I’d like to comment on the opening stanza of Francis Lucille’s fine philosophical translation of Parmenides’s poem “On Reality” (free PDF).

Lucille:

Now then, I [the Goddess tells Parmenides] will instruct you; hear what I say:
Two paths are open to investigation.
The first says: being is and non­being is not.
It is the path of certainty, because it follows the truth.
The other says: being is not, therefore non­being is.
This misdirected path, I tell you, cannot lead to a sound conviction
For, if this statement were true, it would not be possible for you to conceive of non­being, nor to
name it.

And now the set of propositions I gleaned from the poem.

Propositions

1.) Being is; non-being is not.

2.) Being is complete, immutable, and eternal.

3.) Being cannot come into being. Being cannot go out of being (or cease to be).

4.) Non-being cannot come into being and so cannot go out of being.

5.) Non-being cannot be, cannot be experienced.

6.) Non-being, which cannot be conceived or named, is strictly nonsensical.

Here, then, is the nondual metaphysical teaching in a nutshell. In fact, proposition #1 is sufficient.

Only being is; being cannot become or unbecome; you cannot become being or unbecome being; in fact, you cannot be anything but being.

Know this.