The Axiom of Non-contradiction
The principle does not simply affirm that what is contradictory cannot be
said (a contra-diction), but goes further to deduce that it cannot be
thought, and even cannot
be. "What cannot be said", of course, means "what cannot be
meaningfully said", and fair enough.
The first trait of the principle leads quite logically to the conclusion that not all can be said, and therefore that not all is said. There is a realm of Silence: apophatism.
The second trait concludes that not all can be logically thought -- and even that not all is thought. There is a realm of Mysticism: the ungraspable.
But the third trait upgrades itself to a principle of Being. What cannot be thought (because it cannot be said, being contra-dictory) simply cannot be. The insight of Parmenides is the basic paradigm of theism. Thinking and Being correspond to Being and Thinking. Being is Thinking, that is Intelligibility, not certainly for an individual mind, but as such. Here is the ultimate basis for the famous ontological argument for God's existence. But this scheme of Parmenides is not the only philosophical paradigm.
If this identification between Thinking and Being were not the case, we would be open to a realm of Emptiness: Being empty of Thought.
--
The Rhythm of Being (paraphrased)