The pragmatics of logical words

Jacques MoeschlerUniversity of Geneva

&University of Verona

VERONAMAY 3 & 17 2011

The main goals of the courseThis course is about formal approaches to pragmatics.

By formal approaches, I mean approaches which assume precise and explicit connections to the syntactic and semantics structures of natural languages.

By pragmatics, I mean the domain of language study devoted to language usage in communication implying mental or cognitive processes, at the production and interpretation levels.

Pragmatics is a level of language processing implying linguistic and non-linguistic information.

Pragmatics is not an ultimate component of linguistics.

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Why studying pragmatics?The main reasons for pragmatic studies are threefold:

1. It is common sense to observe that what speakers say is different from what they mean.

Different concepts have been used: sentence vs. speaker or utterance meaning (Searle), what is said vs. meant (Grice), sense and reference vs. implicature (Grice).

2. A theory of meaning should explain how speaker meaning can be inferred from sentence meaning.

3. A theory of linguistic communication should explain why speaker meaning is different from sentence meaning.

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The domains of pragmaticsPragmatics originates with the theory of implicatures (Grice).

It now encompasses many issues traditionally restricted to semantics, that is, the study of conventional meaning, and beyond…

Presupposition and conventional implicature

Generalised conversational implicature

Tense, aspect, modality and evidentiality (TAME)

Connectives

Negation

Deixis and anaphora

Metaphors and figurative language

Lexical meaning

Discourse relations (temporal & causal relations, argumentation, etc.)

Conversational structure…

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My current research projects in pragmaticsCAUSE (Lexical and non lexical pragmatics of causality in French: descriptive, theoretical and experimental approaches) - SNSF funding (2007-2011)

A model of causality, causal connectives, causality and argumentation, causality and aspectual classes, inferring implicit causal relation in discourse

COMTIS (Improving the coherence of machine translation output by modelling inter-sentential relations) - FNSF Sinergia funding (2010-2012)

Modelling tenses semantics and pragmatics to extract relevant features for automatic text annotation and machine translation.

An informal research project on Historical Present & Represented Speech and Thought (with Anne Reboul and Izumi Tahara) on French, English and Japanese

How to explain that indexicals and tenses are anchored in different times

LogPrag (The semantics and pragmatics of logical words (LWs): negation, connectives and quantifiers) - SNSF project, submitted (2011-2013)

How to explain the pragmatic meanings of LWs

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The topics of this courseThis course will be devoted to the issues linked to the LogPrag project.

I will mainly deal with logical words, their semantics and pragmatics, and their relation.

The three first courses will be organised as follows:

Cours #1: what is a pragmatic account of logical words.

Cours #2: quantifiers and negation: the generalised conversational implicature issue

Course #3: descriptive and metalinguistic negation.

Class #4 will address more general questions on the structure of semantic and pragmatic meanings.

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Why logical words?

Logical words (quantifiers, connectives, negation) are universal in all languages.

Their logical meaning is different from their linguistic one.

LWs are crucial for reasoning.

LWs are very good examples for introducing to the semantics-pragmatics interface.

Their address intriguing issues to linguistic theory, and more precisely to the syntax-semantics interface and and the syntax-pragmatics one.

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The semantics and pragmatics of logical words: Gricean vs. (non-)formalist approaches

VERONA, MAY 3 2011COURSE #1

Agenda

1. Two classical views:

a. the formalist approach

b. The non-formalist approach

2. The Gricean approach

3. Connectives

a. The neo-Gricean approach

b. The post-Gricean approach

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The conceptual map of the talk

possible approaches

the classical approaches

the formalist approach

the non-formalist approach

the Gricean approaches

the neo-Gricean approach

the post-Gricean approach

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Issues and questions

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One main issue is the semantics-pragmatic interface:

How to explain the gap between linguistic and pragmatic meanings?

H: Pragmatic meanings are restrictions on logical meanings (the Restriction Domain Hypothesis).

The second issue is the syntax-pragmatics interface:

What are the formal and structural contributions of HLC (human language computations) to the Conceptual-Intentional Interface?

