Parmenides' Modal Fallacy

In his great poem, Parmenides uses an argument by elimination to select the correct "way of inquiry" from a pool of two, the ways of is and of is not, joined later by a third, "mixed" way of is and is not. Parmenides' first two ways are soon given modal upgrades - is becomes cannot not be, and is not becomes necessarily is not (B2, 3-6) - and these are no longer contradictories of one another. And is the common view right, that Parmenides rejects the "mixed" way because it is a contradiction? I argue that the modal upgrades are the product of an illicit modal shift. This same shift, built into two Exclusion Arguments, gives Parmenides a novel argument to show that the "mixed" way fails. Given the independent failure of the way of is not, Parmenides' argument by elimination is complete.