Parmenides: If anyone, with his mind fixed on all these objections and others like them, denies the existence of ideas of things, and does not assume an idea under which each individual thing is classed, he will be quite at a loss, since he denies that the idea of each thing is always the same, and in this way he will utterly destroy the power of carrying on discussion... Then what will become of philosophy? To what can you turn, if these things are unknown?

Parmenides: If the one is not, nothing is. Then, and we may add, whether the one is or is not, the one and the others in relation to themselves and to each other all in every way are and are not and appear and do not appear.

Parmenides believed that all Being is what he called the One, and denied absolutely the possibility of change. He believed that the cosmos is full (i.e., no void), uncreated, eternal, indestructible, unchangeable, immobile sphere of being, and all sensory evidence to the contrary is illusory. One Parmenidean fragment stated, "Either a thing is or it is not," meaning that creation and destruction is impossible.

Many aspects of Parmenides’s thought remain puzzling even when we have collected all the scraps of evidence from his own writings and those of later thinkers who discussed his views. But his immense significance in philosophical terms has never been obscured by the difficulties in the nitty-gritty of interpretation. For one thing, it is obvious that Parmenides throws at us the challenge of whether we should trust our reason or our senses, in circumstances when they seem to conflict.

Parmenides did for science what Plato would later do for morality and aesthetics as well: he alerts us to the fact that opinions are just opinions, and they may differ widely. There may yet be a single truth, which need not be as anyone thought. To search for knowledge is to search for access to the truth, not to collect other people’s opinions, and philosophy conducts its unrelenting search for truth in the steps of Parmenides, by respecting sound and rigorous logical argument rather than the variegated tapestry of unexamined opinions.

Even if Melissus’s analysis of the concept of existence is faulty, his procedure is very interesting. He challenges the data of sense experience by appealing to conceptual truths, facts about what a certain predicate (here ‘true’) must entail. These facts seem to escape the need to appeal to sense experience. We check up what is true about being true by examining our notion of being true, not by checking any things in the external world. So the argument seems to find a way of challenging the value of sense experience without begging the question. Melissus casts doubt on the senses by privileging the logical grammar of the word ‘true’. But, we might ask, did we learn how to use the word ‘true’ without relying on the senses?