This issue will be developed at the end of the course.

1. The classical views

The initial issue

What is striking in the semantics of logical words is their pragmatic meaning.

Their pragmatic meaning differs from their logical one.

Several conclusions have been drawn:

a. The non-formalist view: There is no connection between human languages and logic: language is about utterances, logic about propositions (Ducrot).

b. The formalist view: There is a connection between language and logic, but only few logical words have linguistic counterparts, for pragmatic reasons (Gazdar).

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a. The formalist viewGazdar’s definition of truth functional connectives (TFC): a connective C is a TFC if it is a function that takes a set (S) of truth values (T) as their sole arguments:

S = {{0}, {1}, {1,0}}

T = {1,0}

C = TS

8 possible TFCs (a reduced list from the 16 possible logical connectives)

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}

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The possible connectives in natural languages

A TFC is a possible connective in natural languages if it satisfies the principle of confessionality.

Principle of confessionality: a TFC must confess the falsity of its arguments.

A TFC c is confessional iff c{0} = 0

List of possible confessional TFC: A*, J*, K*, O*

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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}

O* is excluded for reasons of information (always false)

A* is the inclusion or, J* the exclusive or, K* and.

J* can be derived pragmatically from A* (cf. Point 3)

So the confessional TFCs in natural language are inclusive or and and.

O*

0

0

0

J*

0

1

0

Is the formalist view a realistic picture?

The formalist view is a reductionist analysis of logical connectives.

It does not account for negation and conditionals: they are both non-confessional connectives.

Gazdar’s analysis of negation similarly explains why logical negation is the only possible operator in natural languages.

arguments T N P Q

1 1 0 1 0

0 0 1 1 0

T, P and Q are excluded for reasons of relevance and information.Only N (logical negation) is a possible connectiveN is not confessional!

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T

1

0

P

1

1

Q

0

0

Ducrot’s non-formalist approach leads to a pragmatic 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 utterances:

3. If there is no beer in the fridge, then you are not thirsty.

4. He wants you to give him a whisky.

5. He wants you to give him some water.

Logically, the following entailments are true:

(if P, then Q ) → (if not-Q, then not-P)

(P and Q) → P (P and Q) → Q

So, logical connectives in natural languages cannot be analyzed through their logical properties.

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b. The non-formalist view (Ducrot)

The reductionist answerTo these empirical objections, the formalist answer answers that these (counter-)examples are derived from more abstract logical forms:

(1) is analysed as a linguistic reduction of (2):

1. If you are thirsty, there is some beer in the fridge.

2. There is some beer in the fridge, and you will enjoy it if you are thirsty.

(3) is analysed as a reduction of (4):

3. He wants you to give him a whisky and some water.

4. If you give give him a whisky and if you give him some water, he will be happy.

(4) does not allow an inference as (5):

5. If you give him some water, he will be happy.

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Ducrot’s answer to the reductionist objectionDucrot claims that the reductionist approach is acceptable only if the inferential thesis is accepted: logical connectives do have inferential properties.

For Ducrot, inference is not a property of utterances, but a property of propositions, and linguistics is only indirectly interested with inference.

For him, the domain of natural languages semantics and pragmatics is not inference, but more basic semantic properties, expressed in argumentations and speech acts (orientation and commitments).

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Is there an alternative?

Grice’s seminal article ‘Logic and Conversation’ gives all materials to have a new perspective on logical words: this is the pragmatic turn.

In the Gricean approach, the particular linguistic behaviour of logical words is directly connected with their pragmatic meaning: they trigger conversational implicatures.

The pragmatic turn is linked to two Gricean theory:

The theory of non-natural meaning.

The theory of conversational implicature.

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2. The Gricean approach

What is communication?Communication is the device by which information is conveyed from one source to a destination.

Communication implies the change of the mental state of the destination.

In verbal communication, language is the way through which the speaker’s informative intention is conveyed through the recognition by an audience of her communicative intention.

This general definition encompasses Grice’s theory of meaning: linguistic meaning is non-natural.

