9.4.1: Implicatures and the semantics/pragmatics boundary

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In Chapter 1 we defined the semantic content of an expression as the meaning that is associated with the words themselves, independent of context. We defined pragmatic meaning as the meaning which arises from the context of the utterance. We have implicitly assumed that the truth conditions of a sentence depend only on the “semantic content” or sentence meaning, and not on pragmatic meaning. Many authors have made the same assumption, using the term “truth conditional meaning” as a synonym for “sentence meaning”. However, our discussion of explicatures has demonstrated that this view is too simplistic. Additional challenges to this simplistic view arise from research on implicatures.

As already discussed in Chapter 8, the conventional implicatures associated with words like but or therefore are part of the conventional meaning of these words, and not context-dependent; they would be part of the relevant dictionary definitions and must be learned on a word-by-word basis. Nevertheless, both Frege and Grice argued that these conventional implicatures do not contribute to the truth conditions of a sentence. So conventional meaning is not always truth-conditional. We will discuss this issue in more detail in Chapter 11.

The opposite situation has been argued to hold in the case of generalized conversational implicatures. In §9.2 above we presented compelling evidence which shows that the sequential ‘and then’ use of and is not due to lexical ambiguity (polysemy), but must be a pragmatic inference. It is often cited as a paradigm example of generalized conversational implicature. However, as noted by Levinson (1995; 2000) among others, this inference does affect the truth conditions of the sentence in examples like (20–21). Sentence (20a) could be judged to be true in the same context where (20b) is judged to be false. This difference can only be due to the sequential interpretation of and; if and means only ∧, then the two sentences are logically equivalent. Similarly, if and means only ∧, then (21) should be a contradiction; the fact that it is not can only be due to the sequential interpretation of and.

(20) a. If the old king has died of a heart attack and a republic has been declared, then Tom will be quite content.¹⁵
b. If a republic has been declared and the old king has died of a heart attack, then Tom will be quite content.¹⁶

(21) If he had three beers and drove home, he broke the law; but if he drove home and had three beers, he did not break the law.

Such examples have been extensively debated, and a variety of analyses have been proposed. For example, proponents of Relevance Theory argue that the sequential ‘and then’ use of and is an explicature: a pragmatic inference that contributes to truth conditions.¹⁷ A similar analysis is proposed for most if not all of the inferences that Grice and the “neo-Griceans” have identified as generalized conversational implicatures: within Relevance Theory they are generally treated as explicatures.

This controversy is too complex to address in any detail here, but we might make one observation in passing. At the beginning of Chapter 8 we provided an example (the story of the captain and his mate) of how we can use a true statement to implicate something false. That example involved a particularized conversational implicature, but it is possible to do the same thing with generalized conversational implicatures as well. The following example involves a scalar implicature. It is taken from a news story about how Picasso’s famous mural “Guernica” was returned to Spain after Franco’s death. The phrase Not all of them in this context implicates not none (that is, ‘I have some of them’) by the maxim of Quantity, because none is a stronger (more informative) term than not all.

(22) To demonstrate that the Spanish Government had in fact paid Picasso to paint the mural in 1937 for the Paris International Exhibition, Mr. Fernandez Quintanilla had to secure documents in the archives of the late Luis Araquistain, Spain’s Ambassador to France at the time. But Araquistain’s son, poor and opportunistic, demanded $2 million for the archives, which Mr. Fernandez Quintanilla rejected as outrageous. He managed, however, to obtain from the son photocopies of the pertinent documents, which in 1979 he presented to Roland Dumas [Picasso’s lawyer]…

“This changes everything,” a startled Mr. Dumas told the Spanish envoy when he showed him the photocopies of the Araquistain documents.

“You of course have the originals?” the lawyer asked casually. “Not all of them,” replied Mr. Fernandez Quintanilla, not lying but not telling the truth, either.

[The New York Times, November 2, 1981; cited in Horn (1992)]

Mr. Fernandez Quintanilla was not lying, because the literal sentence meaning of his statement was true. But he was not exactly telling the truth either, because his statement triggered (and was clearly intended to trigger) an implicature that was false; in fact he had none of the originals.

Such examples show that generalized conversational implicatures can be used to communicate false information, even when the literal meaning of the sentence is true. It would be hard to account for this fact if these generalized conversational implicatures are considered to be explicatures, because explicatures do not have a truth value that is independent of the truth value of the literal sentence meaning. Rather, explicatures represent inferences that are needed in order to determine the truth value of the sentence.

9.4.1 Why numeral words are special

Scalar implicatures have received an enormous amount of attention in the recent pragmatics literature. Many early discussions of scalar implicatures relied heavily on examples involving cardinal numbers, which seem to form a natural scale (1, 2, 3, …). However, various authors have pointed out that numbers behave differently from other scalar terms.

