Ledger, Re-counting Plato and Thesleff, Studies in Platonic Chronology

Readers of BMCR reviews of recent stylometric analyses of the Platonic corpus might be forgiven for forgetting that substantive issues of interpretation often rest rather less on the intricate details of such analyses, than on the methodological principles and raw data that emerge from an author’s effort to establish those details.[1] Not that details are unimportant—they are crucial—but methods may be even more so. The two books under review are remarkably dissimilar critical monographs. Ledger uses stylometric methods at the finest level yet, that of individual Greek letters, to analyze Plato’s unconscious style, using historical material with studied restraint. Thesleff is equally sparing, but in the application of stylometric analysis; he chooses instead to focus on neglected aspects of biography and history and thereby to construct a new theoretical model.[2]

Different as they are from one another, both are miles away from the inherited and dominant tradition in Anglo-American Platonic studies, a tradition more articulated than argued, and associated with the revered names of W. K. C. Guthrie and Gregory Vlastos. According to Keyser the received wisdom: the young Plato wrote early or “Socratic” dialogues that preserved the content and style of Socrates’s teachings; as Plato grew older, he developed positions of his own, and particularly the theory of ideas, that were evident in the lively dialogues of the middle period; his late writing increasingly expressed the doctrines cum dogma of a (wise?) old man. Thus, by tracing Plato’s “development,” one can read off the chronological order of the dialogues. In Howland’s words, “It would be difficult to overemphasize the importance in contemporary teaching and scholarship of the standard view of Platonic chrono logy. The very order in which English-speaking undergraduates have for the past 120 years confronted the dialogues, both in the Jowett edition and in the now more popular Collected Dialogues of Plato, reflects the commitments of the standard view” (p. 214). The view, however popular, has long been suspect because it is viciously circular in practice: views about the historical Socrates and Plato are used to establish the chronology of the dialogues, and views about the chronological order of the dialogue s are used to establish facts about the historical Socrates and Plato.[3] The further from the traditional order a Ledger or a Thesleff travels—and here is the crux—the less persuasive is the received view that Plato’s primary accomplishment was the refinement and transmission of philosophical doctrines.

Here is no mere squabble among monks. If Ledger is right, the improvement of analytic computer techniques for application to such problems as authenticity and dating heralds the arrival of unprecedented accuracy in Platonic studies, providing an opportunity to avoid previous stylometric circularity problems by examining aspects of style of which Plato was unconscious. But if Thesleff is right, the layers of revision and collaboration essential to questions of Platonic authorship and chronology cannot be untangled by any amount of computer analysis. If either is wholly right, the other is wrong, and so is the dominant view. There is only one point on which all sides agree, and on which various types of argumentation seem to converge: a group of late dialogues including at least Timaeus, Critias, Sophist, Politicus, Philebus and Laws can be distinguished from the rest on the basis of its very different style.

Ledger deserves a second review in BMCR not only because his is the most far-reaching and, in important ways, unflawed stylometric analysis of Plato’s dialogues to date, but because his book was poorly understood, if not systematically misrepresented, by its first reviewer, Keyser. Having already read Ledger critically when I encountered Keyser’s review, my own first reaction was to ask myself how I could have overlooked such flagrant mistakes, but a return to the text has clarified where the mistakes lie.

Any description of Ledger’s book should remark at the outset on the candor of his presentation: he narrates the failure of some of his tests, not just the success of others, and he maintains a critical attitude toward his results, even when he is most persuaded by them. Similarly, credit should be given for his designing a set of variables and choosing a program of tests that address the two most common objections to stylometric analysis: the underlying assumption of linear development, and circularity. If Plato consciously altered his style back and forth from dialogue to dialogue, or from time to time, for reasons of his own, then not a single stylometric analysis to date could be used to establish a linear chronology, no matter how well it discriminates deliberate stylistic elements in the various dialogues. Yet, regardless of his intentional choices as a writer, if Plato’s style changed linearly over his lifetime in subtle ways of which he was unaware, then Ledger’s method provides a useful stylometric tool for identifying the chronological sequence of the dialogues. And what if Plato’s style changed subtly but not linearly? In that case Ledger’s method would demonstrate only, but not insignificantly, that some dialogues were written at about the same time as some others (pace Keyser, p. 425), although it would be impossible to say on the basis of style alone whether earlier or later.

