Left-Nested Conditionals: Empirical Data

@cite{gibbard-1981} @cite{haegeman-2003} @cite{iatridou-1991} @cite{lassiter-2025}

Theory-neutral empirical observations about left-nested conditionals (LNCs) from @cite{cao-white-lassiter-2025} "Sorting out left-nested conditionals."

Overview

LNCs have the form "If (B if A), C" - a conditional whose antecedent is itself a conditional.

This file documents:

1. Gibbard's classic example and discourse effects
2. Cross-linguistic markers (Japanese, German)
3. NPI/PPI licensing patterns
4. Coordination constraints
5. Only + inversion patterns
6. Modal/generic exceptions

structure Phenomena.Conditionals.LeftNested.LNCDatum : Type

Left-nested conditional empirical datum.

Captures a single LNC example with its properties and judgments.

• sentence : String

  The full sentence

• innerConditional : String

  The inner conditional ("B if A")

• outerConsequent : String

  The outer consequent ("C")

• content : String

  Content type: "bare", "modal", "generic", "quantAdv"

• discourseContext : Option String

  Optional discourse context that improves acceptability

• acceptability : String

  Acceptability judgment: "ok", "odd", "marginal"

• interpretation : String

  Preferred interpretation: "PC", "HC", "ambiguous"

• notes : String

  Additional notes

instance Phenomena.Conditionals.LeftNested.instReprLNCDatum : Repr LNCDatum

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• Phenomena.Conditionals.LeftNested.instReprLNCDatum = { reprPrec := Phenomena.Conditionals.LeftNested.instReprLNCDatum.repr }

def Phenomena.Conditionals.LeftNested.instReprLNCDatum.repr : LNCDatum → Nat → Std.Format

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Gibbard's Example @cite{gibbard-1981}

The classic example of a left-nested conditional, discussed extensively in the philosophical literature on conditionals.

def Phenomena.Conditionals.LeftNested.gibbardOutOfBlue : LNCDatum

Gibbard's classic LNC (out of the blue)

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def Phenomena.Conditionals.LeftNested.gibbardWithContext : LNCDatum

Gibbard's example with discourse context

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Discourse Effects

LNCs improve dramatically when the inner conditional is established in prior discourse.

def Phenomena.Conditionals.LeftNested.ex11_decontextualized : LNCDatum

Example 11: Decontextualized LNC

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def Phenomena.Conditionals.LeftNested.ex12_contextualized : LNCDatum

Example 12: Contextualized LNC

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def Phenomena.Conditionals.LeftNested.ex13_contextual : LNCDatum

Example 13: Another LNC

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def Phenomena.Conditionals.LeftNested.ex14_givenThat : LNCDatum

Example 14: LNC with given-that paraphrase

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Japanese Conditional Markers

Japanese distinguishes:

• -ra / -tara: HC-only marker
• nara: Can mark PCs

LNCs with nara are acceptable; with -ra they are not.

def Phenomena.Conditionals.LeftNested.ex15_japaneseNara : LNCDatum

Example 15: Japanese nara in LNC

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def Phenomena.Conditionals.LeftNested.ex16_japaneseRa : LNCDatum

Example 16: Japanese -ra in LNC

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def Phenomena.Conditionals.LeftNested.ex17_naraEcho : LNCDatum

Example 17: Japanese nara echoing discourse

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German Conditional Markers

German distinguishes:

• falls: HC-only marker (implies speaker uncertainty)
• wenn: Can mark either HC or PC

LNCs with wenn are acceptable; with falls they are marginal/bad.

def Phenomena.Conditionals.LeftNested.ex20_germanWenn : LNCDatum

Example 20: German wenn in LNC

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def Phenomena.Conditionals.LeftNested.ex21_germanFalls : LNCDatum

Example 21: German falls in LNC

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def Phenomena.Conditionals.LeftNested.ex22_fallsModal : LNCDatum

Example 22: German falls with modal

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Polarity Patterns

The PC analysis predicts specific polarity patterns in LNCs:

• PPIs licensed in embedded consequent (B position)
• NPIs blocked in embedded consequent (B position)

def Phenomena.Conditionals.LeftNested.ex29_ppiOk : LNCDatum

Example 29: PPI in embedded consequent (ok)

