The comments here are quite good, but I want to pick up on something that I was interested in.
Consider the quantifier exchange rules:
¬∃xPx ↔ ∀x¬Px (there's not some P iff everything is not P)
∃x¬Px ↔ ¬∀xPx (there's some P iff not everything is P)
if some people in my family are borderline bald then are some people in my family borderline not bald?
Consider now two incompatible properties, Px and Gx, where to be Gx is just to not be Px.
i.e., we could say:
Maybe we could interpret Gx as a vague predicate and interpret Px as a precise predicate' there are now two ways to show their incompatibility, using quantifiers:
¬∃xGx ↔ ∀xPx (there's not some borderline case iff everything is precise)
∃xGx ↔ ¬∀xPx (there's some borderline case iff not everything is precise)
¬∃xPx ↔ ∀xGx (there's not some precise case iff everything is borderline)
∃xPx ↔ ¬∀xGx (there's some precise case iff not everything is borderline)
I think it likely (won't bother saying why) that my consciousness is vague and necessarily not everything. I am trying to work out whether (for any treatments of vagueness) with borderline cases of consciousness a quantifier is true of both consciousness and its negation.
Because if so, borderline cases of consciousness are necessarily not absent from everything.
my consciousness is vague and necessarily not everything.
seems equivalent to saying there's some borderline case (∃xGx). Given the incompatible predicates, this is true iff: not everything is precise (¬∀xPx)
borderline cases of consciousness are necessarily not absent from everything.
This is a bit confusing, but here I think you're saying: (necessarily) everything is borderline (∀xGx). This is true iff ¬∃xPx.
In other words without having to worry about what to believe regarding super/subvaluationism or vagueness or the like, your inference "∃xGx, therefore ¬∃xPx" will not work because: ¬∃xPx ↔ ∀xGx
My takeaway: you will not have to worry about the unrestricted quantifiers handling matters vague and precise at once, unless you think everything is precise or everything is vague. In which case unrestricted quantification over vagueness will tell you what is precise: nothing. Mutatis mutandis for the precise.