Believe as Strong but Subjective Todor Koev University of Konstanz - - PowerPoint PPT Presentation

Believe as Strong but Subjective

Todor Koev

University of Konstanz

Lepore Semantics Workshop, Rutgers University April 26, 2019

The Hintikkan orthodoxy

The verb believe encodes a universal quantifier over possible

• worlds. A belief attribution states that the prejacent is true in

all of the agent’s doxastic alternatives (Hintikka 1969). (1) [[believe]]w = λp λx .∀w′ ∈ Doxx,w : p(w′) Two (related) problems:

Gradability Strength

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Gradability

Believe is a gradable predicate:

John partially believes that ... John fully believes that ... John believes more strongly than Mary that ... ...

Unclear how the gradability property can be captured if the force of believe is fixed by a (universal) quantifier once and for all.

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Strength

No predictions as to how strongly unmodified uses of believe commit the agent to the prejacent. Dox is defined as the set of all worlds compatible with everything the agent “believes”, so the issue of strength is shifted to the metalanguage. Whatever the strength of believe, it needs to be stipulated.

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How strong is believe?

Does (2) entail (a) or just (b)? (2) I believe Tulsi will win the next election.

• a. I’m certain Tulsi will win the next election.
• b. I find it likely Tulsi will win the next election.

Two views (Cr = credence/subjective probability function): (3) Strong view (Sauerland 2008; Clark 2013; a.o.) [[believe]](p)(x) iff Crx(p) = 1 (4) Weak view (Hawthorne et al. 2016) [[believe]](p)(x) iff Crx(p) > θbel, where typically (but not always) θbel = 0.5

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Against ambiguity

How about a weak/strong ambiguity? Conceptual worry: The two alleged readings are logically dependent (the strong entails the weak). Empirical worry: (5) should have a reading along the lines of (6), but it does not. (5) #I believewk he is going to win but I don’t believestr it. (6) It’s likely he is going to win but it’s not certain.

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Claims

Believe is not quantificational. It is a gradable predicate that encodes a measure function. Believe is a maximum-degree absolute predicate (in the sense

• f Kennedy & McNally 2005). In its unmodified use it refers

to the top of the scale. Believe is strong but subjective. The intuition of weakness arises as a particular type of scalar inference that denies full public commitments.

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Roadmap

Data

Supporting data Seemingly contradicting data

Proposal

Gradability Conjunction closure Hedging

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Supporting data : Gradability 1

Unger’s 1971 typology of gradable adjectives:

relative adjectives (e.g. tall): the comparison standard is contextually selected from the middle of the scale absolute adjectives (e.g. full): the comparison standard is fixed as the minimum or the maximum of the scale

Kennedy & McNally 2005: the relative/absolute distinction boils down to differences in scale structure:

totally open scale (0,1) relative standard

• nly lower closed scale [0,1)

minimum standard

• nly upper closed scale (0,1]

maximum standard totally closed scale [0,1] maximum standard

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Supporting data : Gradability 2

Believe combines with a whole suite of degree modifiers. (7) believe more strongly than comparatives (8) believe as strongly as equatives (9) partially believe minimality modifiers (10) strongly believe maximality modifiers (11) believe 95 percent proportional modifiers The compatibility with minimum, maximum, and proportional modifiers argues that believe is associated with a totally closed scale, by assumption [0,1] ⊆ R. According to Kennedy & McNally 2005, believe must be a maximum-degree absolute predicate, i.e. it is strong.

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Supporting data : Missing quantity implicatures

Non-strong scalar terms routinely trigger scalar implicatures. (12) Most of the students came to the party. Not all of the students came to the party. (13) According to Mary, most of the students came to the party. According to Mary, not all of the students came to the party. Believe does not (usually) trigger such inferences. (14) Kamala believes America needs universal health care. Kamala is not convinced America needs UHC. (15) According to the press, Kamala believes America needs universal health care. According to the press, Kamala is not convinced America needs universal health care.

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Supporting data : Closure under conjunction 1

The conjunction closure property (M = any modal): (16) M(p)∧M(q) M(p ∧q) Strong modals are closed under conjunction. (17) It’s certain Sean is in Rome and it’s certain he is catholic. It’s certain Sean is in Rome and he is catholic. Non-strong modals are not. (18) Each week Jack spends (in no particular order) 3 nights at the local pub and gets drunk, 2 nights at the same pub but stays sober, and 2 nights at home where he also gets drunk. On a given night, I say: Jack is probably at the pub. True, chance=5/7 Jack is probably drunk. True, chance=5/7 Jack is probably at the pub drunk. False, chance=3/7

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Supporting data : Closure under conjunction 2

Believe is closed under conjunction, so it must be strong. (19) Ron believes Mia is hawt and he also believes she is going to marry him. Ron believes that Mia is hawt and that she is going to marry him. What about the Lottery Paradox (Kyburg 1961)?

