Quantification and Nominal Anaphora

Quantification and nominal anaphora is a rich and complex area of research, which has attracked many people; especially since the development of dynamic semantics in the early eigthies. One way to obtain a systematic view on this field, is to focus on the quantificational resources employed to interpret anaphoric relationships. In this article, I will develop such a view as far as first-order quantification is concerned; i.e., generalized quantification over the individuals in a domain but not over sets of such individuals. With hindsight, this allows one to discern the three most prominent methods of interpretation: i) DRT: polyadic quantification over open expressions (Kamp 1981, Heim 1982); ii) DPL: principles of scope extension for quantificational antecedents (Groenendijk and Stokhof 1991); iii) ‘Q-types’: contextually restricted quantification (Neale 1990, Heim 1991). In this article, I compare these approaches to determine the extent in which they are applicable in the first-order domain. In particular, which antecedents and which nominal anaphora are interpreted correctly by these methods? The main results describe precisely when polyadic quantification and principles of scope extension give the appropriate truth conditions, and when they fail to do so. Yet, a balanced judgement should include collective quantification, where higher-order variants of the quantifiers for which polyadic quantification and scope extension do work, could be used to give a general mechanism of interpretation after all. This would lead to the interesting observation that anaphora may enforce an increase in the expressive power of the logic needed to formalize natural language. However, the collective part of this research remains to be done (but see van den Berg 1996). Overview The article is structured as follows. Section 1 starts with a study of DRT’s use of polyadic quantification to interpret anaphoric relationships. It recalls the proportion problem, which is then shown to be real: only a few quantifiers evade it. The topic of section 2 is DPL and the principles of scope extension it employs. I describe the familiar problems with these principles, first noted by Evans (1977, 1980), and determine how serious they are. The conclusion is that the principles can be sustained for singular but not for plural anaphora. I make some preliminary remarks on how the latter could be handled. ∗I am grateful to professor Urs Egli and dr. Klaus van Heusinger for inviting me to the Workshop on Reference and Anaphoric Relationships. Thanks also for the audience at this workshop and at the Tenth Amsterdam Colloquium for comments. This research is part of the pionier-project ‘Reasoning with Uncertainty’ sponsored by the Netherlands Organization for Scientific Research (NWO) under grant pgs 22–262. See url http://www.wins.uva.nl/research/pion/index.html for further information on the project. 1I only mention the publications which started work on these methods. In the full paper I hope to do more justice to Dekker 1993 and his later work, and to Pagin and Westerst̊ahl 1993.