The truth shall make you slow: The truth shall make you slow: Superlative Quantifiers as Superlative Quantifiers as

speech act modifiersspeech act modifiers

Aviya Hacohen, Dana Kozlowski & Ariel CohenAviya Hacohen, Dana Kozlowski & Ariel CohenBen-Gurion University of the NegevBen-Gurion University of the Negev

Experimental Pragmatics ConferenceExperimental Pragmatics Conference

Universitat Pompeu Fabra, Barcelona, 2–4 June 2011Universitat Pompeu Fabra, Barcelona, 2–4 June 2011

This study is supported by the Israeli Science Foundation, grant # 376/09

BACKGROUNDBACKGROUND

The classical theory of speech actsThe classical theory of speech acts

Stenius (1967), Searle (1969):Stenius (1967), Searle (1969):

•Speech acts are not propositions; they are communicative acts

•Speech acts cannot be embedded under propositional operators (e.g. quantifiers)

An alternative theory of speech actsAn alternative theory of speech acts

Krifka (2001; to appear)Krifka (2001; to appear)

Speech acts cancan sometimes be embedded

Which is correct?Which is correct?In this talk:

Superlative quantifiers as a test case

The meaning of superlative quantifiersThe meaning of superlative quantifiersSuperlative quantifiers (SQs):Superlative quantifiers (SQs): at least, at most

Commonly assumed to have the same truth-conditions as comparative quantifiers

(1) John petted at least three at least three rabbits

John petted more than two more than two rabbits

(2) John petted at most three at most three rabbits

John petted fewer than four fewer than four rabbits

But this is wrong (Guerts & Nouwen 2007)…But this is wrong (Guerts & Nouwen 2007)…

Theories of Superlative QuantifiersTheories of Superlative Quantifiers

Guerts & Nouwen (2007)Guerts & Nouwen (2007)SQs are complex epistemic operators

(1) John petted at least three at least three rabbits =

‘It is epistemically necessarynecessary that John petted three rabbits, and it is epistemically possiblepossible that he petted more.’

x(RABBITS(x) |x|=3 pet(j,x))

x(RABBITS(x) |x|>3 pet(j,x))

Büring (2007), Cummins & Katsos (2010)Büring (2007), Cummins & Katsos (2010)SQs are disjunctions

(1) John petted at least three at least three rabbits =

‘John petted exactly three exactly three rabbits oror John petted more than three more than three rabbits.’

|RABBITSx.pet(j,x)|=3

|RABBITSx.pet(j,x)|>3

Cohen & Krifka (to appear)Cohen & Krifka (to appear)SQs are illocutionary operators embedded

under quantification

(1) John Petted at least three at least three rabbits =

(A) `The minimal n for which the speaker does not deny that John petted exactly n rabbits is n=3’

(B) ‘For all n<3, the speaker denies that John petted

exactly n rabbits.’∀n(n<3 → ASSERT(|RABBITS∩λx.pet(j,x)|n)

If John petted one rabbit (1) is false.Indeed, one of the assertions in (B) is false.

If John petted four rabbits (1) is true.All of the assertions in (B) are true.But how do we know that the speaker does not also

deny that John petted 4 rabbits? This would still be compatible with (A)!

Therefore, we need (C) as well

(C) ‘For all n3, the speaker does not deny that John petted exactly n rabbits.’

∀n(n3 → ~ASSERT(|RABBITS∩λx.pet(j,x)|n)

Crucially, (C) does not follow semantically from (A)

However, (C) does follow from (A) pragmatically, by implicature:

If the speaker wanted to deny that John petted exactly n rabbits for some value of n3, she should have said so.

Hence, falsityfalsity is determined semantically, but truthtruth is determined pragmatically

TESTING THE THEORIES:TESTING THE THEORIES:

PREDICTIONS FOR PROCESSINGPREDICTIONS FOR PROCESSING(for linguistic predictions, see Cohen & Krifka to appear)

Prediction common to all theoriesPrediction common to all theories

Prediction 1Prediction 1Processing of superlative quantifiers will take longer

than comparative quantifiers

This prediction has been borne out by Geurts et al. (2010) and Cummins & Katsos (2010)

Unique predictionUnique predictionCohen & Krifka (to appear):

1) Judgments of true true SQ sentences require calculation of scalar implicaturescalar implicature

2) Judgments of false false SQ sentences do notnot

3) Computing scalar implicatures takes time (see, e.g., Bott & Noveck, 2004)

Prediction 2Prediction 2True SQ sentences will take longer to process than

false ones

Competing theories: no such prediction

METHODSMETHODS

Frequency effectsFrequency effects•At least is much more frequent than at most

•To control for frequency effects, we chose Hebrew as the language of the stimuli

