Abstract
This chapter introduces the subject matter of the book, and reviews some insightful but unsatisfactory theories. The distinction between regular and irregular negations is defined and illustrated, along with the distinction between negations and the more general class of negatives. A total of six types of irregular negations will be identified, along with four types of irregular negatives that are not negations. We will review characteristic features or marks of irregularity, such as intonation contour, polarity reversal, echoicity, and use for objection or denial, including a number that have received little attention. None are definitive of irregular negations. The chapter will conclude by raising the question whether the observed ambiguity of negations is semantic or pragmatic, and distinguishing different types of semantic ambiguity.
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Obversion is the rule of Aristotelian logic according to which the result of changing the quality of a categorical proposition and replacing its predicate with a complementary predicate is an equivalent proposition (Davis 1986: Ch. 5). Thus the O (negative particular) proposition Some S are not P is equivalent to the I (affirmative particular) proposition Some S are non-P. For singular propositions, obversion is given by (2)(b). The rule is presupposed in the modern logical tradition by the practice of symbolizing both ‘s is not P’ and ‘s is non-P’ as ‘–Ps.’
- 3.
See Horn 1989: 2, 6–18; 2015; Ladusaw 1996: 322, 324; Herberger 2011: 1642. Horn draws his terminology from Aristotle’s distinction between contrary and contradictory opposition. But to my knowledge, the negation or denial of a proposition for Aristotle must be contradictory, as Horn (1989: 35, 268) himself affirms. See e.g. Aristotle’s Categories 13b27-35; On Interpretation, Ch. 10.
- 4.
The symbol ‘ä’ represents the vowel sound in ‘ah’ and ‘ma,’ ‘ā’ the vowel sound in ‘pay’ and ‘ate.’
- 5.
See Horn 1989: 385; Geurts 1998; Davis 2010, 2011, 2013. The formulation (f)n is colloquial. In formal writing, we would enclose Vulcan is hot in quotation marks or italicize it. There are no quotation marks in speech, but the subordinated sentence would receive a distinctive intonation contour. See Sect. 3.6.2.
- 6.
When s does not exist, ‘s is P’ and ‘s is not P’ are jointly exhaustive only if the latter is irregular (Sect. 1.4).
- 7.
Double negation fails for Hornian “contrary negation” because contraries fail to be jointly exhaustive, not because they are irregular in any way. To see this, assume that when a contrary operator ¬ is applied to A is red, it yields a sentence equivalent to A is yellow, that when ¬ is applied to A is yellow it results in a sentence equivalent to A is blue, and so on. Then ¬¬(A is red) is equivalent to A is blue, which does not follow from A is red. Contrast Ladusaw (1996: 322, 324). Note that unlike the contradictory morpheme non-, contrary morphemes do not iterate in English. Non-non-red has a clear meaning. Un-unhappy and in-inexpensive are not even English words.
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Since a negation for us is an interpreted sentence, a negation cannot strictly speaking be ambiguous. What is ambiguous is the word sequence (a sentence) that can be interpreted as a regular or irregular negation.
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Horn 1989: 368; 374–5; 392–413; 496. See also Bolinger 1972: §3.2; Karttunen and Peters 1979: 46–7; Kempson 1986: 88; Burton-Roberts 1989: 118; Seuren 1990: 449–52; Chapman 1996: 390–1; Israel 1996: 621n1; Ladusaw 1996: 327; Carston 1998: 332ff; Geurts 1998: 275, 278–80, 303; van der Sandt 2003: §7; Kay and Michaelis 2012: 2288.
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NPIs are permitted in some constructions without not, including interrogatives, the antecedents of conditionals, the subordinate clauses of some emotion factives, and quantifiers with a negative sense. Thus Does Mary have any money? and If Mary has any money, she will buy flowers are grammatical, as are Mary regrets that she touched any poison ivy and Few children own any stocks. For a more complete list, see Ladusaw 1996: §3.1; Huddleston and Pullum 2002: 822–38; and Giannakidou 2011: §3. Note too that any is an NPI when it is indefinite or particular in meaning, but not when it is generic or universal. That is why Any cat hunts mice and Don Juan chases any woman are licit but not Figaro married any woman (contrast Giannakidou 2011: 1693). Note finally the asymmetry between positive and negative polarity items. Whereas NPIs are positively ungrammatical in the contexts that admit PPIs, PPIs are disfavored but not ungrammatical in the negative contexts that admit NPIs (contrast Ladusaw 1996: 326–7). The behavior of polarity items is extremely complex.
- 15.
Ladd’s (1980: 153) hypothesis that “The meaning of fall-rise is thus something like focus within a given set” fits many of our examples, but not presupposition-canceling denials.
