What is the "Parmedian world"?

I would go with having to do with this philisopher:

http://en.wikipedia.org/wiki/Parmenides

@Imadethisupwithnoforethought Ooooooo. Thank you sooo much. That makes so much more sense! A thousand lurves!

It comes from Parmenides, indeed, like you said, a greek philosopher.
“Parmedian world” has probably got something to do with the little I know of him, namely that he believed “Being” to be the first principle (like Thales: Water, Anaximenes: Air, etc…).

He also believed that the world (Being) is without change, because you’ve got Being on the one hand and Not-Being on the other. Being is, and Not-Being is not.
And Being is without change because it could not have come from Not-Being.
Nor could it have come from Being (because what-is, is, and can therefore not grow).

So ultimately he’s just saying there is no change, even though we perceive change in our eyes. (That’s also where the first distinction between reality/illusion comes from I think)

I hope this clarifies it a little, I’m rather bad at explaining.

@Hacksawhawk Yes, totally. The not changing, I think that’s the part the author is going for. Man, I really wish that all textbooks would have that little part in the corner where they define all their terms. Thanks so much!