Chapter 2 presents the challenge that Parmenides’s philosophy presents for a scientific treatment of motion and change. It lays out the criteria for philosophy that we find established in Parmenides’s poem under his particular interpretations: consistency, rational admissibility, and a principle of sufficient reason. A careful examination of his use of negation shows that negation for him is a separation operator that indicates the extreme opposite to the thing negated. The counterpart to this understanding of negation is a connection operator that expresses absolute identity. A further step explains how Parmenides’s operators and his criteria for philosophy make it impossible to give any account of motion and change. Finally, it is shown that the cosmology in the doxa part of Parmenides’s poem should be understood as his attempt to expound a best possible cosmology and its short-comings – the rationale being that if even the best possible cosmology cannot fulfil the criteria for philosophy, no one else’s cosmology needs to be considered.