Non-bifurcatory Diairesis and Greek Music Theory: A resource for Plato in the Statesman?

At 287c of the Statesman the Eleatic Visitor — or, more deeply, Plato — faces a daunting task. Because statesmanship has been shown to collaborate with “countless” other arts that share with it the work of “caring” for the city, to understand statesmanship requires distinguishing these arts into an intelligible set of kinds and recognizing how these might go together. Accordingly, the Visitor abandons the mode of division he has practiced without exception up until this moment, bifurcation or “halving,” and offers, instead, a sorting of the arts into fifteen kinds of work. How was Plato able to get his bearings towards the heterogeneous multiplicity of the arts in order to do this sorting? In this paper I suggest that he may have found a paradigm in the double octave matrix of notes from which, according to contemporary musical theory, the seven musical “modes” are drawn. To show the plausibility of this suggestion, I first reconstruct the double octave matrix, which was later to be called the Greater Perfect System, and then show a striking series of points of substantive and structural analogy that hold between this matrix and the Visitor’s division of the arts into fifteen kinds.