Abstract
On its semantics, a numeral modified by more/fewer than imposes a single bound on the quantity under discussion: more than 80 is true if that quantity exceeds 80. But the use of such an expression potentially invites pragmatic inferences, and these can take several distinct forms: for instance, that the speaker is ignorant of the precise quantity, that the numeral mentioned is a particularly significant point of reference, or that the true value of the quantity lies somewhere between the numeral mentioned and an inferable upper (or lower) bound. This latter inference has been a particular focus of interest in the literature, but the interplay between these inferences has not always received comparable attention. In this chapter, I discuss how these competing considerations bear upon a speaker’s choice of utterance, and consider what a rational hearer would need to do in order to reconstruct the relevant aspects of the speaker’s knowledge state.
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Notes
- 1.
A reviewer queried whether we are in fact talking about divisibility given order of magnitude. The short answer is: not exactly. We typically say that two numbers are of the same order of magnitude if they belong to the same class with respect to a particular logarithmic base, usually 10. Thus, for instance, 16 and 32 are of the same order of magnitude, both lying between 101 and 102. But on Jansen and Pollmann’s (2001) definition, 16 is round (because it is one of the first ten multiples of two) while 32 is not. Conversely, if we chose, say, base 2 in our definition of order of magnitude, 60 and 80 would be of different orders of magnitude (they fall on opposite sides of 26), but definitionally exhibit the same roundness on the basis of the same divisibility properties.
- 2.
I assume here that discrimination between quantities at one Weber fraction’s distance is sufficiently reliable for a conscientious speaker to rely upon it—that is, if the quantity is more than one Weber fraction above n, the speaker is willing to say more than n. Given the definition of the Weber fraction this too is an oversimplification, although it is not crucial for the current purpose.
- 3.
For simplicity I restrict this discussion to the scenario in which the speaker wants to address a particular QUD, rather than, for instance, wishing to convey a particular kind of argumentative force (cf. Ariel 2004), or being primed to use particular linguistic material (cf. Cummins 2015). The precise nature of the speaker’s motivation for choosing an informationally weaker utterance using more than n is not crucial to the following discussion.
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Cummins, C. (2022). Uncertainty, Quantity and Relevance Inferences from Modified Numerals. In: Gotzner, N., Sauerland, U. (eds) Measurements, Numerals and Scales. Palgrave Studies in Pragmatics, Language and Cognition. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-73323-0_4
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