@cite{mizuno-2024} — Anderson Conditionals Crosslinguistically

@cite{anderson-1951} @cite{condoravdi-2002} @cite{schlenker-2004} @cite{von-fintel-iatridou-2023}

Teruyuki Mizuno (2024). "Strategies for Anderson Conditionals: Their Implications for the Typology of O-Marking and X-Marking." Semantics and Pragmatics 17(8): 1–14.

Key Empirical Generalizations

1. English requires X-marking: O-marking (present tense) renders Anderson conditionals trivially true — the consequent holds throughout the non-expanded domain D (ex. 2).
2. Japanese requires O-marking: X-marking (Past -ta in the consequent) yields a counterfactual reading, contradicting the Anderson follow-up (ex. 4a with #ta). O-marking (Non-Past -ru) is felicitous because Historical Present expands D without CF morphology (ex. 4a with ru).
3. Mandarin patterns with Japanese: perfective le functions as X-marking, blocking both Anderson and FLV readings (ex. 13a).
4. FLV correlation: X-marking availability for Anderson conditionals and for Future Less Vivid conditionals stand or fall together (§4.2).

Data Sources

• Examples (1)–(2): English X-marking vs O-marking
• Example (4a): Japanese O-marking (ru) vs X-marking (#ta)
• Example (7a): Japanese radical HP case (indexicals ototoi, kinoo evaluate against utterance time)
• Example (13a): Mandarin O-marking (no le) vs X-marking (#le)
• §4.2 (8)–(10): English vs Japanese FLV
• §4.2 (11)–(13): Mandarin FLV and Anderson

structure Mizuno2024.AndersonDatum : Type

A datum for Anderson conditional strategies.

Each datum records how a language expresses (or fails to express) an Anderson conditional, and whether the resulting form is felicitous for the Anderson reading.

• language : String

  Language name

• exampleNumber : String

  Example number in @cite{mizuno-2024}

• antecedentForm : String

  Morphological form of the antecedent

• consequentForm : String

  Morphological form of the consequent

• hasXMarking : Bool

  Whether this datum uses X-marking (counterfactual morphology). Where X-marking surfaces varies by language: in English, both antecedent and consequent; in Japanese, Past -ta in consequent; in Mandarin, perfective le in consequent.

• felicitousForAnderson : Bool

  Whether the form is felicitous for an Anderson reading

• gloss : String

  Gloss of the example

• translation : String

  English translation

def Mizuno2024.instReprAndersonDatum.repr : AndersonDatum → ℕ → Std.Format

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@[implicit_reducible]

instance Mizuno2024.instReprAndersonDatum : Repr AndersonDatum

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• Mizuno2024.instReprAndersonDatum = { reprPrec := Mizuno2024.instReprAndersonDatum.repr }

structure Mizuno2024.FLVAvailabilityDatum : Type

A datum for FLV X-marking availability per language.

• language : String

  Language name

• xMarkingAvailable : Bool

  Whether X-marking is available for FLV conditionals

def Mizuno2024.instReprFLVAvailabilityDatum.repr : FLVAvailabilityDatum → ℕ → Std.Format

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@[implicit_reducible]

instance Mizuno2024.instReprFLVAvailabilityDatum : Repr FLVAvailabilityDatum

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• Mizuno2024.instReprFLVAvailabilityDatum = { reprPrec := Mizuno2024.instReprFLVAvailabilityDatum.repr }

def Mizuno2024.english_xMarking : AndersonDatum

English Anderson conditional with X-marking (@cite{mizuno-2024}, ex. 1a).

@cite{anderson-1951}: "If Jones had taken arsenic, he would show exactly those symptoms which he does in fact show."

X-marking in antecedent (past perfect). The consequent describes observed reality ("is now showing"), recovering the actual world despite counterfactual morphology. Felicitous for Anderson reading.

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def Mizuno2024.english_oMarking : AndersonDatum

English Anderson conditional with O-marking (@cite{mizuno-2024}, ex. 2).

O-marking (present tense) renders the conditional trivially true: the domain is not expanded, so the consequent (an observed fact) holds in all accessible worlds. Infelicitous for Anderson reading (@cite{stalnaker-1975}, @cite{von-fintel-1999-subjunctive}).

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def Mizuno2024.japanese_oMarking : AndersonDatum

Japanese Anderson conditional with O-marking (@cite{mizuno-2024}, ex. 4a, -ru variant). Non-Past -ru in the consequent triggers Historical Present: the evaluation time shifts backward, expanding the domain under branching time (@cite{schlenker-2004}, @cite{condoravdi-2002}). Felicitous for Anderson reading.

Tasikani, Jones-si-ga sakuya hiso-o nom-eba, kare-ga ima mise-tei-ru syoozyoo-to mattaku onazi syoozyoo-o ima mise-ru hazuda. 'You're right. If Jones took arsenic last night, he would show exactly the same symptoms as he is now showing.'

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def Mizuno2024.japanese_xMarking : AndersonDatum

Japanese Anderson conditional with X-marking (@cite{mizuno-2024}, ex. 4a, #ta variant). Past -ta in the consequent gives a counterfactual reading that implies the falsity of the antecedent, contradicting the Anderson follow-up (4b). The entire sequence is infelicitous.

