The line "is this a dagger which I see before me" is from Macbeth, not Hamlet. C'mon, Sparknotes! I expect better from you.
Is it possible that Parmenides was referring to the object orientation of our thoughts with his famous saying that "what is is and what is not is not"? Consider that when separating an object from its background, we can conceive of the object as something but can not conceive the background as a thing. The object is "what is", while the background is "what is not". This interpretation fits well with several ideas of the time, for example that opposites had a special position in our thought, that the universe is one (Zeno's paradoxes