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Non-natural meaning«A meantNN something by x» is (roughly) equivalent to «A intended the utterance of x to produce some effect (i) in an audience by means of the recognition of his intention (ii)» (Grice, Meaning).

So, non-natural meaning supposes

i. the recognition of the speaker’s (Agent’s) informative intention of and

ii. the recognition of her communicative intention.

Non-natural meaning is under the control of volition and is non-factive, whereas natural meaning is factive and out of the control of volition (Reboul 2007).

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A consequence of the Gricean approach to meaningGrice’s definition of meaning led him to a general theory of utterance interpretation (Logic and Conversation).

In his article, Grice makes the hypothesis that utterance interpretation presupposes

1. the respect of a general principle, the Cooperative Principle (CP)

2. the use (respect) or exploitation (ostensive violation) of 9 maxims of conversation

a. 2 maxims of quantity

b. 2 maxims of quality

c. 1 maxim of relation

d. 4 maxims of manner

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The cooperative principle (CP)

«Make your contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged» (Grice 1989, 26)

The CP states that participants in a communication are rational agents and have expectations of cooperation.

These expectations are fulfilled in 9 conversational maxims.

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The conversational maximsQuantity

i. Make your contribution as informative as is required.

ii. Do not make your contribution more informative than is required.

Quality

i. Do not say what you believe to be false.

ii. Do not say for which you lack adequate evidence.

Relation: Be relevant.

Manner: Be perspicuous.

i. Avoid obscurity of expression

ii. Avoid ambiguity

iii. Be brief

iv. Be orderly

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Meaning and conversationIn Grice’s second theory of meaning, the recovery of the informative intention implies the recovery of the implicated meaning.

Grice makes a crucial difference between what is SAID and what is IMPLICATED.

What is implicated is triggered by the respect or the ostensive exploitation of a conversational maxim.

What is meant is called an implicature.

Grice distinguishes four types of implicatures:

Conventional implicatures

Non-conversational implicature

Generalised conversational implicatures

Particularised conversational implicatures

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WHAT IS SAID vs. IMPLICATED

PRAGMATIC

SEMANTICS

CONVEYED

SAID IMPLICATED

CONVENTIONALLY

CONVERSATIONALLY

CONVENTIONALIMPLICATURE

CONVERSATIONAL IMPLICATURE

GENERALISED PARTICULARISED

NON CONVENTIONALLY

NON CONVERSATIONALLY

NON-CONVERSATIONALIMPLICATURE

OUT OF THE SCOPE OF PRAGMATICS

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Conventional implicaturesConventional implicatures are non-calculable, non-cancellable, detachable, conventional, carried by what is said, determinate.

They are triggered by a specific word vs. a specific content.

They are non truth-functional:

(1) is true iff (2) is true.

(3) and (4) are not contributions to the truth of (2).

(3) and (4) cannot be denied by the speaker of (1).

1. Even John likes Mary.

2. John likes Mary.

3. Other persons besides John like Mary.

4. John is the least likely one to like Mary.

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Conversational implicatures

Conversational implicatures are triggered by

the presumption of the respect of the cooperative principle

the use or the exploitation (ostensive violation) of one of the maxims of conversation.

They are calculable, cancellable, non-detachable, non-conventional, not carried by what is said but by the saying of it, indeterminate:

generalised conversational implicatures are presumptive meanings (Levinson 2000): they are triggered by particular words;

particularised conversational implicatures are nonce implicatures (Carston 2002): they are context-dependent.

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Generalised vs. particularised implicatures1. John went into a house yesterday and found a tortoise inside

the front door.

+> John entered a house he is not familiar with

2. How is John going? — Oh quite well, I think; he likes his colleagues, and he hasn’t been to prison yet.

+> John is the sort of person likely to yield to the temptation provided by his occupation, etc.

The triggering of an implicature is caused by a maxim of conversation.

Unless for particularised implicatures, implicatures are non-contextual inferences.

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Ostensive-inferential communicationOne implication of Grice’s view of communication is the following: communication is an ostensive-inferential process.

