How to be Universal when you are Existential: Negative Polarity Items in the Comparative: Entailment along a Scale

Fauconnier (1975a) noticed that existential quantification, if it is related to a scale endpoint, can force entailment along the scale and as such have the effect of universal quantification: assume a partially ordered set (X, ) and a predicate φ such that for all x, y X, x y, if φ is true of x, it is also true of y; then if there exists an element z that is ordered before all other elements and φ(z) is true, then φ is true for all elements in X. This paper claims that the clausal Comparative licences context sensitive Negative Polarity Items (NPIs) like English any and ever, and German jemals (‘ever’), due to its property of enabling entailment along a scale. I argue that the licensing condition of any and ever/jemals is not itself the ‘semantic scope of a downward entailing function’ (Ladusaw 1979), but rather that a downward entailing function provides one appropriate kind of context that satisfies the actual condition which is part of the NPI’s meaning (following Kadmon & Landman 1993; Krifka 1994, 1995; Jackson 1995): any and ever/jemals are indefinites that are licensed in particularly strong statements. The new idea is to define an assertion containing an indefinite NPI as strong if the existentially quantified formula entails a particular wide scope universal statement: assume that ‘Babajaga doesn’t see any tree’ means that it is not true that there exists some tree that Babajaga sees. This entails that for all trees, Babajaga does not see them. In general, entailment will be granted if existential quantification is either in the scope of a downward entailing function or occurs in the context of a scale, the latter enabling entailment along the scale: if ‘Babajaga is smarter than any witch’ actually means that Babajaga is smarter than one of the smartest witches, then this entails that for all witches, Babajaga is smarter. ‘Thus, we’d better not try to reverse the relations.’ Michel Foucault, Les Mots et les Choses