IS-Sensitive Quantifier Expressions

Well-known data shows that assessors’ understandings of certain types of quantifier expres- sion are sensitive to IS. However, the mechanisms proposed in the literature to model the effects of IS are generally not extended to the determiner ‘every’. Furthermore, I will ar- gue that extant accounts fail to elaborate the factors triggering and blocking their proposed mechanisms.

The clearest example of quantifier expressions that are influenced by IS consists of quan- tificational adverbs, such as ‘always’, ‘often’ and ‘rarely’.9 The focus-sensitivity of these adverbs is illustrated by the following sentences, originally given in Rooth (1985):

8. (a) In St. Petersburg, officers always escorted [balleRInas]F.

(b) In St. Petersburg, [OFficers]F always escorted ballerinas.

(8a) is naturally paraphrased as ‘Always, when officers escorted someone in St. Petersburg, it was ballerinas they escorted’, while (8b) is paraphrased as ‘Always, when ballerinas were escorted by someone in St. Petersburg, it was officers they were escorted by’.

Arguments have also been advanced that the way we understand the determiners ‘few’ and ‘many’ is sensitive to focus. For example, Herburger (1997) perceives focus to have a truth-conditional effect on the following sentences, which were originally presented in Westerst˚ahl (1985):10

9. (a) Many Scandinavians have won [the Nobel Prize in LITerature]F.

(b) Many [ScandiNAvians]F have won the Nobel Prize in Literature.

(9a) and (9b) may be paraphrased respectively as ‘Many of the individuals of Scandinavia are winners of the Nobel Prize in Literature’ and ‘Many of the winners of the Nobel Prize in Literature are Scandinavians’.

Although the data are subtler, some have claimed that assessors’ understanding of de- terminers other than ‘few’ and ‘many’ is similarly affected by focus. For example Eckardt (1999) presents sentences like the following:

10. Ludwig washed most cars with [X-polish]F.

9_{Note that the definition of ‘quantifier expressions’ given in §(1.1.2) might be taken to suggest that quantifi-}

cational adverbs should not count as quantifier expressions, since they often occur without overt expressions that are understood to denote the set over which they quantify. I will nevertheless follow the standard approach from the literature on quantificational adverbs whereby they are analysed as denoting some kind of relation between sets.

The interpretation predicted by the standard truth conditions for (10) may be paraphrased as ‘Most cars were washed by Ludwig with X-polish’; however, Eckardt (1999) (p.167) claims that occurrences of (10) are instead naturally paraphrased as ‘Most cars that were washed by Ludwig were washed by Ludwig with X-polish’.

The examples above suggest that the way we understand occurrences of sentences with quantifier expressions may be affected by IS. Some hold that IS plays adirect role in the semantics of quantifier expressions (e.g. Rooth (1985), Partee (1991), Diesing (1992), Krifka (1992), Herburger (1997) and Herburger (2000)). Direct approaches propose that, for cer- tain quantifier expressions, lexical material that occurs as part of the focus is mapped to the quantifier’s second argument, whereas lexical material external to the focus is mapped to the first argument. Others have proposed anindirectconnection between IS and the un- derstanding of quantifier expressions (e.g. Rooth (1992), B ¨uring (1994), von Fintel (1994), B ¨uring (1996), Roberts (1996), Partee (1999), Sharvit and Stateva (2002), Beaver and Clark (2003), Mart´ı (2003) and Beaver and Clark (2008)), whereby the mapping from lexical ma- terial to a quantifier’s arguments is fixed by the semantics in a manner insensitive to IS. However, lexical material external to the focus may interact with the context in such a way that it affects the understanding of the quantifier’s first argument.

In order to delineate one way in which IS may affect the understanding of a quantifier expression, I define the following:

Focus-Based Domain Restriction Definition:An occurrence of a sentence has under- gonefocus-based domain restrictionwhen it receives a domain restricted understanding involving a proper subset of the syntactic restrictor’s extension that has been supplied by means of focus-external lexical material in the sentence (e.g. (10)).

Direct and indirect accounts of the influence of IS on the understanding of quantifier ex- pressions rarely use their proposed mechanisms to provide focus-based domain restricted understandings of determiners such as ‘every’. Most extant accounts are solely designed to handle quantificational adverbs, since these are the paradigm example of quantifier ex- pressions susceptible to the influence of IS. While Herburger (2000) extends her mechanism to indefinite determiners, she claims that it is inapplicable to definite determiners. Eckardt (1999) proposes a mechanism that allows focus-based domain restricted understandings for definite determiners, but claims that it is only applicable with particular choices of focus.11 Von Fintel (1994) is silent on the matter of whether his mechanism is applicable to determin- ers, though B ¨uring (1996) assumes that it is.

Furthermore, extant accounts have little to say about the Triggering Question. Accounts that solely target quantificational adverbs imply that their mechanisms are triggered for the vast majority of occurrences of such expressions.12 This position is not unreasonable: for, firstly, quantificational adverbs are normally taken to lack a syntactic restrictor, hence some mechanism must always apply to yield a quantifier that has a pair of arguments. Secondly,

11_{That is, Eckardt (1999) (p.177) claims that it is only possible when the determiner does not c-command the}

constituent in focus.

12_{Whilst Herburger (2000) notes a couple of cases where her mechanism of Focal Mapping applies to one overt}

or covert quantifier expression whilst leaving another overt quantificational adverb within the same sentence unaffected, she classifies this as ‘a second, less salient kind’ of reading (Herburger (2000), p.61). She does not predict when this reading will emerge.

the literature commonly holds that it is ‘practically obligatory’ to understand an occurrence of a quantificational adverb in such a way that the first argument of its extension is fixed by IS.13 An answer to the Triggering Question with respect to quantificational adverbs there- fore may well be trivial. However, §(3.1) argued that interesting, non-trivial answers to the Triggering Question are available with respect to determiners. Yet those accounts that ex- tend their mechanisms to determiners still do not provide predictions about the factors that trigger and block these mechanisms.14

It may therefore be concluded that, while mechanisms of focus-based domain restriction have been developed within the literature, a discussion of the factors that trigger and block these mechanisms is absent.