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). [[believe]] w = λ p λ x . ∀ w ′ ∈ Dox x , w : p ( w ′ ) (1) Two (related) problems: Gradability Strength 2 / 30
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. 3 / 30
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. 4 / 30
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 Cr x ( p ) = 1 (4) Weak view (Hawthorne et al. 2016) [[believe]]( p )( x ) iff Cr x ( p ) > θ bel , where typically (but not always) θ bel = 0 . 5 5 / 30
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 believe wk he is going to win but I don’t believe str it. (6) It’s likely he is going to win but it’s not certain. 6 / 30
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 of 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. 7 / 30
Roadmap Data Supporting data Seemingly contradicting data Proposal Gradability Conjunction closure Hedging 8 / 30
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 only lower closed scale [0 , 1) � minimum standard only upper closed scale (0 , 1] � maximum standard totally closed scale [0 , 1] � maximum standard 9 / 30
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. 10 / 30
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. 11 / 30
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 12 / 30
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. 13 / 30
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. 14 / 30
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. 15 / 30
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. 16 / 30
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). 17 / 30
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. 18 / 30
Degree semantics 1 A degree-based semantics for believe (cf. Cresswell 1976; von Stechow 1984; Kennedy 1999). (27) [[believe]] = λ p λ d λ x . Cr x ( p ) ≥ d Without overt degree morphology, the threshold value is contributed by a silent pos morpheme (Kennedy & McNally 2005). [[ pos ]] C = λ P λ x . ∃ d [ standard ( d , P , C ) ∧ P ( d )( x )] (28) (29) standard ( d , P , C ) d > avg { µ P ( x ) | x ∈ C } if P is relative = d > min ( S P ) if P is min degree d = max ( S P ) if P is max degree 19 / 30
Degree semantics 2 Believe is maximal degree. (30) [[ pos [believes it’s raining]]] = λ x . ∃ d [ d = 1 ∧ Cr x ([[rain]]) ≥ d ] = λ x . Cr x ([[rain]]) = 1 [ believe p ] can combine with overt degree modifiers that otherwise attach to gradable adjectives. Example: (31) [[partially]] = λ P λ x . ∃ d [ d > min ( S P ) ∧ P ( d )( x )] (32) [[partially [believes eating pizza is healthy]]] = λ x . ∃ d [ d > 0 ∧ Cr x ([[eat pizza healthy]]) ≥ d ] = λ x . Cr x ([[eat pizza healthy]]) > 0 20 / 30
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