•Hebrew has two forms (lexol hapaxot ‘at least’ and lexol hayoter ‘at most’) with roughly the same (low) frequency

•For completeness, we also added the much more frequent form lefaxot ‘at least’

Experimental designExperimental design5 experimental conditions:

Superlative quantifiersSuperlative quantifiers

1) lefaxotlefaxot ‘at least’

2) lexollexol hapaxothapaxot ‘at least’

3) lexol hayoter lexol hayoter ‘at most’

Comparative quantifiersComparative quantifiers

1) yoter me- yoter me- ‘more than’

2) paxot me- paxot me- ‘less than’

X 12 items

ProcedureProcedure

Experiment AExperiment A• Sentence verification task: the participant judges

if a written sentence truthfully describes an accompanying picture

• Experimental structure: I see Q N XsI see Q N Xs

QQ = superlative/comparative quantifierNN = 3, 4, 5XX = everyday object

•Stimuli presented and reaction time data recorded using E-Prime

צלחות בתמונה4 לכל הפחותלכל הפחותאני רואה I see at least at least 4 plates in the picture

Example item from Example item from lexol hapaxot lexol hapaxot ‘at least’ ‘at least’ conditioncondition

כוסות בתמונה3 לכל היותרלכל היותראני רואה I see at most at most 3 glasses in the picture

Example item from Example item from lexol hayoterlexol hayoter ‘at most’ ‘at most’ conditioncondition

ParticipantsParticipants28 adults, native speakers of Hebrew

Aged 22-46 (Mean 27)

17 female, 11 male

RESULTS AND DISCUSSIONRESULTS AND DISCUSSION

RTs for superlative vs. comparative conditionsRTs for superlative vs. comparative conditions

PP < 0.01 < 0.01

Prediction 1: borne outborne out, replicating previous findings (Geurts et al. 2010; Katsos & Cummins 2010)

RTs for true vs. false superlative quantifiersRTs for true vs. false superlative quantifiers

RTs for true vs. false comparative quantifiersRTs for true vs. false comparative quantifiers

• Prediction 2: borne outborne out

• True SQ sentences take longer to process than false ones

• The interaction between quantifier (lexol hapaxot, lexok hayoter or lefaxot) and truth judgment (true or false) was not significant (p=0.15), indicating that all three SQs demonstrate a similar effect

• Our results support Cohen and Krifka’s theory

• Competing theories make no predictions regarding the difference between true and false SQs

• Nevertheless, could these findings be made compatible with one of the competing theories?

• Arguably, there are logical forms that may take longer to evaluate for truth than falsity

• For instance: generally, a false conjunction takes fewer steps to evaluate than a true conjunction

• Maybe, a competing theory could argue that the logical form it proposes is of this type

• Our findings could then be made compatible with such a theory

• To control for this possibility, we carried out a second experiment

צלחות בתמונה4 לפחותלפחותאני רואה I see at least at least 4 plates in the picture

Design and procedure experiment BDesign and procedure experiment BSame as before, except sentence precedes picture

by 2 seconds

Rationale and predictionsRationale and predictions

• This delay should allow subjects to compute the required implicature (Bott & Noveck 2004)

• Cohen & Krifka’s prediction: the RT difference between true and false judgments should disappear

• Competing theories: processing of logical forms should not be affected by the delay

ParticipantsParticipants27 adults, native speakers of Hebrew

Aged 21-53 (Mean 28)

17 female, 10 male

PP = 0.38 = 0.38

RTs for true vs. false superlative quantifiersRTs for true vs. false superlative quantifiers

(experiment B)(experiment B)

DiscussionDiscussion

•The delay allows subjects to compute the implicature Support for Cohen and Krifka’s theory

•In contrast, logical form can only be evaluated once the picture is seen

If the results of exp. A were not due to implicature but to verification of logical form, the delay should not have made a difference

General discussionGeneral discussion

•The results support Cohen and Krifka’s theory

•Crucially, this theory proposes that illocutionary operators are embedded under quantifiers

Speech acts, while not propositions, are full-fledged participants in the semantic game

THANK YOU!THANK YOU!ReferencesReferences

Büring, D. (2007), ‘The least "at least" can do’. In C.B. Chang and H.J. Haynie (eds.), Proceedings of WCCFL 26. Cascadilla Press. Somerville, MA. 114–20.

Cohen, A. and M. Krifka, `Superlative quantifiers as meta-speech acts.' To appear in The Baltic International Year-book of Cognition, Logic and Communication.

Cummins, C. and N. Katsos, (2010), `Comparative and Superlative Quantifiers: Pragmatic Effects of Comparison Type’ Journal of Semantics 27: 271-305

Geurts, B., and R. Nouwen, (2007). `At Least et al.: The semantics of scalar modifiers’. Language 83:533-559.