It is well-known that not may have scope over the universally quantified subject, even though it cannot c-command the subject. When surface structure does not correspond to logical form, we can resort to such scope-shifting operations as QR or reconstruction. However, I propose that those syntactic operations do not work for the relative scope of negation. Instead, I argue that a relational analysis of negation enables us to explain the phenomena without recourse to those syntactic operations. That is, I claim that not takes VP as a first argument and the subject as a second argument, negating the relation between the two arguments.

Kwang-sup Kim. 2003. QR and Minimalism. Studies in Modern Grammar 31, 47-69. In the Minimalist Program there are two opposite views about QR. Hornstein(1999) claims that there is no QR, and the effect of QR is a by-product of A-movement. He proposes that the A-approach enables us to explain the locality QR, while maintaining the Modularity Hypothesis. On the other hand, Fox (2000) departs from the Modularity Hypothesis, arguing that there is QR and QR takes place only when it gives a semantic effect. After pointing out empirical problems of both approaches, this paper proposes that QR can be eliminated by making use of AGREE operation. Furthermore, this paper advocates the position that the Modularity Hypothesis must be maintained.