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Aristotle Categories, Ch. 10, 13b17-20; Russell 1905, 1919; Quine 1953: Chs. 1 and 9; 1960: §37; Grice 1981; Kempson 1975; Wilson 1975; Boër and Lycan 1976; Atlas 1977, 1989; Gazdar 1979; Horn 1985, 1989: 362–70; 1996: 305; Carston 1998; Herberger 2011: 1648. When extended, Aristotle’s view in the Categories undermines the Aristotelian logic of general propositions set out in the Prior Analytics, as Strawson observed. Russell treated proper names differently from definite descriptions, regarding Vulcan is hot as meaningless (and thus neither true nor false). It was Quine who extended Russell’s view to names.
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Contrast Ladusaw 1996: 322. Some infer that if it is possible for neither Vulcan is hot nor Vulcan is not hot to be true, then they are not jointly exhaustive and thus not contradictory (see Herberger 2011: 1644). This inference is valid only if being jointly exhaustive and contradictory entail that one must be true, not just that both cannot be false. I believe that Vulcan is hot and Vulcan is not hot should be classified as contradictory even if neither is true because they cannot both be false, and one must be true if either has a truth value. Note that to say that a sentence is neither true nor false is not to say that it has no truth conditions or could not be true, as Herberger (2011: 1644) suggests. It is possible for Vulcan to exist and be cold, in which case Vulcan is not hot would be true. (5)n differs markedly from (30) in this respect.
- 20.
They are “opposing” in the traditional Aristotelian sense of having the same subject and predicate but differing in quantity or quality. But they are not opposed in the conventional sense of being incompatible (a familiar source of confusion for introductory logic students).
- 21.
The Aristotelian tradition classified Some S is non-P as affirmative even though it is equivalent by obversion to Some S is not P, which is classified as negative. The basis for this classification is unclear given that No S is P is negative in the Aristotelian tradition. It will not matter for our purposes whether Some S is non-P is classified as positive or negative. We do not need a precise definition of ‘negative.’
- 22.
Horn (1989: 494) provides attested examples of sentences like (31) intended as logically regular negations, including the following passage from John Le Carre’s The Little Drummer Girl: “She swung round, she took two strides to him, waiting for someone to stop her, but someone didn’t.” See also Linebarger 1980: 57; Carston 1998: 320; Breheny 2008: 99.
- 23.
Horn (1989: 315ff; 2015) thinks that John does not believe there is a god on its neg-raising interpretation is “weaker” or “more attenuated” than John believes there is no god, and so rejects a synonymy claim. What I believe he is pointing to is the fact that the former is less clear than the latter because of its ambiguity. That is compatible with the neg-raising meaning of the former being equivalent to the meaning of the latter. Horn (1989: 350ff) similarly notes that I don’t think your jumpsuit is entirely appropriate is more polite than I think your jumpsuit is not entirely appropriate. But that is because the strong interpretation of the former is not forced on the addressee, as Horn notes. With the ambiguous form, the speaker has some deniability if needed. Other examples of comparative weakness Horn cites are genuine and do establish non-synonymy. For example, I think she’s not happy and I don’t think she is happy (on its neg-raising interpretation) are weaker than I think she is unhappy because someone who is neither happy nor unhappy is not happy. Bolinger (1972: 38) also denies synonymy, contrasting (a) I don’t think he likes it; maybe he does, but I don’t think so with (b) I think he doesn’t like it; maybe he does, but I don’t think so. Bolinger marks (b) with an asterisk. But while (a) is a more natural form of expression, (b) is perfectly grammatical.
- 24.
In previous publications, I classified irregular contraries as irregular negations because they do not satisfy truth-value reversal and have another regular interpretation (see e.g., Davis 2011). I did not pay sufficient attention to their failure to be negations. (They are “contrary negations” in Horn’s (1989) broad use of ‘negation’; but as I use the term, the only negations are contradictory negations, as noted in Sect. 1.1.)
- 25.
The raising metaphor may be confusing given that syntactic trees are generally drawn upside down, with their “branches” hanging down. So a subordinate-clause node is said to be “lower” than the main clause because it is lower on the page even though it is higher in the tree.
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S is not willing to V is similar in having an NR interpretation on which it means S is unwilling to V. The latter is equivalent to S is willing to not V, not to V but stronger than S is willing to not V rather than V. John may be willing to not play rather than play even though he is willing to play; but in that case he is not unwilling to play. S believes not p rather than p, in contrast, is equivalent to S believes that not p, not that p.
- 27.
