This essay explicates the primary interpretative import of B1: 31-32 in Parmenides poem (On Nature)—lines which have radical implications for the overall argument, and which the traditional arrangement forces into an irreconcilable dilemma. I argue that the “negative” reading of lines 31-32 is preferable, even on the traditional arrangement. This negative reading denies that a third thing is to be taught to the reader by the goddess—a positive account of how the apparent world is to be “acceptably” understood. I then (...) suggest that a rearrangement of the fragments would make more sense overall, while further supporting the “negative” reading as more natural and coherent. In particular, the rearrangement dispels the objection that, “if mortal opinions were not true, why would Parmenides include such a lengthy false account of the apparent world--an account which explicitly denies the conclusions of the earlier section, Truth?”. (shrink)