Pearson (2015): The Interpretation of the Logophoric Pronoun in Ewe

Pearson gives a semantics for the Ewe logophoric pronoun yè. On the view of Heim and von Stechow, after Chierchia, an attitude verb binds yè through the individual abstractor it introduces, so the pronoun has the attitude holder as antecedent and must be read de se. Her fieldwork finds it read de se or de re. She keeps the binding and lets yè also sit in a covert constituent with a concept generator, a map from a res to an individual concept. A generator is suitable when it is reliable, returning the res in the actual world or the holder for one of the holder's epistemic alternatives, and its concepts lie in the holder's conceptual cover.

Main statements

• sayDeRe_of_sayDeSe: the de se reading is the de re reading through the self concept, so it entails the de re reading when the holder is acquainted with herself as herself.
• claimDeRe_reliable: a de re claim about a res needs a concept in the cover that reliably returns it.
• ye_de_se_de_re_ambiguous: when John praises a paper he does not recognize as his own, the de se reading is false and the de re reading true.
• napoleon_contrast: when John believes himself Napoleon and calls the patient he sees on television delusional, John claims he is delusional is true and John claims Napoleon is delusional false.

Implementation notes

• Concepts are functions from centered worlds, the attitude alternatives of Lewis, to individuals, and a cover of Semantics/Reference/Acquaintance supplies acquaintance.
• Reliability is checked over a finite res domain, and each scenario is a finite model with one attitude alternative.
• The contrast between yè and PRO, a minimal pronoun that takes no long-distance antecedent, is not formalized.

References

• [Pea15]
• [Chi90]
• [PS03]
• [CS14]
• [Alo01]
• [Lew79a]
• [Kra09b]

Concept generators

@[reducible, inline]

abbrev Pearson2015.Centered (W : Type u_1) (E : Type u_2) : Type (max u_1 u_2)

A centered attitude alternative is a world with the individual the attitude holder identifies as herself there.

Equations

• Pearson2015.Centered W E = (W × E)

@[reducible, inline]

abbrev Pearson2015.Concept (W : Type u_1) (E : Type u_2) : Type (max u_2 u_1)

An individual concept is a function from centered worlds to individuals, an element of a Cover.

Equations

• Pearson2015.Concept W E = (Pearson2015.Centered W E → E)

@[reducible, inline]

abbrev Pearson2015.ConceptGenerator (W : Type u_1) (E : Type u_2) : Type (max u_2 u_1)

A concept generator takes a res to an individual concept.

Equations

• Pearson2015.ConceptGenerator W E = (E → Pearson2015.Concept W E)

@[reducible, inline]

abbrev Pearson2015.CProp (W : Type u_1) (E : Type u_2) : Type (max u_1 u_2)

A centered property holds of an individual at a world.

Equations

• Pearson2015.CProp W E = (E → W → Prop)

def Pearson2015.epiAlt {W : Type u_1} {E : Type u_2} (alts : List (Centered W E)) : List E

The epistemic alternatives of the attitude holder are the centers of her attitude alternatives.

Equations

• Pearson2015.epiAlt alts = List.map Prod.snd alts

def Pearson2015.selfConcept {W : Type u_1} {E : Type u_2} : Concept W E

The self concept returns the center of each alternative.

Equations

• Pearson2015.selfConcept = Prod.snd

def Pearson2015.sayDeSe {W : Type u_1} {E : Type u_2} (alts : List (Centered W E)) (P : CProp W E) : Prop

On the de se denotation of say (76), the embedded property holds of the center at each attitude alternative.

Equations

• Pearson2015.sayDeSe alts P = ∀ (p : Pearson2015.Centered W E), p ∈ alts → P p.2 p.1

def Pearson2015.Reliable {W : Type u_1} {E : Type u_2} [DecidableEq E] (alts : List (Centered W E)) (G : ConceptGenerator W E) (x : E) (w : W) (dom : List E) : Prop

A generator is reliable for holder x in w over the res domain dom (82) when for each res u its concept returns u in the actual world, or u is an epistemic alternative of x and the concept returns x.

Equations

• Pearson2015.Reliable alts G x w dom = ∀ (u : E), u ∈ dom → G u (w, x) = u ∨ u ∈ Pearson2015.epiAlt alts ∧ G u (w, x) = x

def Pearson2015.Suitable {W : Type u_1} {E : Type u_2} [DecidableEq E] (cover : Reference.Cover (Centered W E) E) (alts : List (Centered W E)) (G : ConceptGenerator W E) (x : E) (w : W) (dom : List E) : Prop

A generator is suitable for x in w (82) when it is reliable and acquaintance-based, each concept it produces lying in the holder's cover.

Equations

• Pearson2015.Suitable cover alts G x w dom = (Pearson2015.Reliable alts G x w dom ∧ ∀ (u : E), u ∈ dom → G u ∈ cover)

def Pearson2015.sayDeRe {W : Type u_1} {E : Type u_2} [DecidableEq E] (cover : Reference.Cover (Centered W E) E) (alts : List (Centered W E)) (P : CProp W E) (x : E) (w : W) (dom : List E) : Prop

On the de re denotation of say for a pronoun res (77), (79), some suitable generator, fed the center as res, picks an individual with the property at each alternative.