The ambiguity of sentences like (36)(a) and (b) is well-known (see e.g., Huddleston and Pullum 2002: 804, 815). But its relationship to the ambiguity of (34) does not seem to have been recognized. I never encountered the term ‘neg-lowering’ in any of the works I have read on negations, but did find it in Harlow (1995: 333), where it is used as the name of a transformational process Lakoff (1970: 169–71) proposed that moves a negative morpheme from a subordinate clause in deep structure or logical form to the main clause in surface structure. Lakoff used it to account for the interpretation of a sentence like Bill did not pass because he drank too much as the negation of an explanation rather than the explanation of a negation. I think this ambiguity is more simply ascribed to whether did not has within its scope pass or pass because he drank too much. Neither interpretation is syntactically irregular. Lakoff himself did not use either ‘neg-raising’ or ‘neg-lowering.’ ‘Not-transportation’ was his term for neg-raising (Lakoff 1970: 30–1).
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Sentences like (36)(d) have a presupposition-canceling interpretation. Consider: Vulcan cannot be hot: it does not exist. The root of the negation whose truth is being denied is Vulcan can be hot.
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See also Gazdar 1979: 67; Horn 1985: 135; 1990: 495, 500; 1992a: 265; 2002: 77; 2004: 10; Burton-Roberts 1989: 111, 118ff; van der Sandt: 1991: 334–5, 337; 2003: §3, §4; Carston 1996: 312, 320, 325, 327; Chapman 1996: 389, 392; Ladusaw 1996: 323; Levinson 2000: 212; Huddleston and Pullum 2002: 790; Huang 2007: 44; Kay and Michaelis 2012: 2287; Yoshimura 2013: §3.1 (concerning Japanese sentences containing node wa nai ‘It is not that’). Horn (1989: 363, 374–7, 420–434) discusses many others who have held similar views, and credits the term ‘metalinguistic’ to Ducrot 1972. Contrast Jespersen 1933: 300–1, who noted the irregularity of limiting-implicature denials but did not classify them as metalinguistic; and Geurts 1998: 278, 294.
- 31.
“The correct generalization about the metalinguistic cases is that the material in the scope of the metalinguistic operator, or some of it at least, is echoically used” (Carston 1988: 320). This is “the single essential and unifying property” (1998: 318). See also Carston 1996: 312, 320–322, 325n7, 327; 1998: 317, 321; 2002: 296–7, 302. It is hard to get a firm fix on Carston’s view. She follows Sperber and Wilson (1986, 1987: 708–9) in saying that “A representation is used echoically when it reports what someone else has said or thought and expresses an attitude toward it”—when it is used to “represent a representation”(Carston 1996: 320; see also 2002: 298). Nevertheless, she also claims that the echoic property of a metalinguistic negation need not involve “the content of an actual previous utterance”(1996: 323; see also 1998: 317ff). Carston’s definition of echoic use does not fit any of our examples, since none of them report or represent what someone else has said or thought, even implicitly.
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- 34.
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- 36.
Horn (2002: 72–3) calls ‘any’ a weak NPI.
- 37.
- 38.
Van der Sandt 1991: 334–5; 2003: 62–3; 2006: 575. Cf. Karttunen and Peters 1979: 47, discussed in Horn 1989: 149, 369; Geurts 1998: 283–6. It is not clear how Van der Sandt intends to treat “connotations (conventional implicatures, style, and register).” I assume they are to be included in the implicatures. Subsequent formulations of Van der Sandt’s theory are complex because he uses discourse representation theory (Kamp and Reyle 1993; Geurts 1999) to generate the truth conditions for ‘not-p’ from those of the previous utterance ‘p*’ (and the “common ground”). I focus on the truth conditions assigned, and not the method of generating them.
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This is not necessarily the meaning the root “would have had if it had been uttered there” as an independent sentence (Van der Sandt 1991: 335). It is possible that if Dena had uttered Vulcan is hot as an independent assertion, she would have been describing Vulcan Inc. stock or speaking in code.
- 41.
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Cf. Carston 1998: 327–8.
- 43.
If The queen of England owns some English land has other presuppositions or truth conditions, they go inside –[ ].
- 44.
It is even harder to give It is not possible that 2 + 2 = 5 the same irregular interpretation because it is so obviously impossible that 2 + 2 = 5. But we can hear it by emphasizing ‘possible’ and imagining ‘It is necessary that 2 + 2 = 5’ as the sequent. In that case, we would naturally conclude that the speaker is either confused, or very slow mathematically, or trying to confuse us.
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- 47.
‘F!x’ means “x is uniquely F,” i.e. “Fx & ∀y(Fy ⊃ y = x).”
- 48.
Cf. Bach and Harnish 1979: 174–5; Davies 1983: 71–2. One evaluative-implicature denial is more like limiting- and metalinguistic-implicature denials in this respect: The glass isn’t half empty, it’s half full has become such a stock expression that it is used in connection with things other than glasses. It might be used, for example, to endorse or drive home in5. This particular evaluative-implicature denial is unusual in that it has become an idiom with a generalized meaning.
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Davis, W.A. (2016). Irregular Negatives. In: Irregular Negatives, Implicatures, and Idioms. Perspectives in Pragmatics, Philosophy & Psychology, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-7546-5_1
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