@cite{francescotti-1995}

Even: The Conventional Implicature Approach Reconsidered. Linguistics and Philosophy 18: 153–173.

Francescotti defends and revises the Implicature Account (IA) of "even" against Lycan's quantifier approach. The core contribution is a revised felicity condition: S* must be more surprising than MOST (not ONE, not ALL) of its true neighbors.

Key Claims

(a) "Even" does not make a truth-functional difference; it contributes via conventional implicature (Equivalence Thesis). (b) "Even" is epistemic: it implies surprise, unexpectedness, or unlikelihood. (c) "Even" is scalar: unexpectedness comes in degrees. (d) Felicity requires S* to be more surprising than MOST true neighbors — not just one (@cite{bennett-1982}), not all (@cite{karttunen-peters-1979}).

Formalization

We derive the Equivalence Thesis and threshold choice from the English fragment entry, then encode the two key counterexamples as finite scenarios and prove that only Francescotti's "most" threshold gives the correct predictions for both.

theorem Phenomena.Focus.Studies.Francescotti1995.equivalence_thesis : Fragments.English.FocusParticles.even_.truthFunctional = false

Equivalence Thesis (§V(a)): "Even A is F" is true just in case "A is F" is true. "Even" does not make a truth-functional difference. Derived from the fragment entry.

theorem Phenomena.Focus.Studies.Francescotti1995.even_contributes_via_ci : Fragments.English.FocusParticles.even_.contributionLayer = Core.Semantics.ContentLayer.ContentLayer.implicature

"Even" contributes via conventional implicature, not assertion. Derived from the fragment entry.

theorem Phenomena.Focus.Studies.Francescotti1995.even_threshold_is_most : Fragments.English.FocusParticles.even_.threshold = some Semantics.FocusParticles.EvenThreshold.most

The fragment specifies Francescotti's "most" threshold.

structure Phenomena.Focus.Studies.Francescotti1995.EvenScenario : Type

A scenario for testing "even" felicity predictions. Each scenario specifies surprise levels for the prejacent and its contextually-determined neighbors, plus the observed felicity judgment.

• description : String

  Description

• prejacent : ℕ

  Surprise level of S* (higher = more surprising = less likely)

• neighbors : List ℕ

  Surprise levels of the neighbor alternatives

• felicitous : Bool

  Observed felicity (true = felicitous)

def Phenomena.Focus.Studies.Francescotti1995.instReprEvenScenario.repr : EvenScenario → ℕ → Std.Format

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instance Phenomena.Focus.Studies.Francescotti1995.instReprEvenScenario : Repr EvenScenario

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• Phenomena.Focus.Studies.Francescotti1995.instReprEvenScenario = { reprPrec := Phenomena.Focus.Studies.Francescotti1995.instReprEvenScenario.repr }

def Phenomena.Focus.Studies.Francescotti1995.predict (s : EvenScenario) (t : Semantics.FocusParticles.EvenThreshold) : Bool

Predict felicity for a scenario under a given threshold.

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• Phenomena.Focus.Studies.Francescotti1995.predict s t = Semantics.FocusParticles.evenPresupWith s.prejacent s.neighbors (fun (a b : ℕ) => decide (a > b)) t

def Phenomena.Focus.Studies.Francescotti1995.predictFromFragment (s : EvenScenario) : Bool

Predict felicity using the threshold from the English fragment.

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Scenario 1: "Even Albert passed the exam"

Albert is one of the best chemistry students. He and Marie (the very best) are both very likely to pass. Three weaker students have higher surprise for passing.

Bennett predicts felicitous (Albert exceeds Marie), but the sentence is actually infelicitous — Albert's passing is completely unsurprising.

def Phenomena.Focus.Studies.Francescotti1995.scenario1 : EvenScenario

Albert passing is unsurprising (level 2); Marie even less so (level 1). Three other students have high surprise (5, 7, 8).

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theorem Phenomena.Focus.Studies.Francescotti1995.bennett_wrong_on_scenario1 : predict scenario1 Semantics.FocusParticles.EvenThreshold.existential ≠ scenario1.felicitous

Bennett (∃) wrongly predicts felicitous: Albert(2) exceeds Marie(1).

theorem Phenomena.Focus.Studies.Francescotti1995.kp_correct_on_scenario1 : predict scenario1 Semantics.FocusParticles.EvenThreshold.universal = scenario1.felicitous

K-P (∀) correctly predicts infelicitous here (but will fail on scenario 2).

theorem Phenomena.Focus.Studies.Francescotti1995.francescotti_correct_on_scenario1 : predict scenario1 Semantics.FocusParticles.EvenThreshold.most = scenario1.felicitous

Francescotti (most) correctly predicts infelicitous: Albert(2) exceeds only 1 of 4 neighbors (25% < 50%).

