If you ask someone what the opposite of "all" was, most times the answer will be "none", such as the example of "no one" is the opposite of "everyone". There are three antonyms for "all" on Thesaurus.com: none, zero, and incompletely. I'm most concerned about the last one, "incompletely".
As a math student, I am taking a maths logic course, and a couple of logical quantifiers are frequently brought up: ∃ (there exists), and ∀ (all/every). The negation of these is specifically defined as "there does not exist" and "not all/every" respectively.
Everyone knows John becomes
Not everyone knows John
Someone knows John becomes
No one knows John
Which would be more appropriate to define as the opposite of "all" in English? Is the antonym "not all" or "none"? My understanding is that there can only exist one antonym per word, but is it really binary? To refer back to mathematics:
Everyone knows John can mean both
No one knows John and
Not everyone knows John. Both of these fall outside the domain of which
Everyone knows John would be true.
Maybe I'm reading too into it.
edit; this isn't a mathematics question. I only introduced mathematical logic to have some kind of reference to what the "antonym" (actually negation) of "all" is. This question is essentially asking whether the antonym of "all" is "not all", "none", or both.