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E-book: Constraints on Numerical Expressions

(Chancellor's Fellow, University of Edinburgh)
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This book considers how expressions involving number are used by speakers and understood by hearers. A speaker's choice of expression can be a complex problem even in relatively simple-looking domains. In the case of numerical expressions, there are often many choices that would be semantically acceptable: for instance, if 'more than 200' is true, then so is 'more than 199', 'more than 150', and 'more than 100', among others. A speaker does not choose between these options arbitrarily but also does not consistently follow any simple rule. The hearer is interested not just in what has been said but also in any further inferences that can be drawn.

Chris Cummins offers a set of criteria that individually influence the speaker's choice of expression. The process of choosing what to say is then treated as a problem of multiple constraint satisfaction. This approach enables multiple different considerations, drawn from principles of semantics, philosophy, psycholinguistics and the psychology of number, simultaneously to be integrated within a single coherent account. This constraint-based model offers novel predictions about usage and interpretation that are borne out experimentally and in corpus research. It also explains problematic data in numerical quantification that have previously been handled by more stipulative means, and offers a potential line of attack for addressing the problem of the speaker's choice in more general linguistic environments.
General preface ix
List of figures
x
List of tables
xi
Abbreviations xiii
1 Introduction
1(9)
2 Constructing a constraint-based model
10(42)
2.1 Introduction
10(2)
2.2 OT modelling of the speaker's choice of utterance
12(3)
2.3 Constitution of an OT system
15(3)
2.4 Proposed constraints and their empirical basis
18(29)
2.5 Additional potential constraints
47(4)
2.6 Summary
51(1)
3 Deriving predictions from the constraint-based account
52(32)
3.1 Constraint interaction in classical OT
53(5)
3.2 Alternative formalisms
58(11)
3.3 The effect of constraint interaction on the speaker
69(10)
3.4 Modelling the effects of constraints on the hearer
79(4)
3.5 Summary
83(1)
4 Towards a pragmatic account of superlative quantifier usage
84(46)
4.1 Overview
84(2)
4.2 Problems with the traditional view of comparative and superlative quantifiers
86(2)
4.3 A semantically modal account of superlative quantifier meaning
88(2)
4.4 Some empirical investigations of quantifier meaning
90(5)
4.5 A pragmatic account of superlative quantifier meaning
95(3)
4.6 Demonstrating the complexity of non-strict comparison
98(5)
4.7 Consequences of the complexity of non-strict comparison
103(2)
4.8 Experimental evidence in favour of the disjunctive account of superlative quantifiers
105(19)
4.9 A constraint-based account of, at least, superlative quantifiers
124(5)
4.10 Summary
129(1)
5 Scalar implicatures from numerically quantified expressions
130(26)
5.1 Pragmatic enrichments of bare numerals
130(3)
5.2 The failure of implicature for comparative and superlative quantifiers
133(3)
5.3 Implicatures predicted by the constraint-based account
136(7)
5.4 Predicted effect of priming on implicature
143(8)
5.5 Inferring the contextual activation of numerals
151(4)
5.6 Summary
155(1)
6 Corpus evidence for constraints on numerical expressions
156(21)
6.1 Constraints and corpus frequencies
156(2)
6.2 Predictions arising from markedness constraints
158(3)
6.3 Some methodological issues in corpus research on numerically quantified expressions
161(3)
6.4 Corpus evidence for the predictions on quantifier usage
164(11)
6.5 Summary
175(2)
7 Overview and outlook
177(10)
7.1 The story so far
177(2)
7.2 Evidential basis for the constraint-based model
179(2)
7.3 Informativeness and the nature of numerical representations
181(3)
7.4 Gradient priming effects
184(1)
7.5 Extension to other domains of usage
185(2)
Appendix A Sample materials for Experiment 1 187(2)
Appendix B Sample materials for Experiment 2 189(1)
Appendix C Test conditions for Experiment 3 190(1)
Appendix D Materials for Experiment 4 191(2)
Appendix E Materials for Experiment 5 193(2)
Appendix F Materials for Experiment 6 195(2)
Appendix G Materials for Experiment 7 197(2)
Appendix H Materials for Experiment 9 199(5)
References 204(7)
Index 211
Chris Cummins is a researcher in experimental semantics and pragmatics, currently employed as a Chancellor's Fellow at the University of Edinburgh. Prior to this, he worked at Bielefeld University within the DFG-funded Collaborative Research Centre (SFB) 673, 'Alignment in Communication'. He obtained his PhD from the University of Cambridge, supervised by Napoleon Katsos. His research interests include the mechanisms of implicature and presupposition, the psychology of dialogue, and more generally issues in experimental and statistical methodology.
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