The logical foundation of pragmatic meaning: Arguments from logical words

FACULTÉ DES LETTRES Département de linguistique 19ICL – Latsis Lecture – 23 July 2013

The logical founda=on of pragma=c meaning:

Arguments from logical words

Jacques Moeschler Department of linguis=cs, University of Geneva


A first ques=on

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One of the classical issue in seman=cs and pragma=cs is the rela=on between logic and language Along the history of linguis=cs, different answers have been given They can be sketched in the classical opposi=on between formalist and non-‐formalist approaches (Grice 1989, Moeschler & Reboul 1994)

In a nutshell, the formalists claim that the seman=cs of natural languages is logic-‐based The non-‐formalists claim that there is no connec=on between logic (which is about proposi=ons) and linguis=cs (which is about uVerances)


The purpose of my talkI would like to come back to the classical approaches: the formalist and the non-‐formalist views I will make a short summary of an alternate solu=on: the pragma=c approach The whole discussion will be about logical words (LWs), that is, linguis=c counterparts of logical constants as connec2ves My proposal is that despite the discrepancy between logical and pragma=c meanings of LWs, there is a cogni=ve founda=on for a minimal and logical meaning of LWs in natural languages

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1. The classical views

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The ini=al issueWhat is striking in the seman=cs of logical words is their pragma=c meaning: it differs from their logical one For instance, condi=onals are oYen understood as bicondi=onals (Geis & Zwicky 1971) 1. If you cut the lawn, you will get 20 € 2. If you don’t cut the lawn, you won’t get 20€ Several conclusions have been drawn: a. The non-‐formalist view: There is no connec=on between human

languages and logic: connec=ves have a non-‐truth condi=onal seman=cs (Ducrot).

b. The formalist view: There is a connec=on between language and logic, but only few logical words have linguis=c counterparts, for pragma=c reasons (Gazdar).

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The formalist viewGazdar’s defini=on of truth func=onal connec=ves (TFC)

A connec=ve C is a TFC if it is a func=on that takes a set ({1}, {0}, {1,0}) of truth values {1,0} as their sole arguments.

Gazdar iden=fies 8 possible TFC in natural languages. He gives a constraint for a TFC to be a connec=ve in natural languages.

A TFC is a possible connec=ve in natural languages if it sa=sfies the principle of confessionality: a TFC must confess the falsity of its arguments

c{0} = 0

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The possible connec=ves in natural languages

D*, E*, V* and X* are not confessional, that is, they have no linguis=c counterpart The confessional connec=ves are A*, J*, K*, O*, but

O* is excluded for reason of informa2on J* (exclusive or) can be derived pragma2cally from A* (inclusive or)

Hence, the confessional connec=ves in NL are or (J*) and and (K*), that is the inclusive disjunc2on and the conjunc2on

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A* D* E* J* K* O* V* X* arguments

1 0 1 0 1 0 1 0 {1}

1 1 0 1 0 0 1 0 {1,0}

0 1 1 0 0 0 1 1 {0}


Is the formalist view a realis=c picture?

The formalist view is a reduc=onist analysis of logical connec=ves. It does not account for condi2onals (if) – a non-‐confessional connec2ve Gazdar’s analysis of nega=on similarly explains why logical nega=on is the only possible operator in natural languages.

arguments T N P Q

1 1 0 1 0

0 0 1 1 0

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T is linguis=cally realized (it is true that P), but is it excluded for reason of relevance, as P and Q for reason of informa2on (same truth value)


The non-‐formalist viewThe non-‐formalist view is based on examples which rule out the logical meanings of connec=ves, for instance when a conjunc=on is in the antecedent of a condi=onal (Cohen):

1. If the old king has died of a heart a@ack and a republic has been declared, then Tom will be content.

2. If a republic has been declared and the old king has died of a heart a@ack, then Tom will be content. and = and then Therefore: if P and Q, then R ≠ if Q and P, then R But P and Q is logically equivalent to Q and P

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Ducrot’s examplesDucrot’s analysis of the non-‐formalist view leads to a pragma=c analysis:

1. If you are thirsty, there is some beer in the fridge. 2. He wants you to give him a whisky and some water. These examples do not entail the following uVerances:

3. If there is no beer in the fridge, then you are not thirsty. 4. a. He wants you to give him a whisky.

b. He wants you to give him some water. Hence logical connec=ves in natural languages cannot be analyzed through their logical proper=es

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Is there an alterna=ve?