Lack of belief that any individual ticket won, belief that some ticket won. About the norms of rational belief, not about the way the verb believe is used by speakers.

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Seemingly contradicting data : Gradation

If believe is strong, it should be able to strengthen weaker modals and it should not allow for further strengthening. However: believe cannot strengthen think, which some authors view as weak (Hawthorne et al. 2016). (20) ??Tim thinks it’s raining, but he doesn’t believe that it is.

Response: Think is synonymous with believe (but not gradable).

Also: believe can be strengthened by know. (21) Scientists believe there is water on Mars. In fact, they know it.

However, know is presuppositionally stronger (and perhaps truth-conditionally different) but need not raise the certainty level of the agent.

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Seemingly contradicting data : Neg-raising

Believe is a classic neg-raising predicate. (22) John doesn’t believe it’s raining. John believes it’s not raining. Are neg-raising and modal strength correlated? Hawthorne et al.’s 2016 hypothesis: Neg-raising occurs with “weak” verbs (want, like) but not with “strong” verbs (need, love), so believe must be weak. Horn’s 1989 crosslinguistic generalization contradicts this hypothesis:

Weak scalars (possible, allowed) never license neg-raising. Midscalars (likely) typically do. Strong scalars (know, certain) may or may not license it.

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Seemingly contradicting data : Hedging 1

A statement of belief can be understood as a hedge. (23) I believe it’s raining, but I’m not sure that it is. (Hawthorne et al. 2016) My claim: Hedging uses establish a contrast between privately held convictions (“subjective” certainty) and publicly expressed commitments (“objective” certainty). (23) ≈ “The speaker is fully confident that it is raining but she does not want to publicly commit to it (presumably because she lacks sufficient evidence)”. There is no contradiction between strong believe and reduced commitment.

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Seemingly contradicting data : Hedging 2

Hedging is sensitive to the QUD, so it is likely due to an additional inference. (24) I believe Tulsi will win the next election.

• a. Weak: We are making predictions about who the

next president of the US is going to be.

• b. Strong: We are playing a game where everyone is

required to state some of their beliefs. Generalization: The weak reading is not available if the belief component is relevant to the QUD. (25) {Is capitalism better than socialism?} I believe capitalism is better than socialism (but I’m not sure). (26) {Tell me about your political beliefs.} I believe capitalism is better than socialism (?but I’m not sure).

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The proposal in brief

A gradable semantics for believe which explains the interaction with degree morphology. A straightforward derivation of the conjunction closure property. Believe as encoding a subjective measure that is compatible with weak public commitments.

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Degree semantics 1

A degree-based semantics for believe (cf. Cresswell 1976; von Stechow 1984; Kennedy 1999). (27) [[believe]] = λpλdλx.Crx(p) ≥ d Without overt degree morphology, the threshold value is contributed by a silent pos morpheme (Kennedy & McNally 2005). (28) [[pos]]C = λPλx.∃d[standard(d,P,C)∧P(d)(x)] (29) standard(d,P,C) =    d > avg{µP(x)|x ∈ C} if P is relative d > min(SP) if P is min degree d = max(SP) if P is max degree

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Degree semantics 2

Believe is maximal degree. (30) [[pos [believes it’s raining]]] = λx.∃d [d = 1∧Crx([[rain]]) ≥ d] = λx.Crx([[rain]]) = 1 [believe p] can combine with overt degree modifiers that

• therwise attach to gradable adjectives. Example:

(31) [[partially]] = λPλx.∃d[d > min(SP)∧P(d)(x)] (32) [[partially [believes eating pizza is healthy]]] = λx .∃d[d > 0∧Crx([[eat pizza healthy]]) ≥ d] = λx .Crx([[eat pizza healthy]]) > 0

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Conjunction closure

Closure property (reminder): (33) M(p)∧M(q) M(p ∧q) Closure follows from the degree-based semantics because of the following fact of probability theory: (34) If Crx(p) = 1 and Crx(q) = 1, then Crx(p ∩q) = 1. Thus, x believes p and x believes q entail x believes [p and q].

