Dr. Kennedy (Manchester) has kindly prepared replies to those who commented on the thread about his research earlier in the summer:
I thank the Leiter Report for making room here to respond to the many rich comments about my Apeiron paper on symbolic structures in Plato's dialogues. The stakes in this debate are high. Unravelling these symbolic systems promises to revolutionise our understanding of Plato and Platonism.
There has been a great deal of progress made since the Apeiron paper was written. For those in the UK, I will be speaking to classicists about these developments at Manchester (23 Sept.), The Institute for Classical Studies in London (4 Oct.), and Leeds (27 Oct.). My forthcoming book, The Musical Structure of Plato's Dialogues (Acumen, Spring 2011), substantially expands the evidence in the paper.
1) NEW DOCTRINES? Aaron Boyden, Mohan Matthen, and marcus say that my arguments expose musical structure but not new doctrines. MSPD has a chapter entitled 'Extracting Doctrine from Structure.' My strategy, however, was to publish the evidence for the musical structure first.
The passages marking the notes repeat at regular intervals and therefore can be studied objectively and rigorously. A future book will show that there are other types of symbols which carry Pythagorean doctrine.
Phillip Horky wonders if the symbolic structures really have a Pythagorean provenance. I agree that they may partially reflect Plato's innovations and that it may be difficult to parse the relation to the work of Archytas or Philolaus. There are strong indications, however, that the structures fit into the Pythagorean tradition. Most obviously, the hidden musico-mathematical structures bear a family resemblance to the hidden 'music of the spheres.'
2) WHICH SCALE? Dennis Des Chene objects that the scale I detect cannot be a conventional Greek scale. He is right. The 'scale' should more properly be called a 'division of the canon.' Ancient references to such a 12-note division are listed in my paper; see also David Creese's new book on the monochord (Cambridge, 2010).
3) MOTIVATION? Tim O'Keefe questions whether a Pythagorean philosophy would need to be reserved and hidden. Richard Janko's article 'Socrates the Freethinker' makes a strong, general case that such fringe philosophies were persecuted, leading their proponents to hide them with symbolisms of various kinds (in Kamtekar and Ahbel-Rappe's Companion to Socrates).
4) METHODOLOGY? Philippe Lemoine and James Harold worry that I could find structures in any text or that there might be 'confirmation bias.' This is a serious worry. The Apeiron paper deals with it first by providing many different kinds of evidence, some of which are immune to this kind of problem. Moreover, it directly argues that my methods are falsifiable, i.e., there are some texts similar to Plato's which do not have this musical structure. Finally, however, MSPD (see, e.g., ch. 3 online) will show that there is a depth and specificity to the interpretations which, I think, rules out problems with confirmation bias.
5) GOLDEN MEAN? Tad Brennan and Mohan Mattan object to the Divided Line Argument near the end of the Apeiron paper. I did long hesitate to include this argument because so much mumbo-jumbo has been written about the Golden Mean.
Tad Brennan and Mohan Mattan might be caricatured as complaining that the claimed allusions to the Golden Mean are not explicit. This misses the boat entirely. Allusions are by definition not explicit.
My argument is not just 'there is a reference to the middle at such and such a location, and so it is a reference to the Golden Mean' -- which would be lame. Rather my inductive argument rests upon an accumulation of evidence:
a) By measuring the lengths of speeches and dialogues and by finding parallel concepts at similar relative locations we have evidence that Plato was counting lines, which we know from historical evidence was routine in that context.
b) This is corroborated by independent evidence in the dialogues that they are divided into twelve parts, which would necessitate line-counting.
c) This is corroborated in turn by the musical evidence: by the known importance of the 12-fold-scale, by the correlation between the contents of the passages and the relative harmony of the notes, etc.
d) All this is corroborated by the connections to ancient Pythagoreanism: by their use of 'symbols,' by their doctrines about underlying musical structures, by the assertions that Plato was a Pythagorean, by the neo-Pythagoreans' emphasis upon the 12-fold scale, etc.
At this point we have a strong, general case (much amplified in MSPD) that the dialogues have a stichometric and musical structure. Now we bring that to bear on the specific question of the passages about the Golden Mean:
e) Other scholars have identified the Divided Line as an allusion to the Golden Mean, and have given various, strong arguments of their own.
f) We know from a variety of sources that the Golden Mean was known about the time Plato was writing, that Proclus may have asserted that Plato derived theorems about it, and that it was important to Pythagorean mathematics (Herz-Fishler).
g) Surprisingly, the Divided Line passage is at a location that corresponds to the value of the Golden Mean.
h) Surprisingly, the Parmenides also has a passage near 61.8 percent with specific similarities to the language of Euclid's definition of the Golden Mean.
i) Less obviously, other dialogues discuss means and middles near that point.
The conclusion from all this is that it is now more probable that the other scholars were correct, and that Plato's tantilizing Divided Line is a deliberate and deliberately vague allusion to the Golden Mean.
Tad Brennan does wonder, quite reasonably, whether all of Plato's references to a middle or the Great and the Small might then count as vague allusions to the Golden Mean. It's true that they demand an explanation. During the last few years I have felt like I was learning a foreign language without a dictionary. I have found that the dialogues are as dense with symbols as the writings of Dante, Spenser, Mann, or Woolf. As Tad Brennan says, we will have to investigate every passage which bears a similarity to the one marking the Golden Mean.
MPSD is a thorough close-reading of the musical symbols throughout the texts of two dialogues, and aims to be a model for such a comprehensive investigation.
A philosopher might say that whenever a single piece of evidence is pushed I fall back on the accumulation of evidence. But this is true, I think, of all inductive arguments and of all symbolic interpretation.
It is difficult to mount an inductive argument because a large body of mutually reinforcing evidence must be adduced. It is correspondingly difficult to criticise an inductive argument because some wholesale or pervasive problem with the evidence must be detected. No such problem has been identified in the body of evidence presented in the Apeiron paper.
6) I thank everyone who made a comment and look forward to continuing this debate.