It is a commonplace among scholars that the early Pythagoreans posited an immortal soul. The earliest source to associate immortality of the soul to the Pythagoreans unequivocally, Dicaearchus of Messana, stipulates that they held that (a) the soul is immortal; (b) it changes into other kinds of animals; (c) there is eternal recurrence; and (d) embodied animate creatures are of the same genus. A problem with Dicaearchus' account is that each of these doctrines can also be found in the dialogues of Plato. Given Dicaearchus' penchant for conflating Platonic with Pythagorean philosophy, we cannot employ this account for a historical understanding of Pythagorean psychology in a straightforward way. This chapter instead investigates Pythagorean psychology through analysis of two passages of Aristotle’s De anima that are often not brought to bear on the question. One passage draws important comparisons between the psychology of the Pythagoreans and Democritean and Ecphantic atomism, suggesting that the early Pythagoreans held a material theory of soul; by reference to arguments similar to Cebes' in Plato's Phaedo (87b-e), the other explains how a transmigratory soul could nevertheless be mortal. The early Pythagoreans are thus likely to have held that the soul is material, mortal, and transmigratory.

Deployment of the notion of kosmos has been much discussed in the scholarship on Presocratic philosophy. But diakosmos and diakosmêsis have been almost entirely neglected. This chapter argues that in describing the business of articulating ‘mortal belief’ as diakosmos, Parmenides bequeathed to his successors among the Presocratics a question – intended as deflationary – about the main agenda for physics and physical explanation: how the universe is arranged. He coined a concept designed to articulate it. Diakosmos was a concept his successors were determined to reinflate, but only at the price of contestation between believers in a single world produced by design and proponents of infinite undesigned worlds. And in Aristotle, diakosmêsis is re-invested with a hint of the deflationary.