Does $\exists x(Bx)$, where $B$ = blue, mean "there is something (but not everything) that is blue" or "at least one thing is blue"

Question

Does $\exists x(Bx)$ mean that

1. "something is blue but not everything"

   or

2. "something is blue perhaps everything

Answer 1

The point of quantifiers is to indicate whether there exists at least one of a certain thing or there doesn't. For the former, we use $\exists$; this says nothing of whether anything else exists. For the latter, say we want to say nothing is blue: we can either write $\neg\exists x(Bx)$, or equivalently $\forall x(\neg Bx)$. Note that the universal quantifier isn't intended to say whether anything exists, so "all things are non-blue" is consistent with "come to think of it, all things are blue too, because nothing exists".