  Embedded question: "I wonder what John can eat"

• echo : SAIContext

  Echo question: "John can eat WHAT?"

• negativeInversion : SAIContext

  Negative fronting: "Never have I seen such a thing"

• conditionalInversion : SAIContext

  Conditional inversion: "Had I known, I would have come"

• exclamative : SAIContext

  Exclamative: "Boy, is it hot!"

• soNeither : SAIContext

  So/neither inversion: "So did I" / "Neither can she"

• embeddedDialectal : SAIContext

  Embedded inversion (dialectal): "I asked could he come"

• sententialNegation : SAIContext

  Sentential negation (parallel to SAI for do-support): "Sue does not eat fish" / "Sue is not eating fish"

• verbRaising : SAIContext

  Verb raising diagnostic (adverb/quantifier placement): "Jean embrasse souvent Marie" vs "*John kisses often Mary"

• tagQuestion : SAIContext

  Tag question: "She likes him, doesn't she?"

• vpEllipsis : SAIContext

  VP ellipsis (stranded tense): "She runs faster than he does"

• emphatic : SAIContext

  Emphatic/verum focus: "Sue DOES eat fish"

instance Phenomena.WordOrder.SubjectAuxInversion.instDecidableEqSAIContext : DecidableEq SAIContext

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• Phenomena.WordOrder.SubjectAuxInversion.instDecidableEqSAIContext x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.WordOrder.SubjectAuxInversion.instReprSAIContext : Repr SAIContext

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• Phenomena.WordOrder.SubjectAuxInversion.instReprSAIContext = { reprPrec := Phenomena.WordOrder.SubjectAuxInversion.instReprSAIContext.repr }

def Phenomena.WordOrder.SubjectAuxInversion.instReprSAIContext.repr : SAIContext → Nat → Std.Format

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def Phenomena.WordOrder.SubjectAuxInversion.instBEqSAIContext.beq : SAIContext → SAIContext → Bool

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• Phenomena.WordOrder.SubjectAuxInversion.instBEqSAIContext.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.WordOrder.SubjectAuxInversion.instBEqSAIContext : BEq SAIContext

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• Phenomena.WordOrder.SubjectAuxInversion.instBEqSAIContext = { beq := Phenomena.WordOrder.SubjectAuxInversion.instBEqSAIContext.beq }

inductive Phenomena.WordOrder.SubjectAuxInversion.Acceptability : Type

Acceptability judgment.

• grammatical : Acceptability
• ungrammatical : Acceptability
• marginal : Acceptability
• dialectal : Acceptability

  Grammatical in some dialects but not Standard American/British English

instance Phenomena.WordOrder.SubjectAuxInversion.instDecidableEqAcceptability : DecidableEq Acceptability

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• Phenomena.WordOrder.SubjectAuxInversion.instDecidableEqAcceptability x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.WordOrder.SubjectAuxInversion.instReprAcceptability.repr : Acceptability → Nat → Std.Format

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instance Phenomena.WordOrder.SubjectAuxInversion.instReprAcceptability : Repr Acceptability

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• Phenomena.WordOrder.SubjectAuxInversion.instReprAcceptability = { reprPrec := Phenomena.WordOrder.SubjectAuxInversion.instReprAcceptability.repr }

instance Phenomena.WordOrder.SubjectAuxInversion.instBEqAcceptability : BEq Acceptability

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• Phenomena.WordOrder.SubjectAuxInversion.instBEqAcceptability = { beq := Phenomena.WordOrder.SubjectAuxInversion.instBEqAcceptability.beq }

def Phenomena.WordOrder.SubjectAuxInversion.instBEqAcceptability.beq : Acceptability → Acceptability → Bool

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• Phenomena.WordOrder.SubjectAuxInversion.instBEqAcceptability.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

structure Phenomena.WordOrder.SubjectAuxInversion.SAIDatum : Type

A single SAI judgment.

• sentence : String

  The example sentence

• inverted : Bool

  Whether the sentence shows auxiliary/verb-before-subject order

• context : SAIContext

  The syntactic context

• acceptability : Acceptability

  Acceptability judgment

• language : String

  Language (default: English)

• description : String

  Description of what this datum tests

• citation : String

  Citation for the datum

def Phenomena.WordOrder.SubjectAuxInversion.instReprSAIDatum.repr : SAIDatum → Nat → Std.Format

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instance Phenomena.WordOrder.SubjectAuxInversion.instReprSAIDatum : Repr SAIDatum

