Quantifier scoping in Ŋarâþ Crîþ

The question of quantifier scoping has plagued Ŋarâþ Crîþ since the v7 days. Consider the following example:

The two interpretations depend on whether an auxiliary verb or a quantifier has a higher scope: (a) has the auxiliary above the quantifier, and (b) has the quantifier above the auxiliary.

This order could vary depending on how ⟨rjotat⟩ was defined. In Ŋarâþ Crîþ v7, ⟨rjotat⟩ was defined as “(Š) fails to, is unable to, cannot (T)”, favoring (b) over (a). If it had been defined as “(T) is not possible” instead, then the definition might have led to interpretation (a).

This question is reminiscent of the interpretation of the English sentence ‘everyone cannot do this’: does it mean ‘not everyone can do this’ or ‘no one can do this’? (Personally, I don’t use the ambiguous version at all.)

Note that the differences in the two interpretations are not important for some auxiliaries:

The problem is the most significant for negative verbs, such as ⟨rjotat⟩ fail to, cannot, ⟨pečit⟩ avoid, or ⟨tersat⟩ refuse to.

What if the quantifier is in an object position?

Initially, I thought that (a) was the more natural interpretation, suggesting that subjects and objects were treated differently in Ŋarâþ Crîþ, but this hypothesis is complicated by the fact that Ŋarâþ Crîþ does not distinguish between verbal and clausal coordination:

Fortunately, however, the ŊCv7 grammar, clearly states that “[t]he pronouns ⟨šino⟩ all and ⟨nema⟩ all are special: they transform predicates such that P(šino) ⟺ ∀x : P(x) and P(nema) ⟺ ∃x : P(x).” In other words, (b) is the correct interpretation for both (1) and (4).

This statement, however, neglects the possibility of other noun phrases preceding a quantifier:

Argument movement

Recently, I’ve been thinking of a model in which nominal arguments are moved out of core clause. Let’s see how this applies to this sentence:

Before any movement, the sentence looks roughly like this:

The particular structure of the unmoved sentence isn’t important here, but I had to use an arbitrary representation.

The first noun phrase to be moved is also the first one that appears in the sentence – in this case, ⟨telu⟩.

Finally, we move the other noun phrase.

If the arguments were moved out in the other order, then we would end up with ⟨tovrafen telu mênču⟩, shown below.

Then (1) has the following structure:

We can generalize ŊCv7’s rule about quantifiers to account for movement: ⟦šino_i [_i α]⟧^a = ∀x ∈ D : ⟦α⟧^a/[i=x]. (Ditto for nema.)

This is also consistent with the rules on nested quantifiers:

Work these out and you’ll get the expected interpretations.