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Hedging : The idea

Believe and know are truth-conditionally (or at least “contextually”) equivalent but know adds a factive inference. (35) [[believe]]w = λpλdλx .Crx,w(p) ≥ d (36) [[know]]w = λpλdλx : p(w).Crx,w(p) ≥ d Uttering a sentence with believe antipresupposes that the presupposition of know (=the complement of believe) is not accepted as true (cf. Heim 1991; Percus 2006; Sauerland 2008). (37) Utterance: John believes it’s raining. Alternative utterance: John knows it’s raining. Antipresupposition: It’s not sure that it’s raining. We can use this mechanism to explain the intuition of weak believe (Chemla 2008).

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Hedging : Subjective v. objective certainty

Two types of certainty:

Subjective certainty (Cr): privately held, need not be based

• n evidence, compatible with weak public commitments.

Objective certainty (Pr): publicly expressed, based on evidence, entails strong commitments.

(38) Crx,w(p) = ιd[x is convinced in w to degree d that p] (39) Prx,w(p) = ιd[x is willing to commit in w to degree d that p] Think of Pr as a more conservative version of Cr: (40) Prx,w(p) ≤ Crx,w(p), for all sincere agents x, worlds w, and propositions p Believe encodes subjective certainty. (Sure encodes objective certainty.)

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Hedging : P-exhaustivity

believe, know constitutes a p(resuppositional)-scale. The set of p-alternatives of a sentence Sα: (41) p-Alt(Sα) = {Sβ |α,β belong to the same p-scale} The set of excludable p-alternatives of S are the p-alternatives with stronger presuppositions. (42) p-Excl(S) = {S′ ∈ p-Alt(S)|∂[[S′]] ⊂ ∂[[S]]} A p-exhaustivity operator (cf. Chierchia et al. 2012; Chierchia 2013). (43) [[p-Exh S]]w = [[S]]w ∧∀S′ ∈ p-Excl(S) : Prsp,w(∂[[S′]]) < 1

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Hedging : How to derive it

Worked example: (44) I believe it’s raining.

• a. p-Exh [I pos believe it’s raining]

= p-Exh [believe rain]

• b. [[believe rain]] = λw.Crsp,w([[rain]]) = 1
• c. p-Alt(believe rain) =

believe rain, know rain

• d. p-Excl(believe rain) =
• know rain
• e. [[p-Exh [believe rain]]]

= λw.Crsp,w([[rain]]) = 1∧Prsp,w([[rain]]) < 1 Last line: The speaker is subjectively certain it is raining but not committed to it (e.g. because she lacks sufficient evidence). The hedging is about modal content (type of certainty), not about modal force (weak or strong).

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QUD sensitivity

Data: Weak readings require that the belief component not be QUD-relevant. Explanation: QUD-relevant p-alternatives are filtered out by the semantic computation. Rationale: P-alternatives are derived from presuppositions, and the latter are typically not at issue.

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QUD sensitivity : Technical details

Relevance as partial answerhood (Groenendijk & Stokhof 1984). (45) Rel(p,Q) iff ∃q ∈ Q : p ∩q = / Excludable p-alternatives have truth conditions that are not QUD-relevant. (46) p-ExclQ(S) = {S′ ∈ p-Alt(S)|∂[[S′]] ⊂ ∂[[S]] and ¬Rel([[S′]],Q)}

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QUD sensitivity : Schematic examples

(47) Know-alternative not relevant weak reading (available)

• a. {Is global warming real?}

Q = {r,¬r}

• b. p-Exh [I believe it is]

p-Alt = {Bsr,Ksr}, p-ExclQ = {Ksr}

• c. Enriched meaning:

Bsr ∧¬Ksr (48) Know-alternative relevant strong reading

• a. {Tell us about your environmental beliefs.}

Q = {Bsr,Bs¬r,...}

• b. p-Exh [I believe global warming is real]

p-Alt = {Bsr,Ksr}, p-ExclQ = /

• c. Enriched meaning:

Bsr

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Conclusion

The mantra: Believe is strong but subjective. Believe encodes a subjective probability measure that takes maximum standards. The intuition of weakness arises as an antipresupposition and is restricted by the QUD.

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Thank you!

I would like to thank Danny Fox, Louise McNally, Maˇ sa Moˇ cnik, Kjell Johan Sæbø, Roger Schwarzschild, and the audiences at Sinn und Bedeutung, the University of Cologne, the University of Konstanz, and MIT. For English judgments, I am indebted to Kurt Erbach, James Griffiths, Kyle Rawlins, and Peter Sutton.

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