The key feature of Ledger’s approach to Platonic stylometry is orthography.[4] After dividing the corpus into 493 1000-word segments, he computer-counted words containing each Greek letter and, to capture something of the highly inflected nature of Greek, and thereby have a better chance of measuring something meaningful about Plato’s style (without the bias that accompanies prior selection of particular grammatical forms), he also counted words with specific letters in the penultimate and ultimate positions.[5] Ledger’s goal was to solve, or help to solve, the problem of Platonic chronology, perhaps unraveling the problem of authenticity along the way; but he well knew that statistical analysis in this computer age offers such a bounty of techniques that it would be necessary first to establish the reliability of various types of multivariate analysis by testing them on questions the answers to which he already knew (pace Keyser, p. 73). Thus he defined 209 similar 1000-word segments from the writings of Aeschines, Isaeus, Isocrates, Lysias, Thucydides, and Xenophon, fed them in with the Plato segments, then asked the computer to use three forms of cluster analysis to identify which segments belonged to which authors.[6] Results were similar. Keyser complains that Ledger “draws an invalid conclusion, which tends to weaken his work: because all the methods he tried gave similar results he argues that the results are more certain—but the methods he lists have been shown (p. 33) to be mathematically more or less equivalent, so the coincidence of results proves nothing” (p. 424). This is a clumsy distortion of the facts: yes, Ledger introduced three methods, but he also explained their relative advantages and biases for different types of data sets. Thus his more modest conclusion is perfectly valid: “substantially similar results … guarantee that the cause is not some chance coincidence of the method used and a particular combination of variables…,” in other words, not the result of the particular bias of a single method.

Ledger diverges at this point into a critical discussion of the failures of his cluster analyses, taking concrete examples from the author-discrimination tests just mentioned. Keyser attacks the examples as if they had been intended to provide evidence of some achievement (pp. 424-5). To the contrary, Ledger concludes the first set of examples with, “the variables we have chosen are not adequate to do the work required of them and we should look elsewhere for information relevant to authorship discrimination” (p. 50)—no less damning a judgment than Keyser’s. And what magnitude of error are we looking at? The first test assigned 94.55% of the 55 segments correctly.[7] Of the second series of examples, it hardly seems fair for Keyser to cry, “it only gets worse,” when Ledger has introduced the series specifically “to illustrate more effectively the difficulties… “; unsurprisingly, error grows in the second test to 15%. Besides, it doesn’t only get worse: when Ledger returns to the issue of refining techniques with a third set of examples and adds other techniques, he achieves 99% accuracy in classification before proceeding to Plato.[8]

Chronological arguments other than stylometric ones are squeezed into the slender chapter devoted to background (pp. 71-91), but the chapter is largely perfunctory; Ledger is conservative about what may count as evidence external to the dialogues, and about cross-references among the dialogues. He will later make use of this material, but only to augment stylometry. Here is one example to give a taste of Ledger’s attitude toward extraneous complications: “it is quite possible that the longer dialogues took several years to write, especially the Republic and the Laws, and their completion may have been delayed while other dialogues of less moment were attended to. We have to assume that this was not the case, simply to restrict the problem to manageable dimensions” (p. 85). Thesleff’s insights about exactly these sorts of issues would have deepened Ledger’s analysis, I believe, not caused him to abort it.

