(Joint work with Jérémy Zehr)

Abstract:

Several experimental studies on vagueness in the last decade indicate that sentences that would correspond to outright contradictions in classical logic are accepted to a significant extent to describe borderline cases of vague predicates (Ripley 2011, Alxatib and Pelletier 2011, Serchuk et al. 2011, Egré et al. 2013). For example, Alxatib and Pelletier found that sentences such as "x is tall and not tall'', or "x is neither tall nor not tall", which Ripley has dubbed "borderline contradictions", are easily judged true of a man of middling height. Different semantics for vagueness, of paraconsistent inspiration, have been motivated on that basis to accommodate borderline contradictions (see Alxatib and Pelletier 2011; Ripley 2012; Cobreros et al. 2012; Alxatib, Pagin and Sauerland 2013; Cobreros et al. 2015). One issue that has not investigated so far is whether conjunctive descriptions ("x is P and not P") and negated disjunctive descriptions ("x is neither P nor not P") are accepted to the same extent. In this paper, I will present the results of an experimental study conducted with Jérémy Zehr (UPenn) on gradable adjectives and their negations, which shows that while both kinds of descriptions are indeed accepted, there is a marked preference for "neither"-descriptions over "and"-descriptions. This finding suggests that "gaps" might be preferred to "gluts" to describe borderline cases, even as both are admitted. It is not straightforwardly accommodated by the extant frameworks, however. I will discuss ways in which it might be explained, and discuss the implications of that asymmetry for the psychology of vague predicates more broadly.