On “zero” and semantic plurality

Abstract

We discuss the semantics of prenominal "zero", as in "I have zero new emails in my inbox". We show that "zero" is not a quantifier like "no" and that giving "zero" a regular numeral semantics is possible and desirable. We formulate such an analysis and its consequences. We show that the existence of a zero numeral has profound consequences for linguistic semantics. We conclude that the fact that languages allow ascription of zero quantity to an entity provides evidence that linguistic semantics has access to what at first sight may seem like an ontological oddity: an entity with zero quantity. In other words, we will show that studying "zero" can inform us about the underlying semantic ontology of natural language.

Numeral semantics

“…In short, under the degree quantifier analysis, “ zero ” gives rise to a meaning that is indistinguishable from that of “ no .” As such, one comes to predict that “ zero ” and “ no ” also license negative polarity items to the same degree. This is, however, not the case empirically, compare (51‐a) and (51‐b) (Bylinina & Nouwen, 2018; Zeijlstra, 2007):…”

“…Whether this property of the analysis makes desirable predictions is less clear. For an argument against the exactly analysis for numerals based on the polarity profile of the numeral “ zero ” see Bylinina and Nouwen (2018). In short, under the degree quantifier analysis, “ zero ” gives rise to a meaning that is indistinguishable from that of “ no .” As such, one comes to predict that “ zero ” and “ no ” also license negative polarity items to the same degree.…”

Measuring the cognitive cost of downward monotonicity by controlling for negative polarity

“…While both are consistent with the empty set, only no X is downward monotone (consider the unacceptability of *zero students have ever opened the book, compared to the acceptability of no student has ever opened the book). Zero X is not a downward monotone quantifier, and in fact, it is not even a quantifier (Bylinina & Nouwen 2018). The everyday interpretation of zero as none, according to Bylinina & Nouwen (2018), comes about via an implicature.…”

“…Zero X is not a downward monotone quantifier, and in fact, it is not even a quantifier (Bylinina & Nouwen 2018). The everyday interpretation of zero as none, according to Bylinina & Nouwen (2018), comes about via an implicature. Thus, if downward monotonicity has a processing effect, no X should be more costly than zero X, despite the superficial similarity between their meanings.…”

“…Although it is beyond the scope of this work, we would like to suggest two possibilities for future research on this topic: (i) the NP number may include zero (number = {0, 1, 2, …}), but zero is not downward monotone (Bylinina & Nouwen 2018), which makes a small number not downward monotone; (ii) the scale of dimensional adjectives is open at its lower end, the zero degree being the limit (Cruse 1986: 206;Kennedy & McNally 2005;Sassoon 2010), therefore the NP small number can also only refer to open scales, excluding the number zero. 6 An anonymous reviewer pointed out that Moxey & Sanford (1993) already made the theoretical distinction between negative polarity and downward monotonicity.…”