Two issues occupy Ledger in the remainder of the book: possible authenticity of the dubia and spuria, including the letters; and the relation of the dialogues to one another, their chronological order in particular. Determining authenticity, his first effort was to mix the 17 dubia/spuria with the known Platonic corpus and the segments from all six other authors, then run a discriminant analysis to find out to which authors the dubia/spuria would be assigned; but this simple approach was unsuccessful because (a) overlap between Xenophon and Plato returned when the five other authors were put back into the pool, and (b) a limitation of the analysis caused every segment to be assigned to someone among the seven authors, whoever wrote them. Besides, as Ledger had already suggested, imitative writing may confuse a computer (p. 93). Each successive variation in technique he tried introduced some new type of distortion, even when it clarified something else.[9] (When the recitation of difficulties becomes tedious, I remind myself of its usefulness to other researchers.) Almost aside, Ledger remarks that the one author whose segments are never misattributed to any other author, regardless of technique, is Isocrates, though segments from his works span forty years; however, a stray segment from another author was once misattributed to Isocrates: the so-called “Lysias” speech from Plato’s Phaedrus (p. 117). If anything should give pause about the effects of genre and imitation on stylometric analysis, I think it should be this. Ultimately, many of the dubia/spuria attract genuine Plato segments to them. Someone in Thesleff’s tradition would perhaps use this information to support notions of collaboration and “school accumulation” after 387. Not Ledger: he argues that the tradition has been too strict, and that the canon can be extended with some confidence, at least to include Epistles 3, 7, and 8, Epinomis, Hippias Major, Alcibiades 1, and Clitophon; and others will be added later. I think Ledger is too lenient.[10]

The most important and controversial chapter, certainly the most speculative, is Ledger’s gathering of the stylometric evidence in support of a linear sequence of dialogues. There is a great deal of technical nitty-gritty, some of it intended as illustration, that will repay close study, but the real meat of the chapter is in three parts, all based on canonical discriminant analysis: which dialogues’ positions shall we treat as established? which set of variables shall we trust? and what conclusions, what sequence, do these two decisions force on us?[11] At the usual risk of oversimplifying: if any subset of dialogues can be designated before some other subset, these two subsets can have their “styles” calculated numerically, using all or some of the original 37 variables; any other dialogue can be described as falling more or less close to the two extremes (cf. Mahanalobis distances, n. 12). If different subsets are designated, results will be different. Similarly, if more or fewer variables are trusted, results will be different. Ledger charted four combinations of before-after dialogues, and eight levels of canonical variable (3-10), then added four miscellaneous runs: all ALETS, all BLETS, all CLETS, and all 37 variables (pp. 188-96). Thus a total of 36 different sequences of the corpus were produced, each (or none) of which may be the true Platonic sequence. Indeed, Ledger’s ultimate sequence is not exactly like any of the 36 candidates. However, his sequence relies heavily on the largest of his four possible before-after groups (Set C: Apology, Charmides, Crito, Euthydemus, Euthyphro, Gorgias, Laches, Lysis, Meno, Phaedo, Protagoras, Republic and Symposium all before Laws, Philebus, Politicus, and Sophist); a more conservative analyst might have chosen the tiny Set A: Republic before Laws (but Ledger has provided the information necessary for anyone to do so). Ledger also relies heavily on variable counts of 5, 6, and 7, arguing that lower numbers may be insufficiently discriminating, and higher numbers might drown discriminations in background noise. This is a judgment call, and my judgment runs to higher numbers of variables, even 37. Given these two reliances, and adjustments for genre, internal cross-references etc., a linear sequence of dialogues is presented in detail (pp. 224-5, quoted in Table 1 below).

The denouement chapter, Explanations, will prove a treat for anyone who’s stuck with Ledger to the end. It attempts to answer the question why multivariate stylometry seems to work in cases like these, that is, what makes the method sensitive to changes in style, with an illustration comparing a Euthyphro segment to one from Critias by BLET alone.

