What could justify the Presocratic conviction that human beings can have knowledge? The answer that I am exploring in a larger project is that most Presocratic thinkers share a commitment to the possibility of a “natural fit” between the world and human understanding. Two claims underlie this commitment: the first is the basic intelligibility of the cosmos. The second is that human beings can come to know things beyond their limited sensory experience, for in properly exercising their capacities for perception, thought, and understanding, they can come to have the knowledge that earlier Greeks thought was reserved for the gods. Here I explore a small part of one chapter of the story I want to tell: Parmenides’ accounts of what-is and of thi...