Abstract
Numerical descriptions furnish us with an apparently precise and objective way of summarising complex datasets. In practice, the issue is less clear-cut, partly because the use of numerical expressions in natural language invites inferences that go beyond their mathematical meaning, and consequently quantitative descriptions can be true but misleading. This raises important practical questions for the hearer: how should they interpret a quantitative description that is being used to further a particular argumentative agenda, and to what extent should they treat it as a good argument for a particular conclusion? In this paper, we discuss this issue with reference to notions of argumentative strength, and consider the strategy that a rational hearer should adopt in interpreting quantitative information that is being used argumentatively by the speaker. We exemplify this with reference to United Kingdom universities’ reporting of their REF 2014 evaluations. We argue that this reporting is typical of argumentative discourse involving quantitative information in two important respects. Firstly, a hearer must take into account the speaker’s agenda in order not to be misled by the information provided; but secondly, the speaker’s choice of utterance is typically suboptimal in its argumentative strength, and this creates a considerable challenge for accurate interpretation.
Highlights
How should a rational hearer interpret a statement of numerical quantity, such as 1)?1) More than 30 states voted Democrat in the 1996 United States Presidential election.Assuming that the speaker is accurate, the hearer can begin by deriving the semantic meaning of the quantity expression, and arrive at the interpretation that the cardinality of the set of Democratvoting states in the 1996 election is greater than 30
We briefly introduce the workings of the Research Excellence Framework (REF), consider the motivations and constraints that influence universities’ public statements about the REF results, articulate a series of predictions about these statements that follow from our theory, and evaluate these predictions against the data
We indicate in square brackets the precise ranking that these quotes allude to
Summary
How should a rational hearer interpret a statement of numerical quantity, such as 1)?1) More than 30 states voted Democrat in the 1996 United States Presidential election.Assuming that the speaker is accurate, the hearer can begin by deriving the semantic meaning of the quantity expression, and arrive at the interpretation that the cardinality of the set of Democratvoting states in the 1996 election is greater than 30. If the hearer is willing to make additional assumptions about the speaker’s cooperativity and knowledgeability, they can derive additional pragmatic inferences. They can potentially infer that the speaker is unable to assert informationally stronger alternatives to 1), and either that these alternatives are false or that the speaker is ignorant as to their truth-value. In this case, informationally stronger alternatives potentially include those which give larger or more precise numbers (more than 40, 35) or which describe wider date ranges (in every Presidential election).
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