Natural Information and Conversational Implicatures

1. Natural Information and Conversational Implicatures Anton Benz

2. Overview • Conversational Implicatures • Lewis (1969) on Language Meaning • Lewisising Grice • Applications

3. Conversational Implicatures The Standard Theory

4. 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

5. 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.

6. 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.

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

8. Lewis (1969) on Language Meaning

9. 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.

10. 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 formF. • The hearer interprets the form F by choosing a meaning M’. • Communication is successful if M=M’.

11. Lewis’ Signalling Convention • Let F be a set of forms and M a set of meanings. • A strategy pair (S,H) with S : M FandH : F M • is a signalling conventionif • HS = id|M

12. 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)

13. Two possibilities to define meaning. • Coincide for signalling conventions in semantic interpretation games. • Lewis defines truth conditions of signals F as S1(F).

14. Lewisising Gricean

15. 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.

16. 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.

17. Idea of Explanation of Implicatures • Start with all signalling conventions (S,H) such that H(F) = [F]. • Impose additional pragmatic constraints. • Implicature F +>  is explained if for all remaining (S,H): S1(F) |= 

18. Philosophical Motivation Grice distinguished between • natural meaning • non-natural meaning • Communicated meaning is non-natural meaning.

19. Example • I show Mr. X a photograph of Mr. Y displaying undue familiarity to Mrs. X. • 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

20. 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.

21. 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.

22. Coincides with S1(F) in case of semantic interpretation games. • Generalises to arbitrary games which contain semantic interpretation games in embedded form.

23. Applications

24. Example 1: Scalar Implicature “Some of the boys came to the party” • said: at least two came • implicated: not all came

25.  1; 1 “all” 50% > 100% “most” 0; 0 “some”  0; 0 “most” 50% > 50% > 1; 1 “some”  0; 0 “some”  50% < 1; 1 Example 1: Scalar Implicature The game defined by pure semantics

26. Example 1: Scalar Implicature The (pragmatically) restricted game “all”  100% 1; 1 “most” 50% > 50% > 1; 1 “some”  1; 1 50% < In all branches that contain “some” the initial situation is “50% < ”

27. 1.3 Parikh’s Explanation ¬ 4,5 “some but not all” -4,-3  ¬ “some” 6,7 ρ ¬ 2,3   “some” ρ' -5,-4 ¬ silence  0,0 ρ > ρ'

28. 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.

29. The general situation

30. The situation where it is possible to book a hotel at the tourist information, a place 2, and a place 3. go-to tourist office 1 s. a. : search anywhere 0 s. a. “tourist office” 1 go-to pl. 2 “place 2” s. a. 0 1/2 “place 3” go-to pl. 3 s. a. 0

31. go-to t. o. 1st Step 1 “tourist office” booking possible at tour. off. “place 2” go-to pl. 2 0 “place 3” go-to pl. 3 1/2 go-to t. o. -1 “tourist office” booking not possible “place 2” go-to pl. 2 1 “place 3” go-to pl. 3 1/2

32. 2nd Step “tourist office” booking possible at tour. off. go-to t. o. 1 booking not possible “place 2” go-to pl. 2 1

33. 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

34. Situation where AB holds true: go-to station 1 1 go-to palace “A & B” 1 go-to s “A” go-to p 1 “B” 1 go-to s go-to p 1