I've always understood that you can order the words not and every (or similar words) in the following two ways to convey distinct logical meanings. Every human is not a man. There is no human being ...
From what I understand, in second order propositional logic, ∀¬x and ¬∀x are equivalent statements. Apparently these are not equal. ¬∀x ≡ ∃¬x However, rendered into the English language, consider ...