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
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