Equations

• Pearson2015.sayDeRe cover alts P x w dom = ∃ (G : Pearson2015.ConceptGenerator W E), Pearson2015.Suitable cover alts G x w dom ∧ ∀ (p : Pearson2015.Centered W E), p ∈ alts → P (G p.2 p) p.1

def Pearson2015.claimDeRe {W : Type u_1} {E : Type u_2} [DecidableEq E] (cover : Reference.Cover (Centered W E) E) (alts : List (Centered W E)) (P : CProp W E) (res x : E) (w : W) (dom : List E) : Prop

On the de re denotation for a name res (79), the generator is fed the fixed individual res rather than the center.

Equations

• One or more equations did not get rendered due to their size.

General consequences

theorem Pearson2015.sayDeRe_of_sayDeSe {W : Type u_1} {E : Type u_2} [DecidableEq E] {cover : Reference.Cover (Centered W E) E} {alts : List (Centered W E)} {P : CProp W E} {x : E} {w : W} {dom : List E} (hself : selfConcept ∈ cover) (hdom : ∀ (u : E), u ∈ dom → u = x ∨ u ∈ epiAlt alts) (h : sayDeSe alts P) : sayDeRe cover alts P x w dom

The de se reading is the de re reading through the self concept. When the self concept is in the holder's cover and every res in the domain is the holder or one of her epistemic alternatives, the de se reading entails the de re reading.

theorem Pearson2015.claimDeRe_reliable {W : Type u_1} {E : Type u_2} [DecidableEq E] {cover : Reference.Cover (Centered W E) E} {alts : List (Centered W E)} {P : CProp W E} {res x : E} {w : W} {dom : List E} (h : claimDeRe cover alts P res x w dom) (hres : res ∈ dom) : ∃ (f : Centered W E → E), f ∈ cover ∧ (f (w, x) = res ∨ res ∈ epiAlt alts ∧ f (w, x) = x)

A de re claim about a res in the domain needs a concept in the cover that reliably returns it, the res itself in the actual world, or the holder if the res is one of her epistemic alternatives.

Scenario 1: the de se / de re ambiguity (75), §5.3

John has found an old paper he wrote but does not recognize as his own; impressed, he says "Whoever wrote this is clever". John be yè le cleva, 'John said that yè was clever', is judged true, yet John never self-ascribes cleverness.

@[reducible, inline]

abbrev Pearson2015.Wld : Type

The worlds are the actual world and John's say-alternative.

Equations

• Pearson2015.Wld = Fin 2

@[reducible, inline]

abbrev Pearson2015.Ind : Type

The individuals are John and the author John takes to be someone else.

Equations

• Pearson2015.Ind = Fin 2

def Pearson2015.actual : Wld

Equations

• Pearson2015.actual = 0

def Pearson2015.bel : Wld

Equations

• Pearson2015.bel = 1

def Pearson2015.john : Ind

Equations

• Pearson2015.john = 0

def Pearson2015.auth : Ind

Equations

• Pearson2015.auth = 1

def Pearson2015.sayAlts : List (Centered Wld Ind)

John's single say-alternative is the belief world centered on John.

Equations

• Pearson2015.sayAlts = [(Pearson2015.bel, Pearson2015.john)]

def Pearson2015.dom : List Ind

The res domain holds the attitude holder alone.

Equations

• Pearson2015.dom = [Pearson2015.john]

def Pearson2015.cleverP : CProp Wld Ind

In the belief world the author is clever and John is not.

Equations

• Pearson2015.cleverP y w = (w = Pearson2015.bel ∧ y = Pearson2015.auth)

@[instance_reducible]

instance Pearson2015.instDecidableRelIndWldCleverP : DecidableRel cleverP

Equations

• Pearson2015.instDecidableRelIndWldCleverP x✝¹ x✝ = { decide := decide (x✝ = Pearson2015.bel) && decide (x✝¹ = Pearson2015.auth), reflects_decide := ⋯ }

def Pearson2015.authorConcept : Concept Wld Ind

The concept "the author of the paper" returns John in the actual world and the believed author in John's belief world.

Equations

• Pearson2015.authorConcept p = if p.1 = Pearson2015.actual then Pearson2015.john else Pearson2015.auth

def Pearson2015.authorGen : ConceptGenerator Wld Ind

The generator carrying the author concept for every res.

Equations

• Pearson2015.authorGen x✝ = Pearson2015.authorConcept

def Pearson2015.s1Cover : Reference.Cover (Centered Wld Ind) Ind

John's cover holds the author concept alone.

