(PDF) Plato's "Middle" Cluster

NOTES AND DISCUSSIONS/NOTES DE LECTURE PLATO'S "MIDDLE" CLUSTER DEBRA NAILS IT IS WRONG, Jacob Howland has argued,1 to use any proposed chrono- logical order of Plato's dialogues as an interpretive lens. Wrong, but ex- traordinarily widespread. Wrong in conception and in consequence. Wrong in conception, because all chronological investigations of Plato-whether historical, philosophical, literary critical, or stylometric-are philologically and methodologically flawed in a host of respects. Wrong in consequence, because this preoccupation of contemporary Plato scholarship prohibits "whole ranges of fruitful inquiries and insights suggested by the texture of the dialogues themselves" (212). And Howland is right. While roundly criticizing statistical stylometric analysis, however, he has overlooked a sig- nificant use of that tool by Gerard R. Ledger2 that, albeit incidentally, pro- vides evidence against the chronological sequence proposed within the now dominant scholarly tradition3 with compelling data for the statistical isola- tion of a set of "middle" dialogues previously unrecognized as closely con- nected. As Howland readily acknowledges (209), Ledger advances beyond previ- ous statistical efforts by arguing against the assumption that relative dates of composition can be read directly and linearly from changes in authorial style. Further to his credit, like few other stylometricians, Ledger avoids the bias that accompanies the selection of particular grammatical forms by mea- suring not deliberate but unconscious aspects of Plato's style. To achieve this, he divides the corpus (forty dialogues, letters, dubia and spuria) into 493 1000-word segments, then computes the number of words containing each Greek letter and, to capture something of the highly inflected nature of Greek and thereby stand a better chance of measuring something mean- ingful about Plato's style, he also counts words with specific letters in the 1Jacob Howland, "Re-Reading Plato: The Problem of Platonic Chronology," Phoenix 45 (1991) 189-214. 2G. R. Ledger, Re-Counting Plato: A Computer Analysis of Plato's Style (Oxford 1989). 3A variant sequence was recently defended by Gregory Vlastos, Socrates: Ironist and Moral Philosopher (Cambridge 1991) 46-47. Although Vlastos says he orders the dialogues "solely by the philosophical content" (his emphasis), he also welcomes the support he believes he gets from stylometricians, remarking in the same passage that their agreement is "particularly significant." 62 PHOENIX, VOL. 48 (1994) 1. This content downloaded from 35.8.11.2 on Fri, 25 Dec 2020 15:26:58 UTC All use subject to https://about.jstor.org/terms NOTES AND DISCUSSIONS/NOTES DE LECTURE 63 penultimate and ultimate positions, for a total of 37 variables per segment.4 As a control, Ledger mixes in twelve works by six other ancient authors and treats them the same way.5 Howland's point that Ledger's "procedure be- comes circular" (210), while true of the project as a whole, is misleading because it does not apply to the independent parts. A central strength of Ledger's work is that, at each stage, he provides many raw data for anyone who might wish to analyze them differently, and much information about the wide range of statistical techniques he uses, including those that failed. In what follows, I offer an analysis of some of Ledger's raw data, before the method becomes circular, before he selects particular subsets of vari- ables to trust, before he leans on any presumed chronology (e.g., that the Republic pre-dates the Laws).6 Having computed a numerical indicator of the style (relative frequency of letters) for each of the 52 works in his study, taking into account all 37 variables, Ledger introduces another useful tech- nique, derived from canonical discriminant analysis, a tally of similarities and differences among the works, comparing each to all the others, one by one, and expressing the results as "Mahanalobis distances." In the discus- sion that follows, I shall be referring to "neighbors" of particular works, by which I mean whatever other works have been calculated as having great- est stylistic affinity to (i.e., shortest Mahanalobis distance from) the first. When all the works are analyzed, using all the variables, then plotted in relation to one another on a graph, they cluster the way houses might in a rural area, a few here near the river, a few there on the hillside, and several scattered about on their own.7 Distances among the works (those of Plato and of the other authors) range from 2.66 (for the closest neighbors, Pro- tagoras and Symposium) to 13.94 (the distance between Isocrates' Pana- thenaicus and Plato's Parmenides).s Note that there are two interesting ways of looking at Mahanalobis dis- tances: absolutely, by number (low numbers mean short distances); and relatively (every dialogue has a "nearest neighbor"-even if that neighbor is very far away, and even if that neighbor has many very close neighbors of its own). Consider the closed set of Montreal, Toronto, New Orleans, 4I am simplifying his overall method; for particulars see Ledger (above, n. 2) 4-19. 5Strictly speaking, as an anonymous Phoenix referee points out, there are twenty works: Ledger treats the nine orations of Isaeus as a unit. 6Aristotle Politics 1264b26. 