9.2: Meanings of English words vs. logical operators
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As we hinted in Chapter 4, the logical operators ∧ ‘and’, ∨ ‘or’, and → ‘if… then’ seem to have a different and often narrower range of meaning than the corresponding English words. A number of authors have claimed that the English words are ambiguous, with the logical operators corresponding to just one of the possible senses. Grice argued that each of the English words actually has only a single sense, which is more or less the same as the meaning of the corresponding logical operator, and that the different interpretations arise through pragmatic inferences. Before we examine these claims in more detail, we will first illustrate the variable interpretations of the English words, in order to show why such questions arise in the first place.
Let us begin with and.2 The truth table in Chapter 4 makes it clear that logical ∧ is commutative; that is, p∧q is equivalent to q∧p. This is also true for some uses of English and, such as (1). In other cases, however, such as (2–4), reversing the order of the clauses produces a very different interpretation.
(1) a. The Chinese invented the folding umbrella and the Egyptians invented the sailboat.
b. The Egyptians invented the sailboat and the Chinese invented the folding umbrella.
(2) a. She gave him the key and he opened the door.
b. He opened the door and she gave him the key.
(3) a. The Lone Ranger jumped onto his horse and rode into the sunset.3
b. ?The Lone Ranger rode into the sunset and jumped onto his horse.
(4) a. The janitor left the door open and the prisoner escaped.
b. ?The prisoner escaped and the janitor left the door open.
It has often been noted that when and conjoins clauses which describe specific events, as (2–3), there is a very strong tendency to interpret it as meaning ‘and then’, i.e., to assume a sequential interpretation. When the second event seems to depend on or follow from the first, as in (4a), there is a tendency to assume a causal interpretation, ‘and therefore’. The question to be addressed is, do such examples prove that English and is ambiguous, having two or three (or more) distinct senses?
We stated in Chapter 4 that the ∨ of standard logic is the “inclusive or”, corresponding to the English and/or. We also noted that the English word or is often used in the “exclusive” sense (XOR), meaning ‘either … or … but not both’. Actually either interpretation is possible, depending on the context, as illustrated in (5). (The reader should determine which of these examples contains an or that would most naturally be interpreted with the exclusive reading, and which with the inclusive reading.) Does this variable interpretation mean that English or is ambiguous?
(5) a. Every year the Foundation awards a scholarship to a student of Swedish or Norwegian ancestry.
b. You can take the bus or the train and still arrive by 5 o’clock.
c. If the site is in a particularly sensitive area, or there are safety considerations, we can refuse planning permission.4
d. Stop or I’ll shoot!5
Finally let us briefly consider the meaning of material implication (→) compared with English if. If these two meant the same thing, then according to the truth table for material implication in Chapter 4, all but one of the sentences in (6) should be true. (The reader can refer to the truth table to determine which of these sentences is predicted to be false.) However, most English speakers find all of these sentences very odd; many speakers are unwilling to call any of them true.
(6) a. If Socrates was a woman then 1 + 1 = 3.6
b. If 2 is odd then 2 is even.6
c. If a triangle has three sides then the moon is made of green cheese.
d. If the Chinese invented gunpowder then Martin Luther was German.
Similarly, analyzing English if as material implication in (7) would predict some unlikely inferences, based on the rule of modus tollens.
(7) a. If you’re hungry, there’s some pizza in the fridge.
(predicted inference: #If there’s no pizza in the fridge, then you’re not hungry.)
b. If you really want to know, I think that dress is incredibly ugly.
(predicted inference: #If I don’t think that dress is ugly, then you don’t really want to know.)
Part of the oddness of the “true” sentences in (6) relates to the fact that material implication is defined strictly in terms of truth values; there does not have to be any connection between the meanings of the two propositions. English if, on the other hand, is normally used only where the two propositions do have some sensible connection. Whether this preference can be explained purely in pragmatic terms is an interesting issue, as is the question of how many senses we need to recognize for English if and whether any of these senses are equivalent to →. We will return to these questions in Chapter 19. In the present chapter we focus on the meanings of and and or.
9.2.1 On the ambiguity of and
In Chapter 8 we mentioned that the sequential (‘and then’) use of English and can be analyzed as a generalized conversational implicature motivated by the maxim of manner, under the assumption that its semantic content is simply logical and (∧). An alternative analysis, as mentioned above, involves the claim that English and is polysemous, with logical and (∧) and sequential ‘and then’ as two distinct senses. Clearly both uses of and are possible, given the appropriate context; example (8a) (like (1a) above) is an instance of the logical and use, while (8b) (like (1b-c) above) is most naturally interpreted as involving the sequential ‘and then’ use. The question is whether we are dealing with semantic ambiguity (two distinct senses) or pragmatic inference (one sense plus a potential conversational implicature). How can we decide between these two analyses?
(8) a. Hitler was Austrian and Stalin was Georgian.
b. They got married and had a baby.