Horn (2004) uses examples (23–25) to bring out this difference. On the scale <none, some, many, all>, all is a stronger (more informative) term than many. Therefore, by the maxim of quantity, A’s use of many in (23) entails ‘(at least) many’ and implicates ‘not all’.¹⁸ B’s reply states that the implicature does not in fact hold in the current situation; but this does not render the propositional content of the sentence false. That is why it would be unnatural for B to begin the reply with No, as in B1. The acceptability of reply B2 follows from the fact that implicatures are defeasible.

(23) A: Did many of the guests leave?
B1: ?No, all of them.
B2: Yes, (in fact) all of them.

If numerals behaved in the same way as other scalars, we would expect A’s use of two in (24) to entail ‘at least two’ and implicate ‘not more than two’. However, if B actually does have more than two children, it seems to be more natural here for B to reply with No rather than Yes. This indicates that B is rejecting the literal propositional content of the question, not an implicature.

(24) A: Do you have two children?
B1: No, three.
B2: ?Yes, (in fact) three.

Such examples suggest that numerals like two allow two distinct readings: an ‘at least 2’ reading vs. an ‘exactly 2’ reading, and that neither of these is derived as an implicature from the other. A’s question in (24) is most naturally interpreted as involving the ‘exactly’ reading. However, there are certain contexts (such as discussing a government subsidy that is available for families with two or more children) in which the ‘at least’ reading would be preferred, and in such contexts reply B2 would be more natural.

Example (25a) is acceptable under the ‘exactly 3’ reading of the numeral, under which not three is judged to be true whether the actual number is more than three or less than three. The fact that (25b) is unacceptable shows that the word like does not have an ‘exactly (or merely) like’ reading. Based on the scale hate, <dislike, neutral, like, love/adore> , using the word like entails ‘at least like (=have positive feelings)’ and implicates ‘not more than like (not love/adore)’. Sentence (25b) attempts to negate the both the entailment and the implicature at the same time, and the result is unacceptable.¹⁹

(25) a. Neither of us has three kids — she has two and I have four.
b. # Neither of us liked the movie — she adored it and I hated it.

Horn (1992) notes several other properties which set numerals apart from other scalar terms, and which demonstrate the two distinct readings for numerals:

1. Mathematical statements do not allow “at least” readings (26a). Also, round numbers are more likely to allow “at least” readings than very precise numbers (26b–c).

(26) a. ^* 2 + 2 = 3 (should be true under “at least 3” reading)
b. I have $200 in my bank account, if not more.
c. I have $201.37 in my bank account, #if not more.

2. Numerical scales are potentially reversible depending on the context (27– 28); this kind of reversal is not possible with other scalar terms (29).

(27) a. That bowler is capable of breaking 100 (he might even score 150).
b. That golfer is capable of breaking 100 (he might even score 90).

(28) a. You can survive on 2000 calories per day (or more).
b. You can lose weight on 2000 calories per day (or less).

(29) a. He ate some of your mangoes, if not all/*none of them.
b. This classroom is always warm, if not hot/*cool.

3. The “at least” interpretation is only possible with the distributive reading of numerals, not the collective reading (30); this is not the case with other scalar quantifiers (31).

(30) a. Four salesmen have called me today, if not more.
b. Four students carried this sofa upstairs for me, #if not more.

(31) a. Most of the students have long hair, perhaps all of them.
b. Most of the students surrounded the stadium, perhaps all of them.

4. The “at least” interpretation is disfavored when a numeral is the focus of a question (32), but this is not the case with other scalar quantifiers (33):

(32) Q: Do you have two children?
A1: No, three.
A2: ?Yes, in fact three.

(33) Q: Are many of your friends linguists?
A1: ⁇No, all of them.
A2: Yes, in fact all of them.

It is important to bear in mind that sentences like (34) can have different truth values depending on which reading of the numeral is chosen:

(34) If Mrs. Smith has three children, there will be enough seatbelts for the whole family to ride together.

One possible analysis might be to treat the alternation between the ‘at least n’ vs. ‘exactly n’ readings as a kind of systematic polysemy. However, it seems that most pragmaticists prefer to treat numeral words as being underspecified or indeterminate between the two, with the intended reading in a given context being supplied by explicature.²⁰

¹⁵ Cohen (1971: 58).

¹⁶ Gazdar (1979: 69).

¹⁷ Carston (1988; 2004).

¹⁸ Many is used here in its proportional sense; see Chapter 14 for discussion.

¹⁹ Of course, as pointed out at the end of Chapter 8, given the right context and using a special marked intonation it is sometimes possible to negate the implicature alone, as in: “She didn’t líke the movie — she adóred it.”

²⁰ See for example Horn (1992) and Carston (1998).