Continuations and Natural Language

ed, namely, the property of being called yesterday by Mary, which can be roughly rendered as λx.yesterday(called x) m. What makes continuations essential? The semantic continuation identified in (2) is what the quantifier everyone takes for its semantic argument, its ‘nuclear scope’. In general, identifying the semantic argument of a scope-taking expression is the same thing as identifying (one of its) continuations. Thus scope-taking is the most compelling application of continuations in natural language. But it is not enough for us to show that continuations provide an elegant way to conceptualize scope-taking, given that there are other effective strategies for handling scope-taking that do not explicitly involve continuations, such as Quantifier Raising, Flexible Montague Grammar, and so on. To make a strong case that continuations are essential, we must argue that continuations provide insights that are not available in other approaches. We find inspiration for such insights in neighboring disciplines. Continuations are an idea that has been explored in some depth in the theory of computer programming languages, where they have been used (among many applications) to characterize order of evaluation of expressions in a computer program, as explained in section 12.1. And in general, one of the distinctive advantages of continuations is that they provide a way to reason explicitly about the order in which a computation unfolds. We will argue that a number of phenomena in natural language depend on order of evaluation. These include quantificational binding, crossover, reconstruction, negative polarity licensing, and donkey anaphora. In particular, one of the central results will be a robust explanation of crossover in terms of order of evaluation. (3) a. Everyonei loves hisi mother. b. *Hisi mother loves everyonei. When the quantifier everyone precedes the pronoun his, as in (3a), the binding relationship indicated by the subscripts is available, in which case (3a) expresses a generalization about filial duty: every person loves that person’s mother. But when the quantifier follows the pronoun, as in (3b), the indicated binding relationship is not possible: (3b) cannot express a thought about family relationships in general, namely, that each person’s mother loves that person. We will say that (3b) is a weak crossover violation. Ever since Reinhart (1983), standard approaches to crossover (e.g., Büring (2005)) have rejected the relevance of linear order in favor of purely hierarchical relationships based on c-command. However, as explained in chapter 2, following Shan and Barker (2006), Barker (2012), we believe that c-command is not a WHAT MAKES CONTINUATIONS ESSENTIAL? 3 requirement for quantificational binding. As a result, we follow a minority tradition including Bresnan (1994, 1998), Safir (2004a,b), and Jäger (2005), who argue that in English and in many other languages, some kind of order plays a role in crossover. Crucially, we will develop an explanation for crossover not in terms of linear order, but rather in terms of evaluation order. One reason linear order is not an adequate explanation is that there are systematic cases in which a quantifier can linearly follow a pronoun that it nevertheless can bind: (4) a. Which of hisi relatives does every mani love the most? b. The relative of hisi that every mani loves most is his mother. We explain in some detail how these facts fall out on our continuation-based approach. In brief, the independently-motivated semantics of wh-fronting and relative clause formation delay the evaluation of the pronoun until after the evaluation of the quantifier. So on our continuation-based analysis, these exceptions follow automatically from the meaning of the expressions involved. The net prediction is that it is precisely in reconstruction cases that evaluation order comes apart from linear order. Part I of the book is devoted to an in-depth case study of crossover and related phenomena, including in-situ wh and wh-fronting, donkey anaphora, coordination, and the order-sensitivity of negative polarity licensing. The analysis is expressed in a continuation-based grammar presented in what we call tower notation, as introduced in, e.g., Barker and Shan (2008). This formalism is expressly designed to be as easy to learn as possible, and in particular, easy to work with on paper and on a blackboard. Part II of the book investigates phenomena that do not depend on evaluation order. The first of the two main case studies involves scope-taking adjectives such as same and different. (5) Ann and Bill read the same book. The sentence-internal reading (the reading that does not depend on identifying some salient book from context) is notoriously difficult to treat compositionally (see, e.g., Carlson (1987), Keenan (1992)). Following the parasitic-scope approach of Barker (2007b), we show how a continuation-based analysis follows naturally from an analysis of nominal uses of same. Because parasitic scope requires higher-order continuations that are beyond the expressive power of the grammar from Part I, we develop the analyses in Part II in a continuation-based type-logical grammar first introduced in Barker (2007b). The second main case study in Part II is sluicing. (6) [John made someone happy], but I don’t know who .