Reply #97: This seems to be mere semantic wordplay.

[kiahzero]

The terms "for all" and "there exists" are defined to be opposites, in much the same sense as "and" and "or" are defined to be opposites. If a statement is not true "for all" elements of a set, "there exists," by definition, an element which satisfies that statement. Where it not true that such an element exists, if would similarly not be true that the statement is not true "for all" elements of the set.

I'm sympathetic to your view, but I'm not seeing how you're actually presenting a reasonable objection to this definition.