In à recent issue of Dialogue, Leo Groarke attempts to defend the claim that Parmenides was committed to an atemporal reality.
He argues like this:
(1) In the Parmenidean dictum “[It] is and cannot not be” (B2.4), “is” means “exists”, and is in the present tense (536).
(2) (According to Parmenides) there is nothing that fails to exist (536).
(3) It follows from (1) and (2) that “the past is not” and “the future is not” (537).
(4) If the past and future are not, then the present is not. “All three tenses go down the drain together” (538), and so reality is atem-poral.