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Simple Even Hypothesis: NPIs and Differences in Question Bias

David Krassnig (University of Konstanz)

BACKGROUNDThe simple even hypothesis of negative polarity item (NPI) licensing recently rose to greater prominence with the work of Crniˇc (2014). His model accounts for the NPIs’ clash with upward monotone environments (UME), as well as for the licensing of NPIs in (Strawson) downward monotone environments (DME), and non-monotone environments. This accounts for most environments that were considered troublesome for the simple even hypothesis (cf. Heim, 1984). Only a few issues remain to be solved: The difference in question bias between the biased even ONE questions and the unbiased NPI questions is one of them:

(1) Did John win any medal? (Yes. / No.)

(2) Did John win even ONE medal? (# Yes. / No.)

GOALSThis paper shows that the simple even hypothesis is able to account for the difference in question bias, if we assume that Crniˇc’s (2014) evenNPIis covertly composed of two independent

focus particles: also and only (cf. Guerzoni, 2003).

EVEN AND NPIS Crniˇc’s (2014) account works under four basic assumptions: First, even is free to move at LF without leaving a trace. Second, focus and NPIs generate sets of possible alternatives. Third, even associates with the aforementioned alternatives and generates the scalar presupposition of its prejacent being the least probable member of the focus set. Fourth, NPIs like any are equivalent to indefinites, i.e. they are weak existential quantifiers.

(3) JevenKg,c(C)(p)(w) = p(w) is defined iff ∀q ∈ C[p 6= q → pCc q]

(4) JanyKg,c =JoneKg,c =JaKg,c = [λPhe,ti.[λQhe,ti.∃x[P(x) ∧ Q(x) ∧ card(x) = 1]]] (5) F(Jany/one/aKg,c) = {[λPhe,ti.[λQhe,ti.∃x[P(x) ∧ Q(x) ∧ card(x) = n]]]|n> 1}

An NPI is licensed iff it is within the scope of a covert even and iff the aforementioned even associates with the NPI’s alternatives. Under these conditions NPIs and even ONE expressions are only felicitous if they occur within an environment that either suspends or reverses the entailing relation between the original meaning and its focus alternatives. Otherwise, the original meaning is entailed by all of its focus alternatives, which means that it must be the most probable set member: Items that entail another item are at most as likely as the entailed item itself (cf. Kolmogorov, 1933). The problem with these assumptions is that they do not mesh well with modern question models. Contemporary models either apply even to, both, the affirmative and the negative answer (cf. Guerzoni, 2003), or they apply it to the negative answer only (cf. Guerzoni and Sharvit, 2014). The former approach would classify either question type as biased, whereas the latter predicts that neither question type is biased (Crniˇc, 2014, p. 139 ff.). The latter is illustrated below.

QUESTIONSGuerzoni and Sharvit (2014) assumes that the LF of polar questions contains the affirmative and the negative answer in full detail. The answers are conjoined by a disjunction that is bound by the question operator whether (i.e. polar questions are alternative questions). In the case of NPI questions, the positive answer is then elided by pragmatic omission. The NPI itself is licensed by an even that moves above the negation of the negative answer. This negation reverses the entailing relations in the focus set, ensuring that even’s prejacent is the least probable element of the focus set’s members, since it now entails all other focus alternatives. See the LF structure of (1) and its corresponding Hamblin set below:

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(6) [whetherL] [ 7 ? [John won a medal (or7[even [not) John won any medal]]]] (7) JDid John win any medal?Kg,c= {JJohn won a medalKg,c,

JevenK

g,c(C)(

Jnot [John won any medal])K

g,c}

Crniˇc (2014) and Guerzoni and Sharvit (2014) can therefore account for the licensing of NPIs in questions. However, the problem is that this LF is also the only possible option for (2). There are no other viable constructions that do not violate the constraint on ellipsis (Crniˇc, 2014, p. 140). Crniˇc (2014) can therefore not derive the observed difference in bias.