Communication is ostensive: the communicator shows her communicative intention by producing an utterance.

Communication is inferential: the hearer has to infer the informative intention from the recognition of the communicator’s communicative intention.

Ostension and inference are two sides of a same process:

Ostension is speaker-oriented.

Inference is hearer-oriented.

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Some classical examples - logical connectivesClassical examples can be given by logical connectives: their pragmatic meanings are the results of conversational implicatures.

Temporal use of and (maxim of order - sub maxim of manner)

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

2. Tom and Mary had four children, lived happily and got married.

Bi-conditional use of if (invited inference - maxim of relevance)

3. If you mow the lawn, I give you 10€.

4. If you don’t mow the lawn, I don’t give you 10€.

Exclusive use of or (scalar implicature - first maxim of quantity)

5. Do you want jam or butter?

6. Do you want jam and butter?

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The Gricean issueHow can we explain the restricted interpretation of logical words?

Does it follows the general procedure of implicature comprehension?

1. The speaker (S) said that p.

2. The hearer (H) has no reason to suppose the S is not observing the conversational maxims or at least the Cooperation Principle.

3. (2) implies that S thinks that q.

4. S knows, and knows that H knows that S knows that H understands that it necessary to suppose that S thinks that q.

5. S has done nothing to stop H to think that q.

6. S wants H to think that q.

7. Therefore, S has implicated that q.

Is it associated to general mechanisms defining generalized conversational implicatures?

Some consequencesIf the meaning of logical words is pragmatic in the Gricean sense, then it is an implicature.

Implicatures are non-truth-conditional meaning.

Connectives and quantifiers pragmatic meanings do not contribute to the truth-conditional meaning of the sentences, although they have logical meanings.

Is the Gricean approach linguistically consistent?

I will first show in what sense logical words conveys implicatures, and then test their non-truth-conditional meaning (course #2)

The conclusion I will argue for is that the contribution of logical words is pragmatic, but not at the level of implicature.

They contribute to the explicature of the utterances.

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3. Connectives

Three connectives, three pragmatic enrichments

I will give you examples of three logical connectives: or, and, if.

These connectives do not behave is an similar way.

Their semantic (logical) meaning is not the same.

They trigger different types of implicatures.

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Truth-tables and deduction rules

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P Q P ∧ Q

1 1 1

1 0 0

0 1 0

0 0 0

AND OR IF…THEN

P Q P ∨ Q

1 1 1

1 0 1

0 1 1

0 0 0

P Q P → Q

1 1 1

1 0 0

0 1 1

0 0 1

DEDUCTION RULESP AND QP

P OR QNOT-PQ

P OR QNOT-QP

IF P THEN QP Q

IF P THEN QNOT-Q NOT-P

PP OR Q

PQ P AND Q

P AND QQ

Scalar implicatures - orSome connectives as or are typical cases of scalar or Q-implicatures.

A scalar implicature is based on the following principle:

In a quantitative scale <S,W>, where S is a strong term and W a weak term, the following relations hold:

a. S(x) → W(x) the strong term entails the weak one

b. W(x) +> ¬S(x) the weak term implicates the negation of the strong one

Examples of quantitative scales: <all, some>, <and, or>, <necessary, possible>, <certain, probable, possible>, <none, some not>, <outstanding, excellent, good>, <hot, warm>, <cold, fresh>

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The pragmatic meaning of orOr belongs to a quantitative scale <and,or>.

Semantic and pragmatic relations between and and or:

a. P and Q → P or Q entailment

b. P or Q +> not(P and Q) scalar implicature

☹ Logically, not(P and Q) is equivalent (de Morgan’s law) to not-P or not-Q, which is compatible with the situation where P and Q are false (not-P and not-Q).

The not-P and not-Q reading of P or Q is pragmatically odd.

The not(P and Q) implicature of P or Q must thus be specified.

