Zoom link: https://unm.zoom.us/j/94773182533#success

Abstract: The extreme lateral-ness of the Platonic approach makes it seem as though Plato wished to capture, on papyrus scrolls, every single thing in the world into a single set of texts, to create an encyclopedia of everything as it is in ‘reality’ (all levels of reality). There is little or no linear progression from dialogue to dialogue, and within each individual cosmos of the dialogue, there is also, more often than not, a significant lack of linearity. The dialogues move forwards and backwards, circling back on themselves sometimes, and moving up and down as well. If we read the texts aloud, the universe of the dialogue comes even more alive, and it becomes apparent how impossible it is to fully appreciate the world of the dialogue when absorbed with the eyes alone. The dialogue-monologue combination, heard and spoken, is really more of a mix of performance, cosmology, community, politics, metaphysics, philosophy, spirituality, and pedagogy.  Presenting a vision for human progress and the philosophical potential of the individual, Plato sketches “solutions” to human questions as images of all kinds, of the afterlife, the cosmos, of love and science and advanced metaphysics. He presents the reader with an explanation of everything in such a way, and to such a detailed and synthesized degree, that his ultimate success is as a teacher of the individual soul. Key ingredients of the education he prescribes are specified in the Republic: they are a life of harmonized efforts in mousikē and gumnastikē. The advanced practitioner on their way to the life of philosophy and city-management is charged with more and more complex studies in high level theoretical mathematics and harmonics. My argument is that there is a musically-meaningful, mathematically-measurable syntactic-semantic argument at the architectonic or structural level of the text of Plato’s Republic, and that this argument, or pattern, has philosophical meaning on several different registers, ethical, metaphysical, political and pedagogical. Understood as a whole, the structural argument offers a prism for studying the Platonic pedagogical prescription for happiness and philosophical success. 
     The musico-mathematical structure was first interpreted by John Bremer in the 1980s. However, this was before the claims that he made—which depended on laborious manual handcount of the Greek text—could be verified or legitimized. My contributions are a) first in providing philosophical readers with the technical and historical bases for understanding the musico-mathematical structural argument, and b) secondly, in supplying an original digital verification of the original claims about this structure made previously by Bremer. This dissertation offers an inroad into the musical and harmonical argument for the philosophical reader, without circumventing the central technicalities, so as to make possible a more complete and synthesized reading of the Republic.

     My third contribution is the interpretation of the philosophical implications of this structural argument,which touches at least four different registers (and at least some of the upshot of the pattern is to perceive the categories synthetically, so they are offered for the sake of clarity only): historical, political, ontological and pedagogical/individual. On the academic/historical level, the musico-mathematical structure offers a contribution to the centuries-long discussion about how the text of the Republic is organized. The Bremerian musico-mathematical structure shows us that the Republic is not a series of (10) books or book sections, but a chiastic whole divided into meaningful harmonical divisions.  As such, it turns out that the Republic fits in with the traditional compositional narrative frame of its era. On an ethical register, the structure does explicatory work for the uses of terms like harmonical as bywords for just and happy. Why does 'harmonical' refer to a positive and philosophical way of being for Plato, throughout the Republic? Because there is a normative and holistic harmonical and ontologically-important structure that underlies it and makes it so. On the political register, the musico-mathematical structure presents an ideal image of the whole city, which remains one, but grows like a circle (423b). Following the isometry which Plato sets up in the Republic between city and soul, this pattern for a healthy city also informs our understanding of the harmonical and healthy internal structure of the human soul, which grows and breathes just like its analogue, the harmonically organized state. 

     The musico-mathematical structure shares a key property on the three registers, ethical, pedagogical/political, ontological: it is inherently relational, what Verity Harte calls a structure-laden metaphysics. According to this ontological position, the whole is what it is, based on the parts being as they are, and there is no whole without the parts in their right relationships. The size of the whole may vary, as happens in cities, but internal relationships stay consonant and identical. This abstract way of imaging the healthy and harmonical city sheds light on the specific way in which Plato understands harmonics operating in the healthy and sufficiently philosophical individual human person--which we remember is the original and most important topic in the Republic. If the soul is like a city, and the city is to be like the musico-mathematical pattern it is meant to reflect, then the soul is also healthiest and most philosophical as a united whole which grows like a circle, maintaining the sanctity of its internal parts and their relationship to one another in a particular (structure-laden), mathematically-meaningful, harmonical, chiastic way. This is a difficult message to convey even in his creative and whimsical dialogue form, but for the student willing to learn the harmonics prescribed in Book 7 and to study the composition of the narrative, Plato provides a touchstone of it.