Classical NEG Raising: An Essay on the Syntax of Negation

6. Polyadic Quantification

Polyadic Quantification 6.1 Basics Consider the following ordinary standard English sentence: (1) No one ever showed me anything. Common views of course take the any phrase here to be an NPI, licensed by the c-commanding no one phrase. And common views take a nonstandard English example like (2) (equivalent to (1)) to represent a distinct phenomenon , so-called negative concord: (2) No one ever showed me nothing. (onlinelibrary.wiley.com/doi/10.1111/j.1548-1492.2012.01193.x/abstract) See Labov 1972 for discussion of negative concord in one type of nonstandard English and Haegeman and Zanuttini 1996, Ladusaw 1996a, Déprez 1997, Giannakidou 2000, Zeijlstra 2008, and references in these works, for general discussions of negative concord. However, we find it at best odd to treat related, synonymous sentences like (1) and (2) in closely related variants of the same language as representing entirely distinct grammatical phenomena. Significantly, in the framework adopted in this monograph, we are led to view both (1) and (2) as representations of the same underlying structures. That is, we regard cases like (1) as instances of negative concord, deformed by various NEG deletions.1 To elaborate, we focus on (3): (3) No man loves any woman. On our view, to account for the presence of any in the DP any woman, we would naturally postulate an underlying [NEG SOME], where NEG is deleted. The appearance of any as the morphological representative of SOME then should be a consequence of the SOME→any mapping of chapter 3. 6 50 Chapter 6 The claim that an NPI phrase like any woman in (3) represents an underlying unary-NEG structure [NEG SOME], just as that in (4a) does, is supported by the common distribution of intensives seen in (4b,c): (4) a. Xavier does not love any woman. b. No man loves any woman, not even Sylvia/not any/not a single one. c. Xavier does not love any woman, not even Sylvia/not any/not a single one. In our terms, there are only two possibilities for the underlying structure of any woman in (3), given in (5) (we ignore scope position occurrences for the moment): (5) a. No man loves [[NEG2 SOME] woman] (unary-NEG structure) b. No man loves [[NEG2 [NEG1 SOME]] woman] (reversal structure) We tentatively suggest that both structures are possible for (3). However, they give rise to subtly different (but logically equivalent) interpretations. First, consider structure (5a). Interpreting the two NEGs as independent yields the following equivalent interpretations, represented in predicate logic (supplemented with restricted quantification): (6) a. ¬∃x: x a man. ¬∃y: y a woman. x loves y b. ∀x: x a man. ∃y: y a woman. x loves y Clearly, these do not represent any correct interpretation of (3). We suggest that while (5a) is a possible structure, when (3) is so represented it is not interpreted as in (6). Rather, (3) represents polyadic quantification, with the two quantifier DPs yielding a single polyadic quantifier. Polyadic quantification exists when n-tuples (n > 1) of DPs yield a single quantifier interpreted as quantifying over n-tuples of individuals. For discussions , see Keenan 1987, 1992, 1996, May 1989, Moltmann 1995, 1996, de Swart 1999, de Swart and Sag 2002, and Peters and Westerståhl 2006. Under the polyadic interpretation of (3), the two quantifiers are not interpreted independently. Rather, the meaning is ‘there is no man-woman pair such that x loves y’. This can be represented as follows in logical notation: (7) ¬∃: x a man, y a woman. x loves y The idea that a sentence with multiple negative DPs can be given a polyadic interpretation has much support crosslinguistically. First, for the standard Polyadic Quantification 51 English variety spoken by one of us, No man loves no woman may have the interpretation in (7) (see also May 1989). Second, as illustrated in (2), in various nonstandard English dialects, multiple negative forms are interpreted as containing a single logical negation (Labov 1972), the negative concord reading. Third, parallel negative concord examples are quite productive in other languages (see de Swart and Sag 2002 for an extensive discussion of French). As for (5a) and (5b), we speculate that both structures are possible and that their slightly different interpretations can be diagnosed via appeal to stress patterns and certain continuations. The polyadic reading is clearest if the determiners no and any are both stressed. In...