Tasikani, Jones-si-ga sakuya hiso-o nom-eba, ... syoozyoo-o ima mise-#ta hazuda. Soosuruto, kare-wa hontooni hiso-o non-da no daroo. With Past -ta: infelicitous for Anderson reading.

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def Mizuno2024.japanese_radicalHP : AndersonDatum

Japanese radical HP case (@cite{mizuno-2024}, ex. 7a). The consequent event clearly lies in the past, forced by the temporal adverbial kinoo 'yesterday'. Non-Past is still required — Past makes the sentence counterfactual. Temporal indexicals ototoi 'two days ago' and kinoo 'yesterday' evaluate against the utterance time (θ = origin), paralleling @cite{schlenker-2004}'s HP analysis.

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def Mizuno2024.mandarin_oMarking : AndersonDatum

Mandarin Anderson conditional with O-marking (@cite{mizuno-2024}, ex. 13a, no final le). No perfective le in the consequent → Anderson reading available.

Ruguo Jones zuotian he le pishuang, jiu hui chuxian ta xianzai shiji chuxian de zheyangde zhengzhuang. 'If Jones had drunk arsenic yesterday, he would show exactly the symptoms he is actually showing.'

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def Mizuno2024.mandarin_xMarking : AndersonDatum

Mandarin Anderson conditional with X-marking (@cite{mizuno-2024}, ex. 13a, #le). Perfective le in the consequent blocks the Anderson reading. Like Japanese Past -ta, Mandarin le induces strong counterfactuality, contradicting the Anderson follow-up.

Ruguo Jones zuotian he le pishuang, jiu hui chuxian ta xianzai shiji chuxian de zheyangde zhengzhuang #le. With final le: infelicitous for Anderson reading.

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def Mizuno2024.english_flv : FLVAvailabilityDatum

English: X-marking available for FLV (@cite{mizuno-2024}, ex. 8a). "If John came tomorrow, the party would be fun, ... but he probably won't come tomorrow, I think."

Equations

• Mizuno2024.english_flv = { language := "English", xMarkingAvailable := true }

def Mizuno2024.japanese_flv : FLVAvailabilityDatum

Japanese: X-marking NOT available for FLV (@cite{mizuno-2024}, ex. 9–10). Past -ta in FLV induces strong counterfactuality (10a), contradicting the follow-up (10b). O-marking (Non-Past -u) is required (9a).

Equations

• Mizuno2024.japanese_flv = { language := "Japanese", xMarkingAvailable := false }

def Mizuno2024.mandarin_flv : FLVAvailabilityDatum

Mandarin: X-marking NOT available for FLV (@cite{mizuno-2024}, ex. 11–12). Perfective le in FLV blocks the unlikeliness follow-up (12b). O-marking (no le) is required (11a).

Equations

• Mizuno2024.mandarin_flv = { language := "Mandarin", xMarkingAvailable := false }

theorem Mizuno2024.xMarking_felicity : english_xMarking.felicitousForAnderson = true ∧ japanese_xMarking.felicitousForAnderson = false ∧ mandarin_xMarking.felicitousForAnderson = false

X-marking is felicitous for Anderson in English but not Japanese or Mandarin.

theorem Mizuno2024.oMarking_felicity : english_oMarking.felicitousForAnderson = false ∧ japanese_oMarking.felicitousForAnderson = true ∧ mandarin_oMarking.felicitousForAnderson = true

O-marking is felicitous for Anderson in Japanese and Mandarin but not English.

theorem Mizuno2024.complementary_strategies : english_xMarking.felicitousForAnderson ≠ english_oMarking.felicitousForAnderson ∧ japanese_oMarking.felicitousForAnderson ≠ japanese_xMarking.felicitousForAnderson ∧ mandarin_oMarking.felicitousForAnderson ≠ mandarin_xMarking.felicitousForAnderson

Each language has exactly one felicitous strategy for Anderson conditionals.

def Mizuno2024.english_strategy : Semantics.Modality.Exclusion.MarkingStrategy

English uses X-marking for Anderson conditionals: X-marking is felicitous (ex. 1a), O-marking is not (ex. 2).

Equations

• Mizuno2024.english_strategy = Semantics.Modality.Exclusion.MarkingStrategy.xMarking

def Mizuno2024.japanese_strategy : Semantics.Modality.Exclusion.MarkingStrategy

Japanese uses O-marking for Anderson conditionals: O-marking is felicitous (ex. 4a -ru), X-marking is not (ex. 4a #ta).

Equations

• Mizuno2024.japanese_strategy = Semantics.Modality.Exclusion.MarkingStrategy.oMarking

def Mizuno2024.mandarin_strategy : Semantics.Modality.Exclusion.MarkingStrategy

Mandarin uses O-marking for Anderson conditionals: O-marking is felicitous (ex. 13a without le), X-marking is not (ex. 13a with #le).