7Again I must omit details of the method: Ledger (above, n. 2) 42-43, 128-169. I should add that the actual graph would require 37-dimensional space. 8It would have been helpful if Ledger had calculated the works' "distances" from themselves, i.e., the lower limit on reasonable expectation. These data could have been generated by performing a run in which all works had been divided in half, with the halves treated as individuals. Presumably, the distances between halves would be small, presumably smaller than the distances to even closest neighbors, but data beat pre- sumption every time. This content downloaded from 35.8.11.2 on Fri, 25 Dec 2020 15:26:58 UTC All use subject to https://about.jstor.org/terms 64 PHOENIX and three towns just south of New Orleans. Montreal is Toronto's nearest neighbor, Toronto is Montreal's nearest neighbor, and the distance between them is relatively short; but Toronto's second-nearest neighbor is New Or- leans, even though the distance is great, and even though Toronto is New Orleans' fourth-nearest neighbor. Back to Athens. If Mahanalobis distances are to be trusted as measur- ing something real, then, for a known group of similars (say, the works of Isocrates: Antidosis, Archidamus, De pace, Panegyricus, and Pana- thenaicus), one would expect small distances among the speeches and no interference from outsiders such as Platonic dialogues-even though the writings of Isocrates span some forty years. That is exactly what the data provide. When Ledger lets the computer scatter all 52 works on the basis of stylistic affinity alone, without so much as telling the computer who is the author of what, the five Isocratic speeches form themselves into a hermeti- cally sealed cluster, naming only one another as neighbors to the fourth de- gree; and their average distance is 3.03 at the first position and 3.59 at the fourth. When fifth-nearest neighbors are introduced, forcing other authors' works to be named, they come in at a minimum distance of 7.22-a rise too steep to ignore. Can we expect anything like that coherence for Plato? Close, but not quite. The remarkable cluster of Platonic dialogues is Critias, Epinomis, Epis- tle 7, Laws, Philebus, Politicus, Sophist, and Timaeus, for all of which Ledger lists neighbors to the eighth degree. Through the sixth position, this set of works generates only its own members as neighbors except that Epistle 7's second-nearest neighbor, and the Philebus's fifth-nearest neigh- bor, is Phaedrus.9 In calculating first-position (nearest) neighbors, the av- erage distance between dialogues is 3.64 within a range of 3.34-4.09. If neighbors to the fourth degree are allowed, the range increases to 5.72, and the average distance between neighbors rises to 4.28. As one might say, the works of Isocrates are crowded close together down in the valley; a clus- ter of Platonic dialogues, not quite so densely packed, forms an isolated neighborhood halfway up the mountain. Some distance away lies Phaedrus, which is the gateway to yet another distinguishable community, of which more below. The fact that the Isocratic speeches, and the Platonic dialogues called "late" in the literature-regardless of when they were written-form such 9At the seventh position, considerable deterioration sets in: Xenophon's Memora- bilia appears as neighbor to Epistle 7 and the Phaedrus appears for three additional dia- logues; at the eighth position, the Theaetetus appears for the Philebus, Lysias's Against Eratosthenes appears for the Politicus and the Phaedrus claims two more dialogues. It is worth noting that, although all these works except the Politicus show affinity to the Phaedrus, that dialogue's greatest affinities are to other works altogether; not a single one of its first eight neighbors is one of these dialogues, so that Ledger labels it "transi- tional" (210). This content downloaded from 35.8.11.2 on Fri, 25 Dec 2020 15:26:58 UTC All use subject to https://about.jstor.org/terms NOTES AND DISCUSSIONS/NOTES DE LECTURE 65 Table 1. Absolute Mahanalobis Distances to 4.0 (greater distances are indicated by dashes) Alc. 1 Chrm. Grg. Meno Phd. Phdr. Prt. Resp. Symp. Tht. Alcibiades 1 . - 3.52 3.67 - 3.82 - 3.85 3.88 Charmides . - - - 3.91 Gorgias . 3.66 - - 3.39 3.99 3.79 Meno - - - 3.59 Phaedo . 3.93 3.69 3.32 3.06 3.23 Phaedrus . 3.53 3.27 3.36 3.12 Protagoras . 2.66 3.65 Republic . 3.96 3.61 Symposium . 3.67 Theaetetus tight clusters provides more than a modicum of confidence that using hanalobis distances to measure the vague notion of style is justified. B venturing out to seek other clusters in the Platonic corpus, however, knowledge two restrictions: (a) I attach no significance to stylistic aff greater than 4.5, so if I err I mean to err on the side of miserlines rather than subtract some unavoidably arbitrary number of points for g differences, I do not use Mahanalobis distances at all for claims abou affinity of Menexenus, Parmenides, Cratylus, and Ion-none of which neighbors within shouting distance-to other dialogues or letters. If 4.5 were allowed as the stylistic affinity standard, not only w the genre pieces be excluded, but neither Euthyphro nor Hippias M would make the cut, having no neighbors that close. Several other dialogu would be conspicuous outliers, having only one or a few distances b 4.5: Apology, Crito, Euthydemus, Hippias Major, Laches, and Lysis; explanation for their remoteness lies outside my investigation.10 I w