Horn (2004) mentions several arguments against the lexical ambiguity analysis for and:
i. The same two uses of and are found in most if not all languages. Under the semantic ambiguity analysis, the corresponding conjunction in (almost?) every language would just happen to be ambiguous in the same way as in English.
ii. No natural language contains a conjunction shmand that would be ambiguous between “and also” and “and earlier” readings so that They had a baby shmand they got married would be interpreted either atemporally (logical and) or as “They had a baby and, before that, they got married.”
iii. Not only temporal but causal asymmetry (‘and therefore’, illustrated in (1d)) would need to be treated as a distinct sense. And a variety of other uses (involving “stronger” or more specific uses of the conjunction) arise in different contexts of utterance. How many senses are we prepared to recognize?
iv. The same “ambiguity” exhibited by and arises when two clauses describing related events are simply juxtaposed (They had a baby. They got married.). This suggests that the sequential interpretation is not in fact contributed by the conjunction and.
v. The sequential ‘and then’ interpretation is defeasible, as illustrated in (9).\ This strongly suggests that we are dealing with conversational implicature rather than semantic ambiguity.
(9) They got married and had a baby, but not necessarily in that order
Taken together, these arguments seem quite persuasive. They demonstrate that English and is not polysemous; its semantic content is logical and (∧). The sequential ‘and then’ use can be analyzed as a generalized conversational implicature.
9.2.2 On the ambiguity of or
As noted in Chapter 4, similar questions arise with respect to the meaning(s) of or. The English word or can be used in either the inclusive sense (∨) or the exclusive sense (XOR). The inclusive reading is most likely in (10a–b), while the exclusive reading is most likely in (10c–d).
(10) a. Mary has a son or daughter.7
b. We would like to hire a sales manager who speaks Chinese or Korean.
c. I can’t decide whether to order fried noodles or pizza.
d. Stop or I’ll shoot!8
Barbara Partee points out that examples like (11) are sometimes cited as sentences where only the exclusive reading of or is possible; but in fact, such examples do not distinguish the two senses. These are cases where our knowledge of the world makes it clear that both alternatives cannot possibly be true. She says that such cases involve “intrinsically mutually exclusive alternatives”. Because we know that p∧q cannot be true in such examples, p∨q and pXORq are indistinguishable; if one is true, the other must be true as well.
(11) a. Mary is in Prague or she is in Stuttgart.9
b. Christmas falls on a Friday or Saturday this year.
Grice (1978) argues that English or, like and, is not polysemous. Rather, its semantic content is inclusive or (∨), and the exclusive reading arises through a conversational implicature motivated by the maxim of quantity.
In fact, using or can trigger more than one implicature. If a speaker says p or q but actually knows that p is true, or that q is true, he is not being as informative as required or expected. So the statement p or q triggers the implicature that the speaker does not know p to be true or q to be true. By the same reasoning, it triggers the implicature that the speaker does not know either p or q individually to be false. Now if p and q are both true, and the speaker knows it, it would be more informative (and thus expected) for the speaker to say p and q. If he instead says p or q, he is violating the maxim of quantity. Thus the statement p or q also triggers the implicature that the speaker is not in a position to assert p and q.
Gazdar (1979: 81–82) presents another argument against analyzing English or as being polysemous. If or is ambiguous between an inclusive and an exclusive sense, then when sentences containing or are negated, the result should also be ambiguous, with senses corresponding to ¬(p∨q) vs. ¬(pXORq). The crucial difference is that ¬(pXORq) will be true and ¬(p∨q) false if p∧q is true. (The reader should consult the truth tables in Chapter 4 to see why this is the case.) For example, if or were ambiguous, sentence (12a) should allow a reading which is true if Mary has both a son and a daughter, and (12b) should allow a reading under which I would allow my daughter to marry a man who both smokes and drinks. However, for most English speakers these readings of (12a–b) are not possible, at least when the sentences are read with normal intonation
(12) a. Mary doesn’t have a son or daughter.10
b. The man who marries my daughter must not smoke or drink.
Grice (1978: 47), in the context of discussing the meaning of or, proposed a principle which he called Modified Occam’s Razor: “Senses are not to be multiplied beyond necessity.” This principle would lead us to favor an analysis of words like and and or as having only a single sense, with additional uses being derived by pragmatic inference, unless there is clear evidence in favor of polysemy.
2 We focus here on the use of and to conjoin two clauses (or VPs), since this is closest to the function of logical ∧. We will not be concerned with coordination of other categories in this chapter.
3 Ruth. M. Kempson (1975: 56), cited in Gazdar (1979).
4 Saeed (2009: 113).
5 Saeed (2009: 113).
6 http://en.Wikipedia.org/wiki/Material_conditional
7 Barbara Partee, 2004 lecture notes. http://people.umass.edu/partee/RGGU_2004/RGGU047.pdf
8 Saeed (2009: 113).
9 Barbara Partee, 2004 lecture notes. http://people.umass.edu/partee/RGGU_2004/RGGU047.pdf
10 Barbara Partee, 2004 lecture notes. http://people.umass.edu/partee/RGGU_2004/RGGU047.pdf