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The truth-table of the scalar implicature meaning of or

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P Q P and Q Not(P and Q) Not-P Not-Q Not-P or not-Q

1 1 1 0 0 0 0

1 0 0 1 0 1 1

0 1 0 1 1 0 1

0 0 0 1 1 1 10 0 0 1 1 1 1

1 0 0 1 0 1 1

0 1 0 1 1 0 1

The last row is not the expected reading for the scalar implicature: it is incompatible with any reading for or (inclusive as well as

exclusive).

Cheese or dessertIn a menu:

a. Cheese and dessert

b. Cheese or dessert

or interpretation is necessary exclusive (⊽): the client cannot have both, which is possible with the inclusive reading (∨) of or.

cheese dessert cheese ∨ dessert

1 1 1

1 0 1

0 1 1

0 0 0

cheese dessert cheese ⊽ dessert

1 1 0

1 0 1

0 1 1

0 0 0

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1 1 01 1 1

The meaning of or scalar implicature

The exclusive or is obtained by the conjunction of the logical inclusive or and the scalar implicature: (P orincl Q) and not(P and Q).

In this analysis, the exclusive or is not a new connective in natural language, it is a pragmatic enrichment of the inclusive or.

P P P orincl Q(P v Q)

P and Q Not (P and Q) (P orincl Q) and not(P and Q)

P orexcl Q(P ⊽ Q)

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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The scalar meaning of a connective is not reducible to the W(x) +> ¬S(x) implicatum.

1 0 1 0 1 1 1

0 1 1 0 1 1 1

The Gricean interpretation of andIn the Gricean approach, implicatures are non-truth-conditional.

What is said is truth-functional.

As a consequence, temporal meaning of and is an implicature, and is therefore non-truth-functional.

1. He took off his trousers and went to bed.

2. He went to bed and took off his trousers.

“It is just that there is a general supposition which would be subsidiary to the general maxim of Manner (“Be perspicuous.”) that one presents one’s material in an orderly manner and, if what one is engaged upon is a narrative (if one is talking about events), then the most orderly manner for a narration of events is an order that corresponds to the order in which they took place.” (Grice 1981, 186)

What is said: P ∧ Q

What is implicated: P < Q

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and as an example of I-ImplicatureI-implicatures are associated to stereotypes and enriched interpretation:

i. Let’s W be a weak form and S a strong one, where S(x) → W(x).

ii. If the speaker asserts W(x), then he I-implicates S(x), if the proposition containing S(x) is compatible with what is hold as true.

The enriched interpretation of and belongs to the mutual knowledge theories (cf. Sperber & Wilson 1995 for an argument against MKT).

1. Nath turned the switch and the motor started.

2. Nath turned the switch and then the motor started.

3. Nath turned the switch and because of that the motor started.

4. Nath intended to start the engine.

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Predictions If the semantic meaning of and is its logical one and if its temporal meaning is obtained through an implicature, then the following sentences (Cohen) should have the same truth-values.

(1) If the old king has died of a heart attack and a republic has been declared, then Tom will be quite content.

If P and Q, then R

(2) If a republic has been declared and the old king has died of a heart attack, then Tom will be quite content.

If Q and P, then R

Hence: P and Q ≠ Q and P

Reminder: truth-conditions are about logical meaning and not implicatures; implicatures are non-truth-conditional aspects of meaning.

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Wilson & Sperber’s examples

1. It's always the same at parties: either I get drunk and no-one will talk to me or no-one will talk to me and I get drunk.

2. What happened was not that Peter left and Mary got angry but that Mary got angry and Peter left.

(1) is not redundant: the order of utterance contribute to the determination of truth-conditions.

(P and Q) or (Q and P)

(2) is not a contradiction: the order of utterances determine different truth-conditions, that is, different states of affairs.

not(P and Q) & (Q and P)

This lead us to the Gricean circle.

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The Gricean circleThe Gricean circle states two contradictory propositions:

Implicatures are computed on the basis of the expressed proposition (1).

Implicatures determine the expressed proposition (2).

SAID

IMPLICATED

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A THEORY GIVING RISE TO THE GRICEAN CIRCLE SHOULD BE ABANDONED

if: from material implication to equivalenceA last classical example: the conditional connective is pragmatically interpreted as a bi-conditional.