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• Phenomena.WordOrder.SubjectAuxInversion.instReprSAIDatum = { reprPrec := Phenomena.WordOrder.SubjectAuxInversion.instReprSAIDatum.repr }

def Phenomena.WordOrder.SubjectAuxInversion.instBEqSAIDatum.beq : SAIDatum → SAIDatum → Bool

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• Phenomena.WordOrder.SubjectAuxInversion.instBEqSAIDatum.beq x✝¹ x✝ = false

instance Phenomena.WordOrder.SubjectAuxInversion.instBEqSAIDatum : BEq SAIDatum

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• Phenomena.WordOrder.SubjectAuxInversion.instBEqSAIDatum = { beq := Phenomena.WordOrder.SubjectAuxInversion.instBEqSAIDatum.beq }

Matrix wh-questions

Wh-questions in root clauses require SAI in Standard English. The auxiliary must precede the subject.

def Phenomena.WordOrder.SubjectAuxInversion.ex01 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex02 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex03 : SAIDatum

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Matrix yes/no questions

Polar questions also require SAI.

def Phenomena.WordOrder.SubjectAuxInversion.ex04 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex05 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex06 : SAIDatum

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Embedded questions

Embedded questions in Standard English prohibit SAI. The complementizer or wh-word alone marks the clause as interrogative.

def Phenomena.WordOrder.SubjectAuxInversion.ex07 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex08 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex09 : SAIDatum

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Echo questions

Echo questions preserve declarative word order with prosodic focus on the wh-element. No SAI occurs.

def Phenomena.WordOrder.SubjectAuxInversion.ex10 : SAIDatum

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When a negative or restrictive adverbial is fronted, SAI is obligatory. This is surprising on a purely interrogative analysis of inversion — negative inversion occurs in declaratives, not questions. It is a key argument for treating SAI as a structural phenomenon (head movement to C or feature-driven) rather than an illocutionary one.

def Phenomena.WordOrder.SubjectAuxInversion.ex11 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex12 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex13 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex14 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex15 : SAIDatum

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Counterfactual conditionals allow omission of 'if' with obligatory SAI. This is restricted to 'had', 'were', and 'should', suggesting it is a lexically specific rather than fully productive process.

def Phenomena.WordOrder.SubjectAuxInversion.ex16 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex17 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex18 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex19 : SAIDatum

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SAI also occurs in exclamatives and in 'so'/'neither' constructions. These extend the phenomenon beyond interrogatives.

def Phenomena.WordOrder.SubjectAuxInversion.ex20 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex21 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex22 : SAIDatum

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Standard English prohibits SAI in embedded questions, but several dialects productively allow it. This is a key testing ground for syntactic theory:

• Belfast English: Embedded inversion with specific verbs (wonder, ask, know) but not others (tell).
• Hiberno-English: More general embedded inversion, including with 'if' complements. The dialectal data challenges any analysis that categorically ties SAI to root CP structure. It suggests the [+Q] or [+wh] feature can license T-to-C in embedded clauses under the right parametric conditions.

def Phenomena.WordOrder.SubjectAuxInversion.ex23 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex24 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex25 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex26 : SAIDatum

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@cite{pollock-1989} established that French and English differ fundamentally in verb movement. French lexical verbs obligatorily raise to I (T), placing them before adverbs, negation, and floating quantifiers. English lexical verbs stay in situ, below adverbs and negation.

This contrast is the reason English has do-support and restricts SAI to auxiliaries: English lexical verbs cannot raise to T (let alone to C), so when T must be spelled out in C (for SAI) or above negation, a dummy 'do' is inserted instead.

(Pollock 2) Negation: a. *John likes not Mary. (English: V cannot raise past negation) b. Jean n'aime pas Marie. (French: V raises past negation)

(Pollock 3) Questions / SAI: a. *Likes he Mary? (English: lexical V cannot invert) b. Aime-t-il Marie? (French: lexical V inverts)

(Pollock 4) Adverb placement: a. *John kisses often Mary. (English: V cannot raise past adverb) b. Jean embrasse souvent Marie. (French: V raises past adverb) c. John often kisses Mary. (English: adverb precedes V) d. *Jean souvent embrasse Marie. (French: adverb cannot precede V)

(Pollock 5) Floating quantifiers: a. *My friends love all Mary. (English: V cannot raise past FQ) b. Mes amis aiment tous Marie. (French: V raises past FQ) c. My friends all love Mary. (English: FQ precedes V) d. *Mes amis tous aiment Marie. (French: FQ cannot precede V)

The four diagnostics converge: French V raises, English V does not. English auxiliaries do raise (hence "John has often eaten" is grammatical), which is why they can participate in SAI while lexical verbs cannot.