SPLIT EVEN To circumvent this problem we propose that even is composed of two independently movable focus particles: also and only, as proposed by Guerzoni (2003) for languages where such constructions are overtly seen. We adopt her definitions:

(8) JalsoKg,c(C)(p)(w) is defined iff ∃q[q ∈ C ∧ q 6= p] ∧ q(w) = 1 (cf. Guerzoni, 2003) (9) JonlyNPIKg,c(C)(p)(w) is defined iff ¬∃q ∈ C[q 6= p ∧ q(w) = 1], and

∀q ∈ C[q 6= p → q Cc p] (cf. Guerzoni, 2003)

We extend her account for these languages (e.g. German, Italian, and Dutch) to languages where such constructions are not overtly seen (e.g. English). In line with Crniˇc (2014), we propose that NPIs are licensed iff they are within the scope of both focus particles and iff the NPIs’ alternatives associate with both focus particles. According to Guerzoni (2003), also must move above a DM operator, whereas only remains below the aforementioned operator. This is done in order to avoid a clash of presuppositions. However, this interpretability of only within an UME allows us a greater range of freedom concerning the LF of questions:

(10) a. [whetherL] [ 7 ? [CP (or7[also [not) onlyweakCP]]]]

b. {JJohn won one medalKg,c,Jalso [not [only [John won oneF medal]]K

g,c}

(11) a. [whetherL] [ 7 ? [onlyweakCP (or7 [also [not ) onlyweakCP]]]] b. {Jonly [John won oneF medal]K

g,c,

Jalso [not [only [John won oneFmedal]]K

g,c}

The LF (10) is identical in effect to the LF (7). In (11), however, the question inherits the presupposition of exclusivity carried by evenNPIfrom both the affirmative and negative answer.

Therefore, the addressee is limited to answer within the scope of John having won exactly one medal or no medal at all. It is already considered settled that John did not win n > 1 medals. RHETORICITYThis kind of reading is directly analogous to the reading of minimizer questions

as analysed by van Rooy (2003). Consider the following question and its negative bias:

(12) Did John (even) LIFT A FINGER to help Mary? (# Yes. / No.)

He argues that the minimizer and its presuppositions restrict the possibility of an answer to two possible options: A negative answer that states that no help was given at all, and an affirmative answer that states that the least possible amount of help was given. The question itself already carries the presupposition that John did not give any amount of help greater than the minimally possible amount of help. This means that both answers reflect equally badly on John, which renders a differentiated answer unnecessary, deriving the desired rhetoricity of the question.

MOTIVATIONThat means that the simple even hypothesis is able to account for the difference in question bias under the following assumptions: (a) That evenNPI is covertly split into two

focus particles, and (b) that NPI questions possess the LF (10), whereas even ONE questions possess the LF (11). The difficulty lies in motivating these differing scopes of ellipsis. The LF for NPIs is easily motivated by known observations:

(13) John didn’t win any medal, but Mary did (win a medal).

Here, the elided material does not carry any NPI properties or even-like presuppositions. It is also perfectly felicitous to spell out the elided material. With even ONE, the spelling out of elided material appears to be somewhat more complicated:

(14) John didn’t win even ONE medal, but Mary did (? win a medal / win ONE medal). Both options appear to be a bit ‘weird’ in comparison to (13). The second option, however, appears to be a bit better than the first one. It also gives rise to the notion that Mary only won exactly one medal. This suggest that the difference in scope might be viable and occurs even outside the scope of questions. However, this requires further, far more detailed investigation. If it is viable, however, the simple split-even hypothesis can account for the difference in bias.

References

Crniˇc, Luka. 2014. Against a dogma on NPI licensing. In The art and craft of semantics: A festschrift for Irene Heim, ed. Luka Crniˇc and Uli Sauerland, volume 1, 117–145. Cambridge, Massachusetts: MIT Working Papers in Linguistics 70.

Guerzoni, Elena. 2003. Why even ask? On the pragmatics of questions and the semantics of answers. Doctoral Dissertation, Massachusetts Institute of Technology, Cambridge, Massachusetts.

Guerzoni, Elena, and Yael Sharvit. 2014. ‘Whether or not anything’ but not ‘whether anything or not’. In The art and craft of semantics: A festschrift for Irene Heim, ed. Luka Crniˇc and Uli Sauerland, volume 1, 199–224. Cambridge, Massachusetts: MIT Working Papers in Linguistics 70.

Heim, Irene. 1984. A note on negative polarity and downward entailingness. In Proceedings of NELS, volume 14, 98–107. Amherst, Massachusetts: GLSA Publications.

Kolmogorov, Andrey. 1933. Grundbegriffe der wahrscheinlichkeitsrechnung: Ergebnisse der mathematik. New York: Chelsea Publishing Company. Translated as Foundations of Probability, 1950.

van Rooy, Robert. 2003. Negative polarity items in questions: Strength as relevance. Journal of Semantics 20:239–273.

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Polarity Reversals Under Sluicing