Grice seminal ar=cle ‘Logic and Conversa=on’ gives all materials to have a new perspec=ve on logical words. In the Gricean approach, the special linguis=c behavior of logical words is directly connected with their pragma=c meaning: they trigger conversa2onal implicatures.

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Grice, logic and conversa=on

It is a common place in philosophical logic that there are, or appear to be, divergences in meaning between (…) at least some of what I shall call the FORMAL devices – ¬,⋀,⋁, ⊃, (x), ∃x, ∫x (…) – and (…) what are taken to be their analogs or counterparts in natural language – such expressions as not, and, if, all, some (or at least one), the.

(…) Those who concede that such divergences exist adhere in the main, to one or the other of two rival groups, which for the purpose of this ar=cle I shall call the formalist and the informalist groups.

(…) I wish, rather, to maintain that the common assump2on of the contestants that the divergence do in fact exist is (broadly speaking) a common mistake, and that the mistake arises from an inadequate aSen2on to the nature and importance of the condi2ons governing conversa2on.

Grice 1975, 41-‐43

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2. The Gricean approach

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The logic of conversa=on

Pragma2cs is based on the idea that pragma2c meaning is not equivalent to what is said, but based on inferences triggered through general pragma=c principles and maxims The Gricean view is based on the coopera2on principle and 9 maxims of conversa2on (quan2ty, quality, rela2on and manner)

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Some classical examplesTemporal use of and: and IMPLICATES and then – maxim of manner (order)

1. a. Tom and Mary got married, lived happily and had four children.b. ≠ Tom and Mary had four children, lived happily and got married.

Bicondi2onal use of if: if P, Q IMPLICATES if not-‐P, not-‐Q – maxim of manner (be brief) and relevance

2. a. If you cut the lawn, you’ll get 10€.b. +> If you don’t cut the lawn, you’ll not get 10€.

Exclusive use of or: or IMPLICATES not both – 1st maxim of quan=ty 3. a. Cheese or dessert

b. +> not(cheese and dessert)

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Some consequencesIf the meaning of LWs is pragma2c in the Gricean sense, then it is an implicature.

Implicatures are non-‐truth-‐condi2onal meaning. So, it means that LWs play no role in the truth-‐condi2onal meaning of sentences.

Is the Gricean approach linguis=cally consistent? In this lecture, I would like to show that

1. the Gricean explana=on is not complete (exclusive or) 2. it does not explain the behavior of another logical connec=ve,

nega2on, which illustrates scope issues

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3. Exclusive disjunction

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The pragma=c meaning of or

Or is generally described (Horn) as belonging to a quan=ta=ve scale <and,or>. The seman=c and pragma=c rela=ons between and and or are given by the following seman=c and pragma=c rela=ons

a. P and Q → P or Q P and Q ENTAILS P or Q b. P or Q +> not(P and Q) P or Q IMPLICATES not(P and Q) Now, not(P and Q) is logically equivalent to not-‐P or not-‐Q, which can be compa=ble with a situa=on where P and Q are false (not-‐P and not-‐Q). However, the not-‐P and not-‐Q reading of P or Q is pragma2cally odd. As a result, the implicature not(P and Q) of P or Q must be specified.

