Ramotowska, Marty, Romoli, and Santorio (2025): Counterfactuals and Quantificational Force #
Ramotowska, Marty, Romoli, and Santorio compare three theories of counterfactuals on quantified
sentences in mixed scenarios, where some but not all of the players would have won. The universal
theory of Lewis and Kratzer quantifies over the closest antecedent worlds (2); Stalnaker's
selectional theory evaluates the whole sentence at a selected world and supervaluates over the
candidate selections after composition (5); the homogeneity theory of von Fintel and Križ gives
each counterfactual a third status during composition (6). Unembedded, the last two agree that a
single player's counterfactual has a third status and the first calls it false (Table 1,
unembedded). Embedded under a quantifier they part ways: the universal theory makes the
sentence turn on its polarity (universal_polarity), the selectional theory on its
quantificational force, the universal sentences false and the existential ones true whatever the
question under discussion (selectional_force), and the homogeneity theory leaves every
quantified sentence undefined under either projection algorithm (homogeneity_undefined), so
that only there is a gap for a question under discussion to resolve, as it does for the plural
definite of the same scenario (dissociation). Bassi and Bar-Lev's implicature variant (§8)
mispredicts some and not all (implicature_some, implicature_notAll). The paper's two
experiments find the force effect and no effect of the question under discussion on
counterfactuals, alongside a question effect on plural definites, the pattern of the selectional
theory.
Implementation notes #
A scenario is a similarity ordering, an antecedent, and one consequent per player. Mixedness is stated as the paper's setting has it: every closest antecedent world has a winner and a loser, and every player wins in one closest world and loses in another. The homogeneity theory's projection through a quantifier is the Kleene aggregation of the players' trivalent values, conjunctive or disjunctive over the values or their negations; the paper notes that the choice makes no difference when every instance is undefined, and its Table 3 row for that theory, which rests on a pragmatic resolution of undefinedness by the question under discussion, is not derived. Force is the paper's binary, universal against existential, which differs from the weak/strong labels Barwise and Cooper give no. The mean ratings and mixed-effects models of §5 and §6 are not restated.
References #
Quantified counterfactuals #
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- RamotowskaEtAl2025.instDecidableEqQuant x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- RamotowskaEtAl2025.instReprQuant = { reprPrec := RamotowskaEtAl2025.instReprQuant.repr }
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- One or more equations did not get rendered due to their size.
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Quantificational force is the paper's binary, on which all and none are universal and some and not all existential.
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- RamotowskaEtAl2025.instDecidableEqForce x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- RamotowskaEtAl2025.instReprForce = { reprPrec := RamotowskaEtAl2025.instReprForce.repr }
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- One or more equations did not get rendered due to their size.
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The force of a quantifier.
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A quantifier is positive when it is all or some, and negative when it is none or not all.
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The selectional theory's verdict in a mixed scenario is fixed by force alone.
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The quantifier applied to a domain and a predicate.
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- RamotowskaEtAl2025.Quant.all.eval D P = ∀ d ∈ D, P d
- RamotowskaEtAl2025.Quant.none.eval D P = ∀ d ∈ D, ¬P d
- RamotowskaEtAl2025.Quant.some.eval D P = ∃ d ∈ D, P d
- RamotowskaEtAl2025.Quant.notAll.eval D P = ∃ d ∈ D, ¬P d
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The quantifier projects through the players' trivalent values by the Kleene meet for the universal quantifiers and the Kleene join for the existential ones, over the values or their negations.
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- RamotowskaEtAl2025.Quant.all.aggregate D v = D.inf v
- RamotowskaEtAl2025.Quant.none.aggregate D v = D.inf fun (d : ι) => -v d
- RamotowskaEtAl2025.Quant.some.aggregate D v = D.sup v
- RamotowskaEtAl2025.Quant.notAll.aggregate D v = D.sup fun (d : ι) => -v d
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Mixed scenarios #
A scenario is mixed, win some and lose some, when there are players, every closest antecedent world has a winner and a loser among them, and every player wins in some closest world and loses in another.
- nonempty : D.Nonempty
- worlds (w' : W) : w' ∈ (ord w).minimals A → (∃ d ∈ D, w' ∈ B d) ∧ ∃ d ∈ D, w' ∉ B d
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The theories on a quantified sentence #
The universal theory (2) applies the quantifier to the players' universal counterfactuals.
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- RamotowskaEtAl2025.universal ord A w D B q = q.eval D fun (d : ι) => w ∈ Conditional.closestImp ord A (B d)
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The selectional theory (5) takes the selectional counterfactual of the quantified sentence, the sentence evaluated at the selected world and supervaluated over the candidate selections.
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- RamotowskaEtAl2025.selectional ord A w D B q = Conditional.selectionalCounterfactual ord A {v : W | q.eval D fun (d : ι) => v ∈ B d} w
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On the homogeneity theory (6) each player's counterfactual carries its third status into composition, and the quantifier projects it.
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- RamotowskaEtAl2025.homogeneity ord A w D B q = q.aggregate D fun (d : ι) => Conditional.homogeneityCounterfactual ord A (B d) w
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The implicature theory (§8) pairs the basic existential meaning (23) with its exhaustified universal strengthening (24), the latter computed in the upward-entailing scope of some and the former in the downward-entailing scope of not all.
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- RamotowskaEtAl2025.implicature ord A w D B RamotowskaEtAl2025.Quant.all = ∀ d ∈ D, w ∈ Conditional.closestImp ord A (B d)
- RamotowskaEtAl2025.implicature ord A w D B RamotowskaEtAl2025.Quant.none = ∀ d ∈ D, w ∉ Conditional.might (Conditional.closestImp ord) A (B d)
- RamotowskaEtAl2025.implicature ord A w D B RamotowskaEtAl2025.Quant.some = ∃ d ∈ D, w ∈ Conditional.closestImp ord A (B d)
- RamotowskaEtAl2025.implicature ord A w D B RamotowskaEtAl2025.Quant.notAll = ∃ d ∈ D, w ∉ Conditional.might (Conditional.closestImp ord) A (B d)
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Predictions in mixed scenarios #
In the unembedded case of Table 1 a player's counterfactual is false on the universal theory, indeterminate on the selectional theory, and undefined on the homogeneity theory.
The universal theory turns on polarity, since every player's counterfactual is false, so the positive sentences are false and the negative ones true.
In the selectional row of Table 3 the quantified sentence is determinately false for the universal quantifiers and determinately true for the existential ones, whatever the polarity, because every selected world has a winner and a loser.
No selectional value is a gap, so there is nothing for a question under discussion to resolve.
Every player's counterfactual is undefined, so the quantified sentence is undefined under either projection algorithm, for every quantifier, and the homogeneity theory leaves the sentences to pragmatics.
With the implicature computed in its scope, some says that some player was guaranteed to win (25), which is false in the scenario.
With the basic existential meaning in its scope, not all says that some player could not have won (26), which is false in the scenario.
Experiment 2 dissociates the two constructions. At a world where some but not all of the players won, the plural definite the players won has a gap, while the quantified counterfactuals of the same scenario have none.