I've been thinking about this one since I ran into his name being used on a VF; been doing some thinking on that.
Parmenides had a few views that the makers of this fighter could have seized upon:
1) That Parmenides believed there was a difference between appearance and reality, and that we were mistaken about "the everyday perception of the real world".
2) That he postulated "the void" could not exist, since it was nothing and nothing cannot exist.
3) That (as you previously mentioned), something cannot come from nothing.
Being that this is Macross, to attach that name onto a VF tells me that there is something about this particular VF variant that either:
1) Appears differently than it actually is;
2) Has a weapon/ feature that functions somehow based upon a theory that there is something in space and it uses it in some way to either power said weapon/ feature or employ it somehow using it;
3) Prevents craft/ vessels from folding/ interferes with anything using a fold system (fold reheat, fold carbon, etc.), i.e. "something cannot come from nothing" (a craft coming out of fold would be "coming from nothing" in one sense).
Those are my guesses; I'm probably way off the mark here, but given the use of this name, i did a little digging around (yes, Wikipedia was involved as well as Pepsi :D).