Even NPIs in Questions
Elena Guerzoni (MIT)

-THE PROBLEM: As is known, standard NPIs like 'any' and minimizers NPIs like 'lift a finger' are grammatical in questions. The two categories of NPIs, however, affect the interpretation of the question differently as shown in (1) (an aspect of the problem addressed in Ladusaw '79, but see also Borkin '71).

(1)

a. Did John lift a finger to help? (only Negative Rhetorical)

b. Did anybody call? (also Information Seeking)

This paper focuses on this contrast. My proposal can be seen as an elaboration of Ladusaw's original insight, which attributes the difference between (1a) and (1b) to a general pragmatic principle that links the way a question is asked to the speaker's expectations concerning the answer.

-THE PROPOSAL: Y/n questions denote sets containing a proposition and its negation. However I show that in all contexts when minimizers occur in a y/n question the set of possible answers relative to the context is the singleton containing the negative answer - a situation that yields the effect of a rhetorical question. The reason why only minimizers trigger this effect is that they contain a (silent) 'even' (like Hindi NPIs (Lahiri'98) and Dutch ook maar-NPIs (Rullmann'96)), while 'any' does not (Schmerling '71, Heim'84).

-DISCUSSION: Minimizers like 'lift a finger' denote the low endpoint of a scale. When the two elements involved in their structure ('even' and an expression referring to a lower scale-endpoint) occur in a question only a negative rhetorical reading is indeed available (Wilkinson '96), as shown in (2). Thus, an explanation of the rhetorical reading of (2) will automatically extend to (1a).

My account is based on an analysis of y/n questions as elliptical alternative questions where ellipsis affects the second (negative) disjunct (Bennett'77). I begin by noting that a y/n question containing 'even' has two different LFs depending on the scope of 'even' relative to negation in the ellipsis site (Wilkinson'96); an ambiguity that affects only its presuppositions, given that 'even' lacks truth-conditional import. Thus, in principle, (2) is ambiguous between the two readings A and B:

A.LF1:[even you slvd [t.e.pr][f]]or[not[even you slvd [t.e.pr][f]]]

NOT>EVEN

B.LF2:[even you slvd [t.e..pr.][f]]or[even[not you slvd [t.e.pr.][f]]]

EVEN>NOT

I show, however, that the ambiguity is actually resolved in favor of reading B. This happens because both possible answers to A have an unsatisfiable presupposition, but one answer to B has a presupposition that is satisfiable. Let's now see how this comes about.

Presuppositions project from the LF of a y/n question to its answers (Bennett 77): the positive answer inherits the presuppositions of the positive disjunct, the negative answer those of the negative disjunct. This means that (3a), when uttered as an answer to (2) under reading B, presupposes (4). Similarly the affirmative answer (3b), presupposes (5). On the other hand, under reading A BOTH answers will presuppose (5). It is known that when the focus of 'even' denotes the lower endpoint of a scale the presupposition of 'even' can be satisfied only if 'even' takes scope over a negation as in (4) (Lahiri'98): there can be no context where (5) is true. This situation excludes reading A.

Finally, an answer to B like (3b) is excluded: presuppositions' satisfaction in a context plays a crucial role in determining what counts as a possible answer to a question in that context. Specifically, only those sentences whose presuppositions are true in a context (possibly after accommodation) are good answers in that context. In the present case (3b) fails to satisfy the condition, no matter what the context is.

It follows that in all contexts, a question containing 'even'+the low endpoint of a scale (thus also a minimizer) has only one possible answer: a negative answer. If the set of answers is always a singleton, the question can never be used to seek information. That is why the question is felt to be rhetorical.

-EXTENSION TO WH-QUESTIONS As can be seen in (6a-d) the same phenomenon obtains in wh-questions. The account proposed for yes/no questions extends to these cases under one of the following assumptions 1.Wh- questions are sets of y/n questions (Higginbotham '93) or 2.Wh-phrases quantify over GQs.

-FURTHER IMPLICATIONS: My proposal yields an indirect argument in favor of Wilkinson's scope theory of even and supports an old view on y/n questions as concealed alternative questions (Bennett '77).

Data:

(2)

Q: Did you even solve [the easiest problem]f (only Negative Rhetorical)

(3)

a. A': No, I didn't (even) solve [the easiest problem] [f].

b. A": Yes, I (even) solved [the easiest problem][f].

(4)

Scalar Presupposition: (read 't.e.p'. as 'the easiest problem')

Ax [x ' t.e.pr. --> likelihood(that I didn't solve x) >

likelihood (that I didn't solve t.e.pr.].

= 'the easiest problem is the MOST likely thing for me to have solved'

(5)

#Scalar Presupposition:

Ax [x ' t.e.pr.--> likelihood (that I solved x) >

likelihood (that I solved t.e. pr.)]

= 'the easiest problem is the LEAST likely thing for me to have solved'

(6)

a. Who lifted a finger to help? (only Negative Rhetorical)

b. Which of these girls would hurt a fly? (only Negative Rhetorical)

c. Who has the least bit of taste? (only Negative Rhetorical)

(see also data in Borkin'71)

d. Q: Which of your kids even solved [the easiest problem][f]? (only NR)

A': Mary (even) solved the easiest problem.

#Scalar Presupposition:

Ax [x ' t.e.pr. --> likelihood (that M solved x) >

likelihood (that M solved t.e.pr.)]

A'': No one (of my kids) (even) solved the easiest problem.

even [no one solved t [the easiest problem[f]]]

Scalar Presupposition:

Ax [x ' t.e.pr.--> likelihood (that no one solved x) >

likelihood (that no one solved t.e.pr.)]

Selected References:

Bennett, M. (1997). A Response to Karttunen. In L&P 1., 279-300.

Borkin, Ann (1971). Polarity Items in Questions. CLS

Heim, I (1984). A Note on Negative Polarity and DE-ness. In C. Jones and P. Sells (eds.) Nels 14.

Han,C.& Siegel,L(1996). Syntactic and Semantic Conditions on NPI Licensing in Questions. WCCFL 15.

Ladusaw (1979). Polarity Sensitivity as Inherent Scope Relation. Ph.D. dissertation, Austin.

Lahiri, U. (1998).Focus and Negative Polarity in Hindi. in Natural Language Semantics 6.1., 57-123.

Karttunen, F. & Karttunen, L. (1977). Even Questions. Nels 7, GLSA, UMASS Amherst.

Progovac, L (1993). Negative Polarity and Grammatical Representation. L&P 10

Rullmann, H. (1996). Two Types of Negative Polarity Items. In NELS 26. 335-350.

Schmerling, S. (1971). A Note on Negative Polarity. Papers in Linguistics 4.1.,

Sugizaki, H. (2001). Another Chinese-Type of Question. Ms UCONN.

Wilkinson, K. (1996). The scope of Even. Natural Language Semantics 4.2., 193-215.