Composing alternatives

Linguist and Philos DOI 10.1007/s10988-016-9195-2 ORIGINAL RESEARCH Composing alternatives Ivano Ciardelli1 · Floris Roelofsen1 Nadine Theiler1 · © The Author(s) 2016. This article is published with open access at Springerlink.com Abstract There is a prominent line of work in natural language semantics, rooted in the work of Hamblin, in which the meaning of a sentence is not taken to be a single proposition, but rather a set of propositions—a set of alternatives. This allows for a more fine-grained view on meaning, which has led to improved analyses of a wide range of linguistic phenomena. However, this approach also faces a number of problems. We focus here on two of these, in our view the most fundamental ones. The first has to do with how meanings are composed, i.e., with the type-theoretic operations of function application and abstraction; the second has to do with how meanings are compared, i.e., the notion of entailment. Our aim is to reconcile what we take to be the essence of Hamblin’s proposal with the more orthodox type-theoretic framework rooted in the work of Montague in such a way that both the explanatory utility of the former and the solid formal foundations of the latter are preserved. Our proposal builds on insights from recent work on inquisitive semantics, and it also contributes to the further development of this framework by specifying how the inquisitive meaning of a sentence may be built up compositionally. This paper integrates and extends ideas and results from Theiler (2014) and Ciardelli and Roelofsen (2015). We are grateful to two anonymous reviewers for their useful feedback, to Andreas Haida, Reinhard Muskens, Wataru Uegaki, and Yimei Xiang for helpful comments on earlier presentations of this material, and especially to Maria Aloni, Lucas Champollion, Liz Coppock, Donka Farkas, Jeroen Groenendijk, Edgar Onea, and Anna Szabolcsi for extensive discussion. Financial support from the Netherlands Organization for Scientific Research (NWO) is gratefully acknowledged. B Floris Roelofsen 1 Institute for Logic, Language, and Computation, University of Amsterdam, P. O. Box 94242, 1090 GE Amsterdam, The Netherlands 123 I. Ciardelli et al. Keywords Alternative semantics · Inquisitive semantics · Type-theoretic semantics · Compositionality 1 Introduction There is a prominent and fruitful line of work in natural language semantics which deviates from the standard Montagovian approach (Montague 1970, 1973) in that it takes the semantic value of an expression to be a set of objects in the expression’s usual domain of interpretation, rather than a single object. For instance, the semantic value of a complete sentence is not taken to be a proposition but a set of propositions, the semantic value of an individual-denoting expression is not taken to be an individual but a set of individuals, and so on. In this framework, the elements of the semantic value of an expression are called alternatives, and the framework itself is referred to as alternative semantics. A range of linguistic phenomena have received insightful analyses in alternative semantics, including questions (Hamblin 1973), focus (Rooth 1985), indeterminate pronouns (Shimoyama 2001; Kratzer and Shimoyama 2002), indefinites (Kratzer and Shimoyama 2002; Menéndez-Benito 2005; Aloni 2007), and disjunction (Simons 2005; Alonso-Ovalle 2006; Aloni 2007).1 While this wealth of applications shows that alternatives are a useful tool in the semantic analysis of natural language, the move from the orthodox type-theoretic framework to an alternative-based one also raises some fundamental issues. In this paper, we will be concerned with two of these issues, in our opinion the most basic ones. The first issue, which we will refer to as the compositionality issue, has to do with the fact that in alternative semantics, meanings can no longer be composed by means of the standard type-theoretic operations of function application and abstraction. The second, which we will refer to as the entailment issue, has to do with the fact that meanings in alternative semantics can no longer be compared by means of the standard type-theoretic notion of entailment. Both problems concern very fundamental features of the semantic framework, and moreover, as we shall see, neither of them has a straightforward solution. We will examine why these problems arise. Our diagnosis will be that it is not the presence of alternatives per se that is to be held responsible, but rather some specific features of the architecture of alternative semantics. For two such features we will argue that they are not essential for the utility of the framework, and we will show how making different architectural choices results in a framework in which the observed problems do not arise. While the general aim of this paper is to reconcile alternative-based semantic theories developed in the Hamblin tradition with the more orthodox type-theoretic framework rooted in Montague’s work, it also contributes to a more recent and more specific line of work, namely that of developing the framework of inquisitive semantics (Ciardelli et al. 2013, 2015, among others). Namely, while previous work on inquisitive semantics has laid out a formal notion of sentence meaning that is more fine-grained than the standard truth-conditional notion—comprising both informative 1 We will concentrate here on the role of alternatives at the level of ordinary semantic values, not at the level of focus semantic values (Rooth 1985). We will only briefly discuss the treatment of focus in footnote 30. 123 Composing alternatives meaning = alternatives Alternative Semantics 1 Possibility Semantics all expressions denote sets of alternatives 2 only sentences denote sets of alternatives Compositional Inquisitive Semantics meaning alternatives Fig. 1 Overview of the paper and inquisitive content—it has not been specified in much detail how the meaning of a sentence, construed in this more fine-grained way, is to be composed from the meanings of the words that it consists of. This open issue is addressed here; the framework that we will end up with is a fully compositional inquisitive semantics. We will arrive at this result in two steps, which are summarized in Fig. 1. Our point of departure is a Hamblin-style alternative semantics (in the upper left quadrant of the figure). In the first step, marked as 1 in the diagram, we will give up a certain feature of alternative semantics, namely the assumption that all expressions denote sets of objects in their usual domain of interpretation. Rather, we will assume that this is only the case for sentences. This step will lead us to a framework that we call possibility semantics, in which one of the issues mentioned above, namely the compositionality issue, is avoided. This means that, in this framework, meanings can be composed by means of the standard type-theoretic operations. In the second step, marked as 2 in the di (...truncated)