Equations

• Mizuno2024.mandarin_strategy = Semantics.Modality.Exclusion.MarkingStrategy.oMarking

theorem Mizuno2024.english_strategy_matches : english_strategy.hasXMarking = english_xMarking.hasXMarking

English: strategy predicts X-marking = felicitous datum's marking.

theorem Mizuno2024.japanese_strategy_matches : japanese_strategy.hasXMarking = japanese_oMarking.hasXMarking

Japanese: strategy predicts no X-marking = felicitous datum's marking.

theorem Mizuno2024.mandarin_strategy_matches : mandarin_strategy.hasXMarking = mandarin_oMarking.hasXMarking

Mandarin: strategy predicts no X-marking = felicitous datum's marking.

theorem Mizuno2024.english_xMarking_has_xMarking : english_xMarking.hasXMarking = true

theorem Mizuno2024.english_oMarking_no_xMarking : english_oMarking.hasXMarking = false

theorem Mizuno2024.japanese_oMarking_no_xMarking : japanese_oMarking.hasXMarking = false

theorem Mizuno2024.japanese_xMarking_has_xMarking : japanese_xMarking.hasXMarking = true

theorem Mizuno2024.mandarin_oMarking_no_xMarking : mandarin_oMarking.hasXMarking = false

theorem Mizuno2024.mandarin_xMarking_has_xMarking : mandarin_xMarking.hasXMarking = true

structure Mizuno2024.LanguageProfile : Type

A language profile bundles the Anderson marking strategy with independently recorded FLV X-marking availability.

The FLV availability is an empirical observation, not derived from the Anderson strategy. The correlation between the two is a theorem over the attested data, not a definitional identity.

• language : String
• andersonStrategy : Semantics.Modality.Exclusion.MarkingStrategy
• flvXMarkingAvailable : Bool

def Mizuno2024.instReprLanguageProfile.repr : LanguageProfile → ℕ → Std.Format

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@[implicit_reducible]

instance Mizuno2024.instReprLanguageProfile : Repr LanguageProfile

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• Mizuno2024.instReprLanguageProfile = { reprPrec := Mizuno2024.instReprLanguageProfile.repr }

def Mizuno2024.english_profile : LanguageProfile

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• Mizuno2024.english_profile = { language := "English", andersonStrategy := Semantics.Modality.Exclusion.MarkingStrategy.xMarking, flvXMarkingAvailable := true }

def Mizuno2024.japanese_profile : LanguageProfile

Equations

• Mizuno2024.japanese_profile = { language := "Japanese", andersonStrategy := Semantics.Modality.Exclusion.MarkingStrategy.oMarking, flvXMarkingAvailable := false }

def Mizuno2024.mandarin_profile : LanguageProfile

Equations

• Mizuno2024.mandarin_profile = { language := "Mandarin", andersonStrategy := Semantics.Modality.Exclusion.MarkingStrategy.oMarking, flvXMarkingAvailable := false }

theorem Mizuno2024.flv_anderson_correlation : english_profile.flvXMarkingAvailable = english_profile.andersonStrategy.hasXMarking ∧ japanese_profile.flvXMarkingAvailable = japanese_profile.andersonStrategy.hasXMarking ∧ mandarin_profile.flvXMarkingAvailable = mandarin_profile.andersonStrategy.hasXMarking

@cite{mizuno-2024} §4.2: X-marking for Anderson conditionals and X-marking for FLV conditionals stand or fall together.

This is an empirical generalization over English, Japanese, and Mandarin — not a logical necessity. The correlation could be explained by a Blocking Principle (@cite{chierchia-1998}): covert HP expansion is blocked when overt X-marking is available, but further research is needed.

theorem Mizuno2024.flv_data_matches_profiles : english_profile.flvXMarkingAvailable = english_flv.xMarkingAvailable ∧ japanese_profile.flvXMarkingAvailable = japanese_flv.xMarkingAvailable ∧ mandarin_profile.flvXMarkingAvailable = mandarin_flv.xMarkingAvailable

The FLV data agrees with the language profiles.

theorem Mizuno2024.english_xMarking_layers_match_flv : Iatridou2000.english_flv.pastLayers = Iatridou2000.CounterfactualType.flv.exclFCount

English X-marking for Anderson conditionals uses the same number of past layers as Iatridou's FLV type: 1 layer = 1 modal ExclF.

@cite{mizuno-2024} §4.2 predicts this correlation: X-marking availability for Anderson conditionals and for FLV stand or fall together (English has both). @cite{iatridou-2000} provides the independent morphological count.

theorem Mizuno2024.english_strategy_is_modal_excl : english_strategy.exclDimension = some Semantics.Modality.Exclusion.ExclDimension.modal

English X-marking strategy maps to modal ExclDimension, consistent with @cite{iatridou-2000}'s analysis of counterfactual past as modal exclusion.

theorem Mizuno2024.japanese_strategy_no_excl : japanese_strategy.exclDimension = none

Japanese O-marking strategy has no ExclDimension — no counterfactual morphology. The domain expansion comes from HP backward time shift, not from world exclusion.

theorem Mizuno2024.mandarin_strategy_no_excl : mandarin_strategy.exclDimension = none

Mandarin O-marking strategy has no ExclDimension, paralleling Japanese.