Logic and music in Plato's 'Phaedo'

This paper aims to achieve a better understanding of what Socrates means by "sigma nu mu phi omega nu epsilon iota nu" in the sections of the Phaedo in which he uses the word, and how its use contributes both to the articulation of the hypothetical method and the proof of the soul's immortality. Section I sets out the well-known problems for the most obvious readings of the relation, while Sections II and III argue against two remedies for these problems, the first an interpretation of what the sigma nu mu phi omega nu epsilon iota nu relation consists in, the second an interpretation of what sorts of thing the relation is meant to relate. My positive account in Section IV argues that we should take the musical connotations of the term seriously, and that Plato was thinking of a robust analogy between the way pitches form unities when related by certain intervals, and the way theoretical claims form unities when related by explanatory co-dependence. Section V surveys the work of IV from the point of view of the initial difficulties and suggests further consequences for the hypothetical method, including the logical relation between the sigma nu mu phi omega nu iota nu and delta iota alpha phi omega nu epsilon iota nu relations, and the need for care in ordering the results of a hypothesis.