Ledger’s method and the data he produces are invaluable contributions to the field of Platonic stylometry, and not only for the expert. Because of his minute narration of his procedure, anyone with an interest in Platonic chronology can follow the text and make informed judgments about its successes and failures. Anyone with an appreciation of statistical theory can use Ledger’s data with other interpretive principles to derive variant sequences or to illuminate more circumscribed issues.[12] And those with both computer literacy in the relevant techniques and access to machine-readable Greek texts can perform tests to refute or confirm Ledger’s conclusions. Yet my reservations about Ledger’s interpretation of his results are fundamental. The most serious is his failure of nerve at just those points where his data bring him into conflict with the familiar philosophical establishment, nowhere more obvious than in his decision to place the Parmenides after the Republic, despite his unequivocal results to the contrary. Also significant is that, although Ledger classified each of his segments by genre (seven categories) and repeatedly comments on the possible effects of genre on word-counts (speaking less technically of dialogue, epistle, oratory et al.), no analyses were performed by genre, and he did not discuss the subject systematically, so readers have no assurance that genre-based explanations, and decisions to rearrange the dialogues, were not ad hoc. In general, like Keyser, I would have appreciated more numerical error analysis.[13] There is a wisecrack among physicists: “he measured it with a micrometer, marked it with a pencil, then chopped it with an axe,” which is something short of a cautionary tale that one’s tools ought to be appropriate to one’s task; it would have been helpful if Ledger had told us in a systematic way just what his tolerance for error is. My copy of Re-counting Plato is sprinkled with enough questions about the quality of arguments, minor except those I’ve mentioned specifically already, that I remain unconvinced that stylometric analysis is the fine instrument Ledger requires for so detailed a linear sequence of dialogues. When he said, “I began to believe that, wherever human judgement and computer analysis did not coincide, it was the former which was fallible” (p. 240), he had forgotten that his computer’s analysis had been at every point guided by his own judgment.

Thesleff gives broad compass to human judgment. His Studies in Platonic Chronology is at the same time so rich in theory, and so encyclopedic in its treatment of chronological issues in the Platonic dialogues, ancient sources, and the modern literature that, whether or not one is eventually persuaded to accept Thesleff’s suggested sequence of dialogues (and I’m not), any investigator of the chronological controversies will appreciate the results of such comprehensive research. One almost feels the poltroon to review it critically.

Quoting Lutoslawski’s complaint that Platonists “are generally unaware of the work of their predecessors,” Thesleff ran no risk that such a thing could be said of him: his modern bibliography of well over eight hundred items is woven critically through the text and notes; and his conspectus of 132 contending dialogue sequences and partial sequences, from Tennemann in 1792 to Kahn in 1981 (though it is selective for the nineteenth century), provides each author’s line of reasoning along with his or her suggested sequence. Nor did Thesleff ignore his ancient predecessors: in his section on criteria previously used in establishing chronologies, he invoked the testimony of at least Diogenes Laertius, Aristotle, Nepos, Plutarch, Aeschines, Dionysus of Helicarnassus, Quintillian, and Cicero (though occasionally it was unclear what criteria he was using to accept or reject some particular piece of testimony—beware his use of “obviously” and “of course”); and he made extensive comparative use of relevant works and fragments by Xenophon, Isocrates, Polycrates (primarily through Libanius), Aischines of Sphettos, Antisthenes, Aristophanes, and Aristotle.

Into all of this, arguments of his own are so thoroughly insinuated that focusing on them separately is a delicate vivisection. Thesleff is most theoretically persuasive when he focuses on the material conditions of academic life and composition, such as we know them, in fourth century Athens.[14] What he offers his readers is a well-argued and plausible alternative to the Anglo-American just-so story of Plato’s solo and linear career. Here are the elements of that alternative, with a few of the tantalizing (controversial) bits exposed. (i) Plato must have done some writing as a young man because there is evidence of Aristophanes’s having read or heard some version of a “proto-Republic” before the Ecclesiazusae appeared in 392, but Plato’s dialogues, as we know them, grew out of his experiences as head of the Academy 387-347. (ii) Not only was there ongoing discussion of philosophical issues all around Plato that is likely to have influenced what he wrote, but he probably developed a new genre there, the dramatic prose dialogue, for wider circulation of Academic ideas[15] (though it is historically implausible that Plato should have invented the entire genre of λόγοι σωκρατικοί), so differences in the depth of treatment of particular topics among the dialogues is better explained as related to their different purposes than to some chronology of development; thus “short dialogues are not early” (p. 98). (iii) Closely related to this picture of a community of philosophers influencing one another in various ways is Thesleff’s agreement with an ancient tradition that the dialogues of Plato underwent revision, and sometimes a series of revisions, in his lifetime, but that only the Laws was edited afterward. This, and his next point, make the stylometric search for a linear sequence hopeless, if Thesleff is right. (iv) Like the Homeridae and the Hippocratics, and as precedent for the better-known Hellenistic tradition, Plato’s associates in the Academy wrote in the name of the master, and several dialogues long thought genuine (most intriguingly, Euthyphro, Crito,[16] Laches, Ion et al.) are better understood as semi-authentic accretions around a relatively small core of dialogues actually written by Plato. (v) The infirmities of old age (and absence of eyeglasses in the ancient world), together with the presumed eagerness of younger colleagues to lend assistance, brings Thesleff to suggest that the late dialogues were written with the help of a secretary (ἀναγραφεύς), possibly Philip of Opus, which may help account for their ‘onkos’ style. Thesleff makes no claim to have proven his hypothetical account, though some elements are particularly well grounded; what he hopes to achieve, and what I hope he achieves, is a “dialogue between different manners of interpretation” (p. 25).