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Some examplesIn a menu:

1. fromage et dessert 2. fromage ou dessert ou (or) interpreta=on is necessary exclusive (⊽) in (1): the client cannot have both, which is possible with the inclusive reading (∨) of ou.

fromage dessertfromage ∨ dessert

1 1 1

1 0 1

0 1 1

0 0 0

fromage dessertfromage ⊽ dessert

1 1 0

1 0 1

0 1 1

0 0 0

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The meaning of the exclusive disjunc=on (ou)How to obtain the exclusive meaning of a disjunc2on? The exclusive ou is obtained by the conjunc2on of the logical inclusive ou and its scalar implicature: (P ouincl Q) and not(P et Q). In this analysis, the exclusive ou is not a new connec=ve for natural language: it is a pragma2c enrichment of the inclusive meaning of the logical ou, that is, the result of what is said AND what is implicated

P P P ou P et Q not (P et Q) (P ounot(P et Q) P ou

1 1 1 1 0 0 0

1 0 1 0 1 1 1

0 1 1 0 1 1 1

0 I 0 0 1 0 0

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Implica=on

The implica=on is that pragma=c meaning for connec=ves is obtained via a complex process:

the combina2on of the seman2c of the connec2ve (its logical meaning) and its scalar implicature

This is a first (strong) argument for a logical founda7on of pragma7c meaning Is it cogni=vely grounded?

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4. Negation

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Logical nega=on

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Logical nega=on is proposi2onal: not-‐P means «it is not the case that P» The seman2cs of logical nega2on is simple: it changes the truth-‐value of the proposi=on:

a. a true proposi=on is false under nega=on b. a false proposi=on is true under nega=on However, the use of linguis=c nega=on is never met in the first context

A nega=ve sentence is not false, but true Il ne pleut pas means «the proposi=on IL PLEUT is false»

Pragma=c uses of nega=on are thus restric=ons on nega=on truth-‐condi=ons


Linguis=c nega=onNow, what can be said about the uses of linguis2c nega2on? Linguis=c nega=on has two main uses: descrip2ve and metalinguis2c (Ducrot, Horn). a. When used descrip=vely, nega=on has narrow scope b. When used metalinguis=cally, nega=on either scopes over an implicature or it

has wide scope 1. Abi n’est pas laide

= ABi est non-‐laide 2. Abi n’est pas belle, elle est très belle

= Abi est belle 3. Abi ne regre@e pas d’avoir échoué

= Abi a des regrets & Abi a échoué 4. Abi ne regre@e pas d’avoir échoué: elle a réussi

= Abi a des regrets & Abi a échoué

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How to compute nega=on scope?

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Several criteria can be used to compute nega=on scope 1. Entailments 2. Discourse rela=ons 3. Connec=ves 4. Contexts 5. Contextual effects


EntailmentsThe following rela=ons are the case between the nega2ve sentence (NEG), its posi2ve counterpart (POS) and its correc2on (COR)

1. COR → NEG a. Abi n’est pas laide (NEG), au contraire elle est belle (COR) b. Abi est belle → Abi n’est pas laide

2. COR → POS a. Abi n’est pas belle (NEG), mais extraordinaire (COR) b. Abi est extraordinaire → Abi est belle

3. COR → NEG & NEG-‐PP a. Abi ne regre@e pas d’avoir échoué (NEG), puisqu’elle a réussi (COR) b. Abi a réussi → Abi n’a pas de regret & Abi n’a pas échoué

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Three types of nega=on1. Descrip2ve nega2on

a. COR → NEG b. the discourse rela=on is CORRECTION c. The prototypical connec=ve is au contraire (mais)

2. Metalinguis2c nega2on 1: upward nega2on a. COR → POS b. The discourse rela=on is CONTRAST c. The prototypical connec=ve is mais (*au contraire)

3. Metalinguis2c nega2on 2: presupposi2onal nega2on a. COR → NEG & NEG-‐PP b. The discourse rela=on is EXPLANATION c. The prototypical connec=ves are parce que / puisque (*mais, *au contraire)

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Contexts and contextual effects

Do these types of nega=on have specific contexts? They all have as a context POS (linguis=cally realized or not), but the conjunc=on of NEG and COR have different contextual effects:

a. Downward nega2on: suppression of POS (POS) b. Upward nega2on: strengthening of POS (POS+) c. Presupposi2onal nega2on: suppression of NEG and its

presupposi=on (NEG & PP)

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Summary

The different contexts are consistent with the logical, seman=c and pragma=c features of nega=on.

