Natural Information and Conversational Implicatures

Anton Benz

Overview

Conversational Implicatures Lewis (1969) on Language Meaning Lewisising Grice Applications

Conversational Implicatures

The Standard Theory

Communicated meaning

Grice distinguishes between: What is said. What is implicated.

“Some of the boys came to the party”

said: at least two came implicated: not all came

Assumptions about Conversation

Conversation is a cooperative effort. Each participant recognises in their talk

exchanges a common purpose.

A stands in front of his obviously immobilised car.

A: I am out of petrol. B: There is a garage around the corner.

Joint purpose of B’s response: Solve A’s problem of finding petrol for his car.

How should one formally account for the implicature?

Set H*:= The negation of H

B said that G but not that H*. H* is relevant and G H* G. Hence if G H*, then B should have said

G H* (Quantity). Hence H* cannot be true, and therefore

H.

Problem: We can exchange H and H* and still get a valid inference:

1. B said that G but not that H.

2. H is relevant and G H G.

3. Hence if G H, then B should have said G H (Quantity).

4. Hence H cannot be true, and therefore H*.

Lewis (1969) on Language Meaning

Lewis: Conventions (1969)

Lewis Goal: Explain the conventionality of language meaning.

Method: Meaning is defined as a property of certain solutions to signalling games.

Ultimately a reduction of meaning to a regularity in behaviour.

Semantic Interpretation Game

Communication poses a coordination problem for speaker and hearer.

The speaker wants to communicate some meaning M. In order to communicate this he chooses a form F.

The hearer interprets the form F by choosing a meaning M’.

Communication is successful if M=M’.

Lewis’ Signalling Convention

Let F be a set of forms and M a set of meanings.

A strategy pair (S,H) with

S : M F and H : F M is a signalling convention if

HS = id|M

Meaning in Signalling Conventions

Lewis (IV.4,1996) distinguishes between indicative signals imperative signals

applied to semantic interpretation games: a form F signals that M if S(M)=F a form F signals to interpret it as H(F)

Two possibilities to define meaning. Coincide for signalling conventions in

semantic interpretation games. Lewis defines truth conditions of signals F

as S1(F).

Lewisising Gricean

Assumption: speaker and hearer use language according to a semantic convention.

Goal: Explain how implicatures can emerge out of semantic language use.

Non-reductionist perspective.

Representation of Assumption

Semantics defines interpretation of forms. Let [F] denote the semantic meaning. Hence, assumption: H(F)=[F], i.e.:

H(F) is the semantic meaning of F

F Lewis imperative signal.

Idea of Explanation of Implicatures

1. Start with all signalling conventions (S,H) such that H(F) = [F].

2. Impose additional pragmatic constraints.

3. Implicature F +> is explained if for all remaining (S,H): S1(F) |=

Philosophical Motivation

Grice distinguished between natural meaning non-natural meaning Communicated meaning is non-natural

meaning.

Example

1. I show Mr. X a photograph of Mr. Y displaying undue familiarity to Mrs. X.

2. I draw a picture of Mr. Y behaving in this manner and show it to Mr. X.

The photograph naturally means that Mr. Y was unduly familiar to Mrs. X

The picture non-naturally means that Mr. Y was unduly familiar to Mrs. X

Taking a photo of a scene necessarily entails that the scene is real. Every branch which contains a showing of a

photo must contain a situation which is depicted by it.

The showing of the photo means naturally that there was a situation where Mr. Y was unduly familiar with Mrs. X.

The drawing of a picture does not imply that the depicted scene is real.

Natural Information of Signals

Let G be a semantic interpretation game. Let S be a set of strategy pairs (S,H). The we identify the natural information of a

form F in G with respect to S with:

The set of all branches of G where the speaker chooses F.

Coincides with S1(F) in case of semantic interpretation games.

Generalises to arbitrary games which contain semantic interpretation games in embedded form.

Applications

Example 1: Scalar Implicature

“Some of the boys came to the party”

said: at least two came implicated: not all came

Example 1: Scalar Implicature

“all”

“some”

“most”

“most”

“some”

“some”

100%

50% >

50% <

50% >

50% >

0; 0

1; 1

0; 0

0; 0

1; 1

1; 1

The game defined by pure semantics

Example 1: Scalar Implicature

100%

50% >

50% <

“all”

“some”

“most”

50% >

1; 1

1; 1

1; 1

In all branches that contain “some” the initial situation is “50% < ”

The (pragmatically) restricted game

1.3 Parikh’s Explanation

¬

ρ'

ρ

“some”

“some”

“some but not all”

silence

¬

¬

¬

4,5

-4,-3

6,7

2,3

-5,-4

0,0

ρ > ρ'

Example 2: Relevance Implicature

H approaches the information desk at the city railway station.

H: I need a hotel. Where can I book one? S: There is a tourist office in front of the

building.

implicated: It is possible to book hotels at the tourist office.

The general situation

The situation where it is possible to book a hotel at the tourist information, a place 2, and a place 3.

“place 2”1

0

1

s. a.

go-to tourist office

0

1/2

0

“tourist office”

“place 3”

go-to pl. 2

go-to pl. 3

s. a.

s. a.

s. a. : search anywhere

booking possible at tour. off.

1

0

1/2

-1

1

1/2

booking not possible

“place 2”

“tourist office”

“place 3”

“place 2”

“tourist office”

“place 3”

go-to t. o.

go-to pl. 2

go-to pl. 3

go-to t. o.

go-to pl. 2

go-to pl. 3

1st Step

booking possible at tour. off.

1

1booking not possible

“tourist office”

“place 2”

go-to t. o.

go-to pl. 2

2nd Step

Example 3: Italian Newspaper

Somewhere in the streets of Amsterdam … H: Where can I buy an Italian

newspaper? S: (A) At the station. / (B) At the palace. Not valid: A +> B

Situation where AB holds true:

“A”1

1

1go-to station

1

1

1

“A & B”

“B”

go-to s

go-to palace

go-to p

go-to s

go-to p