Scenario 2: "Even Albert failed the exam"

Albert is one of the best students, so failing is very surprising. Marie is even better, so her failing would be even MORE surprising. Three weaker students have low surprise for failing.

K-P predicts infelicitous (Albert doesn't exceed Marie), but the sentence is actually felicitous — Albert failing IS very surprising.

def Phenomena.Focus.Studies.Francescotti1995.scenario2 : EvenScenario

Albert failing is very surprising (level 8); Marie even more so (level 9). Three weaker students have low surprise for failing (3, 2, 1).

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theorem Phenomena.Focus.Studies.Francescotti1995.bennett_correct_on_scenario2 : predict scenario2 Semantics.FocusParticles.EvenThreshold.existential = scenario2.felicitous

Bennett (∃) correctly predicts felicitous here.

theorem Phenomena.Focus.Studies.Francescotti1995.kp_wrong_on_scenario2 : predict scenario2 Semantics.FocusParticles.EvenThreshold.universal ≠ scenario2.felicitous

K-P (∀) wrongly predicts infelicitous: Albert(8) doesn't exceed Marie(9).

theorem Phenomena.Focus.Studies.Francescotti1995.francescotti_correct_on_scenario2 : predict scenario2 Semantics.FocusParticles.EvenThreshold.most = scenario2.felicitous

Francescotti (most) correctly predicts felicitous: Albert(8) exceeds 3 of 4 neighbors (75% > 50%).

theorem Phenomena.Focus.Studies.Francescotti1995.francescotti_uniquely_correct : predict scenario1 Semantics.FocusParticles.EvenThreshold.most = scenario1.felicitous ∧ predict scenario2 Semantics.FocusParticles.EvenThreshold.most = scenario2.felicitous ∧ predict scenario1 Semantics.FocusParticles.EvenThreshold.existential ≠ scenario1.felicitous ∧ predict scenario2 Semantics.FocusParticles.EvenThreshold.universal ≠ scenario2.felicitous

Francescotti's "most" threshold is the only one that matches observed felicity judgments on both scenarios.

theorem Phenomena.Focus.Studies.Francescotti1995.fragment_predictions_correct : predictFromFragment scenario1 = scenario1.felicitous ∧ predictFromFragment scenario2 = scenario2.felicitous

The English fragment entry for "even" gives correct predictions on both scenarios (since it specifies .most).

Gradient Felicity

Francescotti argues that felicity comes in degrees, determined by: (a) how much S* surpasses neighbors in surprise (degree of excess), and (b) how many neighbors S* surpasses (proportion exceeded).

The Andre/height example (p. 164): if Andre is BY FAR the tallest person, "Even Andre cannot reach the top shelf" is VERY felicitous. If he's tallest by a small margin, it's less felicitous.

def Phenomena.Focus.Studies.Francescotti1995.proportionExceeded (s : EvenScenario) : ℚ

Proportion of alternatives exceeded, as a rational in [0, 1]. Captures Francescotti's gradient: higher = more felicitous.

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def Phenomena.Focus.Studies.Francescotti1995.meanExcess (s : EvenScenario) : ℚ

Average surprise margin over exceeded alternatives. Captures how MUCH S* surpasses its neighbors (dimension (a)).

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def Phenomena.Focus.Studies.Francescotti1995.felicityDegree (s : EvenScenario) : ℚ

Combined felicity degree: proportion × mean excess. Higher values = more felicitous.

Equations

• Phenomena.Focus.Studies.Francescotti1995.felicityDegree s = Phenomena.Focus.Studies.Francescotti1995.proportionExceeded s * Phenomena.Focus.Studies.Francescotti1995.meanExcess s

theorem Phenomena.Focus.Studies.Francescotti1995.scenario2_more_felicitous_than_scenario1 : felicityDegree scenario1 < felicityDegree scenario2

Scenario 2 (Albert failing) has higher felicity degree than scenario 1 (Albert passing), matching the intuition that scenario 2 is felicitous and scenario 1 is not.

def Phenomena.Focus.Studies.Francescotti1995.scenarioAndreFar : EvenScenario

Andre far above average: very high felicity degree.

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def Phenomena.Focus.Studies.Francescotti1995.scenarioAndreBarely : EvenScenario

Andre barely tallest: lower felicity degree.

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theorem Phenomena.Focus.Studies.Francescotti1995.andre_far_more_felicitous : felicityDegree scenarioAndreBarely < felicityDegree scenarioAndreFar

Andre by far exceeds more, matching Francescotti's gradient intuition.