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EntailmentsDiscourse rela2ons Connec2ves

Contextual assump2ons

Cogni2ve effects

Ordinary nega2on

COR ➞ NEG CORRECTION au contraire POS POS

Upward nega2on COR ➞ POS CONTRAST mais POS POS+

Presuppo-‐si2onal nega2on

COR ➞ NEG (P & PP)

EXPLANATION parce que puisque

POS & PP POS + PP


Some implica=ons1. Logical proper2es are not absent from linguis=c uses: they are

pragma2cally enriched by taking into account seman=c and pragma=c criteria

2. Scope is the result of entailments and contextual assump2on 3. Discourse rela2ons and connec2ves must be compa=ble with the

contextual effects of nega=on CORRECTION and au contraire are consistent with the suppression of POS CONTRAST and mais are consistent with the strengthening of POS EXPLANATION and causal connec=ves as parce que/puisque are consistent with the suppression of NEG and PP

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5. Conclusion

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A conclusionLogical words have as seman=cs their logical meanings Their ordinary uses are specifica=ons on their seman=cs

1. Connec2ves: they receive a pragma=c meaning which is a restric=on on their logical truth-‐condi=ons

2. Nega2on a. Its ordinary use is narrow scope, consistent with its

entailments b. When used metalinguis=cally, it is takes a wide scope

(presupposi=onal nega=on) or a restricted scope (scalar implicature)

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What implica=on for the rela=on between language and cogni=on

Even if the connec=on between logic and pragma2c meaning is indirect, the computa=on of pragma2c meaning starts with a logical seman2cs If this assump=on is correct, then there should be a logical founda2on for pragma2c meaning and a strong connec2on between logic and cogni2on Experimental works (Noveck, Papafragou & Musolino for instance) give arguments for the logical meaning of LWs: the first type of meaning acquired by children is not their pragma=c meaning, it is their logical one

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Thanks for your aVen=on


Some referencesCarston R. (2002), Thoughts and U@erances, Oxford, Blackwell. Cohen J.L. (1971), The logical par=cles in natural languages, in Bar-‐Hillel Y. (eds.), Pragma=cs of Natural Languages, Dordrecht, Reidel, 50-‐68 Ducrot O. (1989), Logique, structure, énonciadon, Paris, Minuit Gazdar G. (1979), Pragmadcs. Implicature, Presupposidon, and Logical Form, New York, Academic Press. Geis M. & Zwicky A. (1971), On invited inferences, Linguis=c Inquiry 2, 561-‐566 Grice H.P. (1989), Studies in the Way of Words, Cambridge (Mass.), Harvard University Press. Horn L.R. (2004), Implicature, in Horn & Ward (eds.), The Handbook of Pragmadcs, Oxford, Blackwell, 3-‐28.

Moeschler J. (2010), Nega=on, scope and the descrip=on/metalinguis=c dis=nc=on, Generadve grammar in Geneva 6. Moeschler J. & Reboul A. (1994), Dicdonnaire encyclopédique de pragmadque, Paris, Seuil. Papafragou A. & Musolino J. (2003), Scalar implicatures: experiments at the seman=cs–pragma=cs interface, Cogni=on 86, 253–282. Noveck I. (2001), When children are more logical than adults: Inves=ga=ons of scalar implicature, Cognidon 78/2, 165-‐188. Noveck I. & Reboul A. (2010), Experimental pragma=cs: A Gricean turn in the study of language, Trends in Cognidve Sciences 12/11, 425-‐431.

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The logical foundation of pragmatic meaning: Arguments from logical words

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