Equations

• Pearson2015.s1Cover = {Pearson2015.authorConcept}

theorem Pearson2015.deSe_false : ¬sayDeSe sayAlts cleverP

The de se reading is false, since at John's alternative the center, John, is not clever.

theorem Pearson2015.authorGen_suitable : Suitable s1Cover sayAlts authorGen john actual dom

The author generator is suitable for John, being reliable, as it returns John in the actual world, and in his cover.

theorem Pearson2015.deRe_true : sayDeRe s1Cover sayAlts cleverP john actual dom

The de re reading is true, since through the author concept the individual picked at John's alternative is clever.

theorem Pearson2015.ye_de_se_de_re_ambiguous : ¬sayDeSe sayAlts cleverP ∧ sayDeRe s1Cover sayAlts cleverP john actual dom

yè is de se or de re, the same sentence being false on the de se LF (78) and true on the de re LF (79).

Scenario 2: the Napoleon contrast (80) to (85), §6

John believes he is Napoleon; watching a report he does not recognize himself and says the patient he sees is delusional. John claims he is delusional, with yè read de re, is true; John claims Napoleon is delusional is false, though John believes he is Napoleon: the bound pronoun ranges over John's epistemic alternatives and is overwritten with John, whom he identifies through the in-cover "patient on television" concept, while the name denotes the actual Napoleon, to whom John bears no acquaintance.

@[reducible, inline]

abbrev Pearson2015.Napoleon.Wld : Type

The worlds are the actual world and John's claim-alternative.

Equations

• Pearson2015.Napoleon.Wld = Fin 2

@[reducible, inline]

abbrev Pearson2015.Napoleon.Ind : Type

The individuals are John, the patient John sees on television, and Napoleon.

Equations

• Pearson2015.Napoleon.Ind = Fin 3

def Pearson2015.Napoleon.actualN : Wld

Equations

• Pearson2015.Napoleon.actualN = 0

def Pearson2015.Napoleon.belN : Wld

Equations

• Pearson2015.Napoleon.belN = 1

def Pearson2015.Napoleon.john : Ind

Equations

• Pearson2015.Napoleon.john = 0

def Pearson2015.Napoleon.patient : Ind

Equations

• Pearson2015.Napoleon.patient = 1

def Pearson2015.Napoleon.napoleon : Ind

Equations

• Pearson2015.Napoleon.napoleon = 2

def Pearson2015.Napoleon.claimAlts : List (Centered Wld Ind)

John's claim-alternative is the belief world centered on John.

Equations

• Pearson2015.Napoleon.claimAlts = [(Pearson2015.Napoleon.belN, Pearson2015.Napoleon.john)]

def Pearson2015.Napoleon.delusionalP : CProp Wld Ind

In the belief world the patient is delusional.

Equations

• Pearson2015.Napoleon.delusionalP y w = (w = Pearson2015.Napoleon.belN ∧ y = Pearson2015.Napoleon.patient)

@[instance_reducible]

instance Pearson2015.Napoleon.instDecidableRelIndWldDelusionalP : DecidableRel delusionalP

Equations

• Pearson2015.Napoleon.instDecidableRelIndWldDelusionalP x✝¹ x✝ = { decide := decide (x✝ = Pearson2015.Napoleon.belN) && decide (x✝¹ = Pearson2015.Napoleon.patient), reflects_decide := ⋯ }

def Pearson2015.Napoleon.patientConcept : Concept Wld Ind

The concept "the patient I saw on television" returns John in the actual world and the patient in John's belief world.

Equations

• Pearson2015.Napoleon.patientConcept p = if p.1 = Pearson2015.Napoleon.actualN then Pearson2015.Napoleon.john else Pearson2015.Napoleon.patient

def Pearson2015.Napoleon.patientGen : ConceptGenerator Wld Ind

The generator carrying the patient concept for every res.

Equations

• Pearson2015.Napoleon.patientGen x✝ = Pearson2015.Napoleon.patientConcept

def Pearson2015.Napoleon.johnCover : Reference.Cover (Centered Wld Ind) Ind

John's cover holds the patient concept alone, so no concept in it returns the actual Napoleon.

Equations

• Pearson2015.Napoleon.johnCover = {Pearson2015.Napoleon.patientConcept}

theorem Pearson2015.Napoleon.claimsHe_true : sayDeRe johnCover claimAlts delusionalP john actualN [john]

John claims he is delusional is true de re, since the center, John, fed to the patient generator, is the delusional patient at the alternative.

theorem Pearson2015.Napoleon.claimsNapoleon_false : ¬claimDeRe johnCover claimAlts delusionalP napoleon john actualN [napoleon]

John claims Napoleon is delusional is false, since the only concept in John's cover returns John, not Napoleon, in the actual world, and Napoleon is not an epistemic alternative of John.

theorem Pearson2015.Napoleon.napoleon_contrast : sayDeRe johnCover claimAlts delusionalP john actualN [john] ∧ ¬claimDeRe johnCover claimAlts delusionalP napoleon john actualN [napoleon]

In the Napoleon contrast the bound-pronoun reading is true and the name reading false.