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def Phenomena.Conditionals.LeftNested.ex30_npiBad : LNCDatum

Example 30: NPI in embedded consequent (bad)

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def Phenomena.Conditionals.LeftNested.ex31_ppiSomeone : LNCDatum

Example 31: Another PPI case

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def Phenomena.Conditionals.LeftNested.ex32_npiAnyone : LNCDatum

Example 32: Another NPI case

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Coordination Constraints

@cite{haegeman-2003}: Premise conditionals resist coordination with other conditional clauses. This extends to LNCs.

def Phenomena.Conditionals.LeftNested.ex33_coordinatedHC : LNCDatum

Example 33: Coordinated HCs (ok)

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def Phenomena.Conditionals.LeftNested.ex34_coordinatedLNC : LNCDatum

Example 34: Coordinated with LNC (bad)

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def Phenomena.Conditionals.LeftNested.ex35_coordinationDiagnostic : LNCDatum

Example 35: Coordination diagnostic

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Only + Inversion

Another diagnostic from @cite{haegeman-2003}: PCs block only + subject-aux inversion, while HCs allow it.

def Phenomena.Conditionals.LeftNested.ex36_onlyInversionHC : LNCDatum

Example 36: Only-inversion with HC (ok)

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def Phenomena.Conditionals.LeftNested.ex37_onlyInversionLNC : LNCDatum

Example 37: Only-inversion with LNC (bad)

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def Phenomena.Conditionals.LeftNested.ex38_noInversion : LNCDatum

Example 38: Without inversion (ok)

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Modal and Generic Exceptions

LNCs with modals, quantificational adverbs, or generic interpretations CAN be interpreted as HCs, allowing broader distribution.

def Phenomena.Conditionals.LeftNested.ex40_modal : LNCDatum

Example 40: Modal in inner conditional

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def Phenomena.Conditionals.LeftNested.ex41_quantAdv : LNCDatum

Example 41: Quantificational adverb

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def Phenomena.Conditionals.LeftNested.ex42_generic : LNCDatum

Example 42: Generic reading

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def Phenomena.Conditionals.LeftNested.ex43_habitual : LNCDatum

Example 43: Habitual reading

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def Phenomena.Conditionals.LeftNested.gibbardData : List LNCDatum

All Gibbard-related examples

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• Phenomena.Conditionals.LeftNested.gibbardData = [Phenomena.Conditionals.LeftNested.gibbardOutOfBlue, Phenomena.Conditionals.LeftNested.gibbardWithContext]

def Phenomena.Conditionals.LeftNested.discourseData : List LNCDatum

All discourse contextualization examples

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def Phenomena.Conditionals.LeftNested.japaneseData : List LNCDatum

All Japanese examples

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def Phenomena.Conditionals.LeftNested.germanData : List LNCDatum

All German examples

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def Phenomena.Conditionals.LeftNested.polarityData : List LNCDatum

All polarity examples

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def Phenomena.Conditionals.LeftNested.coordinationData : List LNCDatum

All coordination examples

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def Phenomena.Conditionals.LeftNested.onlyInversionData : List LNCDatum

All only-inversion examples

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def Phenomena.Conditionals.LeftNested.exceptionData : List LNCDatum

All modal/generic exception examples

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def Phenomena.Conditionals.LeftNested.allData : List LNCDatum

All LNC data

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Core Empirical Generalizations

1. Discourse Anchoring

Bare LNCs improve dramatically when the inner conditional is established in prior discourse.

2. Cross-Linguistic Markers

Languages with distinct HC/PC markers show that LNCs pattern with PCs:

• Japanese: nara (PC-compatible) ok, -ra (HC-only) blocked
• German: wenn (both) ok, falls (HC-only) degraded

3. Polarity Patterns

• PPIs licensed in embedded consequent (B position)
• NPIs blocked in embedded consequent (B position) Consistent with PC (not HC) reading.

4. Coordination Constraints

LNCs resist coordination with other conditional clauses, like other PCs.

5. Only + Inversion

LNCs block only + subject-aux inversion, like other PCs.

6. Modal/Generic Exception

LNCs with modals, quantificational adverbs, or generic interpretation CAN be HCs, because these provide "object-level" content that can be genuinely supposed without prior discourse.