Pragmatic inference is not truth-preserving, that is, non-truth-conditional:

1. If you mow the lawn, I’ll give you 10€.

2. If you do mow cut the lawn, I will not give you 10€.

3. If you do not mow the lawn, I’ll give you 10€.

Logically, (1) does not entail (2).

(2) can be true if (1) is true, but (3) can be true either.

However, (1) communicates (2), and not (3).

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Truth-tables

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P Q P → Q1 1 11 0 00 1 10 0 1

P Q P Q1 1 11 0 00 1 00 0 1

MATERIAL IMPLICATION EQUIVALENCE

Theorems

P Q = df (P → Q) ∧ (Q → P)

(P → Q) (¬Q → ¬P)

0 1 1

ImplicationsIn natural language conditionals, there is more than a logical relation.

Whereas (1) is true but meaningless, (2) is true and has a causal meaning, and (3) communicate a counterfactual relation.

All these relations a pragmatically motivated, and not only truth-conditional: in its counterfactual meaning (4), both antecedent and consequent are false:

1. If Verona is Julieta’s town, Jacques is an invited professor.

2. If Julieta dies, Romero will not survive.

3. If it were raining outside, the drumming of the roof would drown out our voices (Karttunen & Peters 1979)

4. If I were rich, my 2CV would be a Ferrari (Fauconnier 1984)

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ConclusionLogical connectives clearly shows the discrepancy between logical meaning and pragmatic meaning.

Pragmatic meaning is always a more restricted one:

and triggers a temporal implicature (I-implicature)

or is pragmatically exclusive and is obtained through a scalar implicature.

if is bi-conditional (I-implicature) and counterfactual.

However, no general account is given and no general principle applies to logical connectives.

What about negation?

Are pragmatic meanings the results of implicature processes?

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ReferencesAllwood J., Andersson L.G. & Dahl Ö. (1977), Logic in Linguistics, Cambridge, CUP.

Cohen J.L. (1971), The logical particles of natural languages, in Bar-Hillel Y. (ed.), Pragmatics of Natural Language, Dordrecht, Reidel, 50-68.

Carston R. (2002), Thoughts and Utterance. The Pragmatics of Explicit Communication, Oxford, Blackwell.

Cornulier B. de (1985), Effets de sens, Paris, Minuit.

Ducrot O. (1989), Logique, structure, énonciation, Paris, Minuit.

Fauconnier G. (1984), Mental Spaces, Cambridge (MA), MIT Press.

Gazdar G. (1979), Pragmatics. Implicature, Presupposition, and Logical Form, New York, Academic Press.

Grice H.P. (1981), Presupposition and conversational implicature, in Cole P. (ed.), Radical Pragmatics, New York, Academic Press, 183-198.

Grice H.P. (1989), Studies in the Way of Words, Cambridge (Mass.), Harvard University Press.

Karttunen L. & Peters S. (1979), Conventional implicature, in Oh C.K. & Dinneen D.A. (eds.) Syntax and Semantics 11: Presupposition, New York, Academic Press, 1-56.

Levinson S.C. (1983), Pragmatics, Cambridge, CUP.

Levinson S.C. (2000), Presumptive Meanings, Cambridge (MA), MIT Press.

Moeschler J. (2007), Introduction to pragmatics, in Rajman M. (ed.), Language and Speech Engineering, Lausanne, EPFL Press, 51-68.

Moeschler J. & Reboul A. (1994), Dictionnaire encyclopédique de pragmatique, Paris, Seuil.

Reboul A. (2007), Langage et cognition humaine, Grenoble, PUG.

Reboul A. & Moeschler J. (1998), La Pragmatique aujourd’hui, Paris, Seuil (Points).

Sperber D. & Wilson D. (1995), Relevance. Communication and Cognition, Oxford, Blackwell.

Wilson D. & Sperber S. (1998), Pragmatics and Time, in Carston R. & Uchida S. (eds.), Relevance Theory: Applications and Implications, Amsterdam, John Benjamins, 1-22.

Thanks for your attention