Nor: Neither Disjunction nor Paradox

1 Introduction

Bivalent coordination constructions involving a negative first conjunct and a second conjunct introduced by nor such as those in (1a) (hence-forth NEG-nor constructions) can be described as disjunctions (1b) or as conjunctions (1c), owing to the logical equivalence of ¬ [] and [¬p] & [¬q].

1. 1.

   1. a. Leo ate neither the rice nor the carrots.

      Leo didn't eat the rice nor did he eat the carrots.

      Leo has never eaten rice nor has he eaten carrots.

   2. b. The following does not hold: Leo ate the rice or the carrots.   ¬ []

   3. c. (Leo didn't eat the rice) AND (Leo didn't eat the carrots)

      [¬p] & [¬q]

Starting from an observation made by Lechner (2000a) about German weder-noch 'neither-nor' coordinations, I will argue that cases of NEG-nor coordination can be constructed (in both German and English) where the logical equivalence does not hold. More specifically, I will show that in certain contexts, negation takes narrow scope with respect to a quantifier embedded in the first conjunct, rather than taking scope over the entire coordination. I will conclude that only a conjunction structure such as (1c), with independent negation in each conjunct, allows for an element in one conjunct to take scope over negation without scoping out of its conjunct.

2 The Problem

In both English and German, the negative element of the first conjunct can appear embedded in the first conjunct, as in (2) ((2a) is Lechner's (4)).¹

1. 2.

   1. a. Peter hat weder das Theorem verstanden noch konnte

      Peter has neither the theorem understood nor could

      Maria dem Beweis folgen.

      Maria the proof follow

      'Neither has Peter understood the theorem, nor could Maria follow the proof.'

   2. b. Leo hasn't ever/has never been to Canada, nor has Julia met the queen.

As Lechner points out, if we assume a disjunction structure, a paradox arises when we look at cases such as (3) ((3a) is Lechner's (6)) where the subject of the first conjunct is a negative polarity item (NPI). Under the assumption that an NPI must be c-commanded by negation (see below for a more detailed discussion on where NPI-licensing takes place), the ungrammaticality of these cases indicates that the negation in the first conjunct is below the subject.

1. 3.

   1. a. *Auch nur einer hat weder das Theorem verstanden

      even only one has neither the theorem understood

      noch konnte jemand dem Beweis folgen.

      nor could somebody the proof follow

      'Neither has only a single person understood the theorem, nor could somebody follow the proof.'

   2. b. *Any toddler has never been to Canada, nor has Leo met the queen.

To exclude these sentences, at the point where NPI-licensing takes place, the structure of the first conjunct in (3b) must be roughly as in (4).

If, however, the negation associated with neither is below the subject, a paradox arises under a disjunction analysis of NEG-nor coordinations. As shown in (5),² under a disjunction analysis, negation must take scope over the whole coordination; otherwise, the meaning would be [¬p] [¬q], which is not what NEG-nor constructions can mean.

1. 5. Disjunction structure

If (5) is the structure where NPI-licensing takes place, a problem arises for examples such as (3). Since negation must take scope over the whole coordination, it would necessarily be in a position where it c-commands the subject of the first conjunct. Hence, the structure in (5) would predict that NPIs embedded anywhere in the coordination should be licensed. As shown in (3), this is not correct.

However, before concluding that a disjunction structure creates a paradox, we must consider (and reject) an alternative analysis for (3). A crucial assumption in the setup of Lechner's paradox was that the structure in (5), which is the structure required to express the correct meaning of NEG-nor constructions, is also the structure where NPI-licensing takes place. An alternative (which was pointed out to me by Yael Sharvit) would be to assume that NPI-licensing must take place at a different level. More specifically, following the common view, NPI-licensing could be assumed to be...