def Phenomena.WordOrder.SubjectAuxInversion.ex_p01 : SAIDatum

Pollock (3): French lexical verb inversion

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def Phenomena.WordOrder.SubjectAuxInversion.ex_p02 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex_p03 : SAIDatum

Pollock (4): Adverb placement diagnostic

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def Phenomena.WordOrder.SubjectAuxInversion.ex_p04 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex_p05 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex_p06 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex_p07 : SAIDatum

Pollock (2): Negation diagnostic

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def Phenomena.WordOrder.SubjectAuxInversion.ex_p08 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex_p09 : SAIDatum

Pollock (5): Floating quantifier diagnostic

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def Phenomena.WordOrder.SubjectAuxInversion.ex_p10 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex_p11 : SAIDatum

English auxiliaries DO raise (unlike lexical verbs) — same diagnostic

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def Phenomena.WordOrder.SubjectAuxInversion.ex_p12 : SAIDatum

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SAI interacts with do-support: when no auxiliary is present, 'do' is inserted to host tense and carry out inversion.

@cite{arregi-pietraszko-2021} unify upward displacement (T-to-C in SAI) and downward displacement (T-to-V lowering) as a single operation: Generalized Head Movement (GenHM). Under GenHM, the same mechanism of M-value sharing drives both. The crucial empirical support is that lexical verbs trigger do-support in all three contexts where tense cannot lower — negation, verum focus, and SAI — while auxiliaries invert directly in all three. This parallel is predicted if SAI and T-lowering are the same operation (displacement of T) with spelling out at the highest strong terminal.

(A&P 36) Lexical verbs — do-support in negation / verum / SAI: a. Sue does not eat fish. (*Sue not eats fish) b. Sue DOES eat fish. (*Sue EATS fish [verum]) c. Where does Sue eat fish? (*Where eats Sue fish?)

(A&P 37) Auxiliaries — direct displacement, no do-support: a. Sue is not eating fish. (*Sue does not be eating fish) b. Sue IS eating fish. (*Sue DOES be eating fish [verum]) c. Where is Sue eating fish? (*Where does Sue be eating fish?)

The do-support facts raise a puzzle for T-to-C analyses: if T moves to C, why is a dummy 'do' needed rather than affix-lowering simply being blocked? Arregi & Pietraszko resolve this by treating the spell-out position as a PF decision, independent of the syntactic feature-sharing operation.

def Phenomena.WordOrder.SubjectAuxInversion.ex27 : SAIDatum

Do-support with lexical verbs in SAI

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def Phenomena.WordOrder.SubjectAuxInversion.ex28 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex29 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex30 : SAIDatum

Auxiliaries invert without do-support

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def Phenomena.WordOrder.SubjectAuxInversion.ex31 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex32 : SAIDatum

The negation/verum parallel (same auxiliary vs lexical verb contrast)

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def Phenomena.WordOrder.SubjectAuxInversion.ex33 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex34 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex35 : SAIDatum

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Three further contexts where tense needs overt support, completing the paradigm of environments that trigger do-insertion with lexical verbs.

def Phenomena.WordOrder.SubjectAuxInversion.ex36 : SAIDatum

Tag question with do-support

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def Phenomena.WordOrder.SubjectAuxInversion.ex37 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex38 : SAIDatum

VP ellipsis with stranded tense

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def Phenomena.WordOrder.SubjectAuxInversion.ex39 : SAIDatum

Verum focus (emphatic 'do')

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def Phenomena.WordOrder.SubjectAuxInversion.ex40 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.ex41 : SAIDatum

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def Phenomena.WordOrder.SubjectAuxInversion.allData : List SAIDatum

All individual SAI data points.

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def Phenomena.WordOrder.SubjectAuxInversion.classicData : List SAIDatum

Classic core data (matrix + embedded questions only).

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def Phenomena.WordOrder.SubjectAuxInversion.nonInterrogativeData : List SAIDatum

Non-interrogative SAI contexts (negative, conditional, exclamative).

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def Phenomena.WordOrder.SubjectAuxInversion.dialectalData : List SAIDatum

Dialectal variation data.

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def Phenomena.WordOrder.SubjectAuxInversion.pollockData : List SAIDatum

French/English verb movement contrast.

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def Phenomena.WordOrder.SubjectAuxInversion.crossLinguisticData : List SAIDatum

Cross-linguistic data (non-English).

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def Phenomena.WordOrder.SubjectAuxInversion.doSupportData : List SAIDatum

Do-support interaction data.

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