Not every quantifier can be negated

Abstract

Semantic theory lacks an explanation as to why some subject NPs (in English and German) can be negated while others cannot. We argue that the theory of quantification called Referential Transparency Theory (RTT; Lücking and Ginzburg, 2022) provides a potential semantic explanation, namely in terms of scalar NPs. The claim is that only scalar NPs can be negated in subject position. We provide a grammar fragment that implements the corresponding constraint, and partially refines previous RTT accounts of noun phrase negation. To empirically substantiate our investigation, we have created a database consisting specifically of data on the negation of noun phrases. We discuss several corpus data that deviate from common semantic theories. The work contributes to the expansion of empirical phenomena of negated NPs and to the linking of negation and scalability in the areas of nominals and adjectives, which could point to an underlying semantic (or cognitive) principle of natural languages (or their users).