A Semantics for Degree Questions Based on Intervals: Negative Islands and Their Obviation

The scope of nominal quantifiers in comparative clauses

“…(See Beck 2010 for a more finegrained picture of all the predictions.) Abrusán & Spector (2011) extend this framework to degree questions. Parallel to the comparative examples above, Π allows them to derive the interpretation of questions that target the maximum allowed degree via a scope ordering > Π and questions about the minimally required degree via Π > .…”

“…For both (4) and (5) there seems to be an additional option of them not being interpreted as inquiring about a minimum or maximum at all, but instead about what the permitted interval is. This is predicted, for instance, on the interval approach to degree questions in (Abrusán & Spector 2011), which we will discuss in more detail below. What is crucial to us at this moment is independent of this variation in readings: While both (4) and (5) are compatible with a maximum-or a minimum-related reading, such a reading is unavailable for degree questions with nominal universal quantifiers, as in (6).…”

Wh-islands in degree questions: A semantic approach

“…Fox & Hackl's (2007) explicit goal is to 5:9 challenge certain widely accepted assumptions regarding the relationship between grammar, pragmatic processes, lexical meaning and contextual factors. Nevertheless, Abrusán & Spector (2011) have challenged Fox & Hackl's (2007) assumption that the Universal Density of Measurement hypothesis is needed to explain the ungrammaticality of negative degree islands. Instead, they argue that it is possible to account for the negative island cases by accepting the Maximal Informativity Principle, but combining it with the assumption (originally proposed by Schwarzschild & Wilkinson 2002, cf.…”

“…The interval-based analysis on the other hand straightforwardly accounts for this truth-value judgment. Following Schwarzschild & Wilkinson (2002) and Heim (2006), Abrusán & Spector (2011) assume that degree adjectives establish a relation between individuals and intervals:…”

“…Having observed that it is necessary to introduce intervals to capture the full range of readings of degree questions, Abrusán & Spector (2011) show that the assumption that degree questions range over intervals can also explain the cases of negative island violations such as (12a) above. In their system this question receives the following interpretation: First, let's show that (18) has a true answer that entails all the true answers if and only if John's speed was 0.…”