Uegaki and Sudo (2019): The hope-wh Puzzle

Uegaki and Sudo explain why non-veridical preferential predicates such as hope, wish, expect and fear reject interrogative complements, while veridical ones such as be happy and like accept them. A preferential predicate compares the degree to which its subject prefers an answer with a threshold set by a comparison class of focus alternatives, and it presupposes Threshold Significance, that some member of the class clears the threshold. With a question, the comparison class lies inside the question, so hope asserts no more than it presupposes and is true whenever defined; a meaning that is trivial in this way is ungrammatical. With a declarative, and for veridical predicates, which require the preferred answer to be true and believed, the meaning stays contingent.

Main statements

• hope_question_iff_significance: with a question, hope asserts its presupposition.
• exists_significance_not_hope_declarative: with a declarative, hope is not trivial.
• veridical_isDistributive, veridicality_breaks_triviality: veridical predicates are clausally distributive and not trivial.

Implementation notes

The non-veridical predicates are the substrate's degree-comparison predicates, Preferential.degreeComparison, and Threshold Significance is Degree.ThresholdSignificant. A veridical predicate is the same degree comparison applied to the answers that are true and believed, (26), with belief a predicate parameter. The concrete models measure preference in the reals. Anand and Hacquard's doxastic condition, (39), the selective focus sensitivity and exhaustivity refinements of section 4, and the about-nominalization of section 5 are not formalized. The examples are the rows of Data.Examples.UegakiSudo2019.

References

• [US19]
• [Vil08]
• [Rom15b]
• [Gaj02]
• [AH13]

Triviality for non-veridical preferentials

theorem UegakiSudo2019.significance_entails_hope_question {W : Type u_1} {E : Type u_2} {D : Type u_3} [LinearOrder D] (μ : E → W → Set W → D) (θ : Set (Set W) → D) {C Q : Set (Set W)} (hCQ : C ⊆ Q) (x : E) (w : W) (h : Degree.ThresholdSignificant (μ x w) θ C) : Preferential.degreeComparison μ θ C x Q w

With the comparison class drawn from the question, (30), Threshold Significance entails the assertion of hope with a question (36).

theorem UegakiSudo2019.hope_question_iff_significance {W : Type u_1} {E : Type u_2} {D : Type u_3} [LinearOrder D] (μ : E → W → Set W → D) (θ : Set (Set W) → D) {C Q : Set (Set W)} (hCQ : C ⊆ Q) (x : E) (w : W) : Preferential.degreeComparison μ θ C x Q w ↔ Degree.ThresholdSignificant (μ x w) θ C

With the comparison class inside the question, the assertion of hope with a question is its presupposition, so the meaning is true whenever defined. This is [Gaj02]'s L-analyticity, which makes hope anti-rogative.

theorem UegakiSudo2019.exists_significance_not_hope_declarative : ∃ (μ : Unit → Bool → Set Bool → ℝ) (θ : Set (Set Bool) → ℝ) (C : Set (Set Bool)), ∃ A ∈ C, Degree.ThresholdSignificant (μ () true) θ C ∧ ¬Preferential.degreeComparison μ θ C () {A} true

Hope with a declarative is not trivial (35). Threshold Significance over the focus alternatives does not settle whether the subject prefers the one proposition of the complement, as a model with a preferred alternative and a dispreferred complement shows.

Veridical preferentials

def UegakiSudo2019.veridical {W : Type u_1} {E : Type u_2} {D : Type u_3} [LinearOrder D] (μ : E → W → Set W → D) (θ : Set (Set W) → D) (believes : E → Set W → W → Prop) (C : Set (Set W)) (x : E) (Q : Set (Set W)) (w : W) : Prop

A veridical preferential such as be happy is the degree comparison over the answers that are true at the world of evaluation and believed by the subject, (24) and (26).

Equations

• UegakiSudo2019.veridical μ θ believes C x Q w = Preferential.degreeComparison μ θ C x (Q ∩ {p : Set W | w ∈ p ∧ believes x p w}) w

theorem UegakiSudo2019.veridical_isDistributive {W : Type u_1} {E : Type u_2} {D : Type u_3} [LinearOrder D] (μ : E → W → Set W → D) (θ : Set (Set W) → D) (believes : E → Set W → W → Prop) (C : Set (Set W)) : Distributivity.IsDistributive (veridical μ θ believes C)

Veridical preferentials are clausally distributive, so it is veridicality, not a failure of distributivity, that lets them take questions.

theorem UegakiSudo2019.veridicality_breaks_triviality : ∃ (μ : Unit → Bool → Set Bool → ℝ) (θ : Set (Set Bool) → ℝ) (believes : Unit → Set Bool → Bool → Prop) (Q : Set (Set Bool)), Degree.ThresholdSignificant (μ () false) θ Q ∧ Preferential.degreeComparison μ θ Q () Q false ∧ ¬veridical μ θ believes Q () Q false

Veridicality breaks the triviality. In a model where Threshold Significance holds, so that the non-veridical assertion is true, the veridical assertion is false at a world where the true answer is not the preferred one. The model has two worlds and the polar question over them, evaluated at the dispreferred world.