Abstract
Certain uses of vague quantifiers few and many intuitively compare a true quantity to a priori expectations about that quantity. A concrete proposal for the truth conditions of such readings stipulates a contextually-stable threshold on a contextually-variable representation of a priori expectations (Clark, H. H. 1991. Words, the world, and their possibilities. In Lockhead G. R. & Pomerantz J. R. (eds.), The perception of structure: Essays in honor of Wendell R Garner, 263–277. Washington, DC: American Psychological Association; Fernando, T. & H. Kamp. 1996. Expecting many. In Galloway T. & Spence J. (eds.), Proceedings of SALT VI, 53–68. Ithaca, NY: Cornell University.) The main goal of this paper is to introduce data-driven computational modeling as a means to implement and test complex semantic theories of this kind, which may be hard to assess based on solitary introspection of meaning intuitions. Based on an empirical measure of a priori expectations, we use Bayesian inference to estimate likely values of the latent threshold parameters given empirical data from production and comprehension tasks. We demonstrate how posterior inference and statistical model comparison can help assess the plausibility of the fixed threshold hypothesis.
Appendix
A Experimental material
book – A friend’s favorite book has been published only recently (and has few/many pages). – How many pages do you think the book has? – intervals: 0–40, 41–80, 81–120, 121–160, 161–200, 201–240, 241–280, 281–320, 321–360, 361–400, 401–440, 441–480, 481–520, 521–560, 560 or more
bus – Vehicle No. 102 is a school bus (which has seats for few/many passengers). – How many passengers do you think can sit in Vehicle No. 102? – intervals: 0–4, 5–9, 10–14, 15–19, 20–24, 25–29, 30–34, 35–39, 40–44, 45–49, 50–54, 55–59, 60–64, 65–69, 70 or more
calls – Lisa is a woman from the US (who made few/many phone calls last week). – How many phone calls do you think Lisa made last week? – intervals: 0–4, 5–9, 10–14, 15–19, 20–24, 25–29, 30–34, 35–39, 40–44, 45–49, 50–54, 55–59, 60–64, 65–69, 70 or more
class – Erin is a first grade student in primary school. (There are few/many children in Erins class.) – How many children do you think are in Erin’s class? – intervals: 0–2, 3–5, 6–8, 9–11, 12–14, 15–17, 18–20, 21–23, 24–26, 27–29, 30–32, 33–35, 36–38, 39–41, 42 or more
coffee – Andy is man from the US (who drank few/many cups of coffee last week). – How many cups of coffee do you think Andy drank last week? – intervals: 0–1, 2–3, 4–5, 6–7, 8–9, 10–11, 12–13, 14–15, 16–17, 18–19, 20–21, 22–23, 24–25, 26–27, 28 or more
cook – Tony is a man from the US (who cooked himself few/many meals at home last month). – How many meals do you think Tony cooked himself at home last month? – intervals: 0–3, 4–7, 8–11, 12–15, 16–19, 20–23, 24–27, 28–31, 32–35, 36–39, 40–43, 44–47, 48–51, 52–55, 56 or more
facebook – Judith is a woman from the US (who has few/many Facebook friends). – How many Facebook friends do you think Judith has? – intervals: 0–69, 70–139, 140–209, 210–279, 280–349, 350–419, 420–489, 490–559, 560–629, 630–699, 700–769, 770–839, 840–909, 910–979, 980 or more
friends – Lelia is a woman from the US (who has few/many friends). – How many friends do you think Lelia has? – intervals: 0–1, 2–3, 4–5, 6–7, 8–9, 10–11, 12–13, 14–15, 16–17, 18–19, 20–21, 22–23, 24–25, 26–27, 28 or more
hair – Betty is a woman from the US (who washed her hair few/many times last month). – How many times do you think Betty washed her hair last month? – intervals: 0–2, 3–5, 6–8, 9–11, 12–14, 15–17, 18–20, 21–23, 24–26, 27–29, 30–32, 33–35, 36–38, 39–41, 42 or more
movie – Nick is a man from the US (who saw few/many movies last year). – How many movies do you think Nick saw last year? – intervals: 0–2, 3–5, 6–8, 9–11, 12–14, 15–17, 18–20, 21–23, 24–26, 27–29, 30–32, 33–35, 36–38, 39–41, 42 or more
poem – A friend wants to read you her favorite poem (which has few/many lines). – How many lines do you think the poem has? – intervals: 0–3, 4–7, 8–11, 12–15, 16–19, 20–23, 24–27, 28–31, 32–35, 36–39, 40–43, 44–47, 48–51, 52–55, 56 or more
restaurants – Sarah is a woman from the US (who went to few/many restaurants last year). – To how many restaurants do you think Sarah went last year? – intervals: 0–3, 4–7, 8–11, 12–15, 16–19, 20–23, 24–27, 28–31, 32–35, 36–39, 40–43, 44–47, 48–51, 52–55, 56 or more
shoes – Melanie is a woman from the US (who owns few/many pairs of shoes). – How many pairs of shoes do you think Melanie owns? – intervals: 0–2, 3–5, 6–8, 9–11, 12–14, 15–17, 18–20, 21–23, 24–26, 27–29, 30–32, 33–35, 36–38, 39–41, 42 or more
tshirts – Liam is a man from the US (who has few/many T-shirts). – How many T-shirts do you think Liam has? – intervals: 0–2, 3–5, 6–8, 9–11, 12–14, 15–17, 18–20, 21–23, 24–26, 27–29, 30–32, 33–35, 36–38, 39–41, 42 or more
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