the week of november 19

more on identifying scope ambiguities

(1)  We showed every subject two of the pictures.

(a)  For every subject x, there were two of the pictures y such that we showed y to x.

(b)  There were two of the pictures y such that we showed y to every subject x.

Sentence (1) seems to have two readings corresponding to 1(a) and 1(b). But as we saw earlier, 1(b) logically implies 1(a), hence we seem to have no case for positing a scope ambiguity for (1). The two alleged readings are not logically independent. The possible situations described by 1(b) are a subset of the possible situations described by 1(a). Interestingly, 2(b) does not logically imply 2(a): check the picture in the handout for Monday and Wednesday to convince yourself of that fact.

(2)  We showed almost every subject two of the pictures.

(a)  For almost every subject x, there were two of the pictures y such that we showed y to x.

(b)  There were two of the pictures y such that we showed y to almost every subject x.

Since 2(a) and 2(b) are logically independent, we have a good case for positing a scope ambiguity for (2). But if there is a scoping mechanism that produces reading 2(b) for a sentence like (2), would we actually want to block that mechanism from applying to (1)? Wouldn't we rather want to say that whatever scoping mechanism has to be invoked to produce reading 2(b) for (2) should be free to apply to (1) as well?  The only thing that would be special about (1) would then be that (1) doesn’t actually provide us with an argument for the existence of such a scoping mechanism.  

indefinite DPs with exceptional scope properties

We looked at examples due to Janet Fodor & Ivan Sag, who argued that once we recognize the possibility that there might be referential uses of indefinites, there seems to be no reason to assume that indefinites have exceptional scope properties. Indefinite DPs might just be ambiguous between DPs with denotations of type e, in which case they are scopeless, and DPs with denotations of type <<et>t>, in which case they are quantifier phrases that have all the properties of other quantifier phrases, whose scope is usually clause bound. Fodor & Sag's argument was challenged by a number of researchers, including Donka Farkas and Dorit Abusch, who produced examples with indefinites that clearly had the exceptional scope properties that Fodor and Sag said did not exist. The issue of wide-scope indefinites has since gained momentum, in particular through Lisa Matthewson's work, who showed that the Salish language St'at'imcets has a designated class of indefinites that do not only show the apparently exceptional scope behavior targeted by Fodor & Sag's paper, but generally take wide scope with respect to negation, intensional operators, and universal quantifiers. Those indefinite DPs are now typically assumed to be either headed by determiners that denote choice functions (functions that map sets of individuals to an individual in the set), or else singleton indefinites in the sense of Schwarzschild (2002). The handout for Monday and Wednesday is here.

New work on indefinites with exceptional scope properties

Luis Alonso Ovalle and Paula Menéndez-Benito: Another look at indefinites in islands.

Authors' abstract: This paper contributes to the semantic typology of indefinites by presenting experimental evidence on the scopal behavior of the Spanish indefinites un and algún, and by discussing the theoretical implications of these data.Two off-line experiments investigate exceptional scope in relative clauses and in conditionals. These studies show that while in relative clauses exceptional scope is possible for both indefinites (although it is harder for algún), in conditionals, exceptional scope is blocked for algún and available (but difficult) for un. The difference between the two types of islands is challenging for most theories of scope, which predict any indefinite to have
the same scopal properties across islands. We propose an account cast within Kratzer and Shimoyama’s 2002 alternative semantics, in which indefinites denote sets of alternatives that expand
until they meet an appropriate operator. The ‘scope’ of an indefinite extends up to the position occupied by the operator. To account for the contrast between the two islands, we claim that conditionals introduce an operator that blocks alternative expansion (Alonso-Ovalle, 2006) but relative clauses allow alternatives to project further up. The difference between the two indefinites
is attributed to the fact that un can be a singleton indefinite, in the sense of Schwarzschild (2002) but algún is a domain widener (Alonso-Ovalle and Menéndez-Benito, 2003 (PDF)).