They're not, and that was exactly the point of my comment: it's a circular argument that you have to take responsibility for, not me. You seem to have missed that—it's your nonsense claims that are in focus when the tautology is being spelled out.
Higher-order functions and closures are different things.
> Well, if you are actually doing the real hardcore FP™, and not just the lame pretentious PF
I wouldn't call the pseudo-functional style "hardcore"—any more than OO is hardcore, given that they're equivalent. It's frequently portrayed as the naive/easy way out. Actual FP, on the other hand, is hardcore. (And pretentious—which is an odd attempt to try to stir me up; do you think I'm an advocate of FP or something? I suggest re-reading.)
> But more often than not, you really do need to use closures to do anything
Yes, which is why I'm not an FP advocate.
I was very clear in my original comment. The pseudo-functional style is a preference for how to write programs, and therefore immediately defensible as valid. What's not defensible, though, is equivocating on the meaning of "function" while simultaneously trying to lump the pseudo-functional style in with FP. The moment one starts making heavy use of closures and carrying around state is the moment one forfeits the right to be smug about how unclean OO is, given the equivalence of objects and closures and given that one is no longer actually practicing FP.
> I'm still in a very good position to challenge your dogmatic beliefs that: heavy-usage of closures is pseudofunctional and unfunctional
No, you're not. It's unfunctional by definition.