rather push in the opposite direction, ignoring these dialogues altoget Because I am curious about this thing I am calling stylistic affinity, becau believe the chances are good that Ledger measured it, aided by Mahana distances, I would push the standard even further, allowing no scores high than 4.0, in an attempt to press for coherence approaching that of "late" group. Table 1 illustrates all and only those dialogues that ach l0Ledger himself has not only interesting ideas about this issue-particularly its nection to the lengths of the dialogues, and the possible application of an absolut metric sum of squares distance-but quite a cache of further results and significance left over from the enormous project he whittled down to 250 pages for its publis am most grateful for his kind correspondence with a stranger about these matters he has investigated so intricately. It is unclear whether a systematic correction f alogue length should be introduced, more so the appropriate magnitude and poss significance of such a correction. I do not have at my disposal the means to e Ledger's research in the direction I would wish in the promising way he suggests, believe that such an extension is warranted. This content downloaded from 35.8.11.2 on Fri, 25 Dec 2020 15:26:58 UTC All use subject to https://about.jstor.org/terms 66 PHOENIX Table 2. Relative Distances: Nearest Neighbors to the Fourth Position (parentheses indicate distances higher than 4.0) Nearest Second Third Fourth Alcibiades 1 Grg. Meno Phdr. Resp. Charmides Resp. (Phd.) (Phdr.) (Tht.) Gorgias Prt. Alc. 1 Meno Symp. Meno Tht. Grg. Alc. 1 (Laches) Phaedo Symp. Tht. Resp. Prt. Phaedrus Tht. Resp. Symp. Prt. Protagoras Symp. Grg. Phdr. Tht. Republic Phdr. Phd. Tht. Alc. 1 Symposium Prt. Phd. Phdr. Tht. Theaetetus Phdr. Phd. Meno Resp. Mahanalobis distances of 4.0 or low as unreliable for signifying stylistic This cluster is even more cohere impressive as the Isocratic group. the "late" dialogues: at the level o is 3.23 (within a range of 2.66-3.9 3.53. At the very center of this of one another, Phaedrus, Prota outside them are Phaedo and Rep Gorgias and Alcibiades 1, then M is represented by the neighbor an The ten dialogues name only on degree except that the Meno poi fourth position (their Mahanalob What have we here? On the purest on a linear chronology have an ar I say "middle," not early, because "late" dialogues and Phaedrus, wh have just identified.12 Are there are incompatible with Vlastos's c of Protagoras, Gorgias, Meno, and dialogues of what Vlastos views a explained. Although Kahn has pro 11Because Ledger evaluates data produc external considerations, and integrates difference, the chronology he finally p pearance (cf. Ledger [above, n. 2] 224-2 12Because I believe with Howland tha than good to the interpretation of Pla chronology, but that is a complex argum This content downloaded from 35.8.11.2 on Fri, 25 Dec 2020 15:26:58 UTC All use subject to https://about.jstor.org/terms NOTES AND DISCUSSIONS/NOTES DE LECTURE 67 chronology provides no better overall fit than Vlastos's. Thesleff, eschew- ing stylometry to argue that the Platonic corpus was substantially edited, revised, and imitated in Plato's lifetime, notes "final" revisions in his pro- posed chronology, but this provides no better than fair compatibility with the stylometric data outlined above. Guthrie's fit is poorest of all, espe- cially because he considers the Theaetetus late. Perhaps more surprising than the chronological issue is the solid performance of Alcibiades 1 (spu- rious to Brandwood, Guthrie, Kahn, Thesleff, and Vlastos);13 but perhaps not so surprising, given that the Epinomis nests so comfortably among the "late" dialogues. As Ledger suggests ([above, note 2] 93), imitative writing may confuse a computer. Still I would repeat, following Howland, that the hidden premise in the portion of this analysis that urges "middle" on us as a chronological cat- egory is that order of composition can be derived directly from affinity of style; that, as already noted, is a claim for which we have precious little independent evidence. Ultimately, even when an unbiased stylistic analy- sis confirms one hypothesis-and some will no doubt feel vindicated by the bright constellation of traditionally "late" dialogues-it dashes a few others in the process.14 DEPARTMENT OF PHILOSOPHY UNIVERSITY OF THE WITWATERSRAND, JOHANNESBURG (1080 KNAPP ST. N.E. GRAND RAPIDS, MI 49505) 13Leonard Brandwood, The Chronology of Plato's Dialogues (Cambridge 1990); W. K. C. Guthrie, A History of Greek Philosophy 4. Plato the Man and His Dialogues: Earlier Period (Cambridge 1975) 50; Charles H. Kahn, "Did Plato Write Socratic Dia- logues?," CQ NS 31 (1981) 305-320; idem, "Plato's Methodology in the Laches," RIPh 40 (1986) 7-21; and idem, "On the Relative Date of the Gorgias and the Protagoras," Oxford Studies in Ancient Philosophy 6 (1988) 69-102; Holger Thesleff, Studies in Pla- tonic Chronology (Helsinki 1982, Commentationes Humanarum Litterarum 70) 236-238; and idem, "Platonic Chronology," Phronesis 34 (1989) 1-26. 14I am grateful for W. Levitan's insistent criticism, and to the anonymous Phoenix referee who called for a missing set of scare-quotes and thereby prevented a major misunderstanding. This content downloaded from 35.8.11.2 on Fri, 25 Dec 2020 15:26:58 UTC All use subject to https://about.jstor.org/terms