Like the Parmenides, Thesleff’s book divides into two unequal parts, identified as ‘critical’ and ‘hypothetical’. It may be useful to give some indication of the breadth of each part. I need hardly say that a work of this type invites the reader to examine the minutiae and do battle wherever appropriate; I’ll stick to broader issues here. Part I is a systematic and critical overview of the approaches heretofore used in the analysis of Platonic chronology: external (historical and biographical) criteria (pp. 22-39), an approach that remains central to Thesleff’s own approach in Part II;[17] arguments based on the thematic content of the dialogues (pp. 40-52), most but not all trading on the notion of the “development” of one or another idea or doctrine across two or more dialogues; others based on literary criteria (pp. 53-67), where Thesleff dissects the distinction between reported (narrative) and dramatic dialogues into ten subdivisions—this too remains important in Part II;[18] still others on stylometry (pp. 67-82), including his own interesting work in cluster analysis, summarized in a footnote (p. 82);[19] and accounts of two problems that feature prominently in Part II, revision and authenticity (pp. 83-96). It is in this first part that Thesleff develops his most compelling case for a theoretical realignment in chronological studies. Part II introduces a six-point formal model for chronological analysis, based on material developed in Part I, and a “method of confrontation”: roughly, the critical comparison of one dialogue to others, one at a time, to determine what useful information might result, which is intended to test the model on the dialogues themselves. Then (and this occupies half the book, pp. 100-235), every dialogue and every pretender is subjected to systematic analysis that includes—in neat order—general considerations, external criteria, internal criteria, and “confrontation” with other dialogues. From the results of these separate analyses, a hypothetical sequence of all the dialogues is derived (summarized in Table 1).

Because the notion that Plato evolved philosophically in ways that show up in the content of his dialogues is so strong, it was necessary for Thesleff to undermine exclusive reliance on such approaches as tracing Plato’s “development.” He devoted considerable effort to the task, and I can do little more than suggest how he went about it. One of his best arguments is effected implicitly by his conspectus of previously proposed dialogue sequences: when the same dialogues are examined for the evolution of Plato’s thought on different topics, different sequences are derived (pp. 8-17). He also listed the 17 themes “most frequently” tracked through the dialogues for their chronological significance (pp. 40-2), and remarked that Aristotle’s interest in the theory of ideas is what has kept it the developmental theme of choice over the centuries. But Thesleff carefully demonstrated, explicitly and repeatedly, that opposite sequences can be produced for the same dialogues on the same topic. Such demonstrations can be lengthy or, as in the following example, elegant: “In the Republic V 430c Socrates says he is prepared to discuss courage more fully another time. This was taken by Siebeck to indicate that the Laches was written later; Ritter (1910b.219) and others who believe that Laches is earlier think that the passage in the Republic is irrelevant for dating the Laches; but Apelt (Staat, p. 468 n. 38) in spite of his usual scepticism in chronological matters, wanted to interpret it as indicating that the Laches was already published” (p. 44). When Thesleff discusses the developmental approach abstractly, he points out its question-begging tendency (p. 40), lists Raeder’s seven points against it (p. 43), and mentions others’ objections, concluding, “And if we accept, as indeed we have to, that there was a continuous oral discussion going on around Plato, we must always take account of the possibility that two passages which seem to stand in direct relation in fact refer to a common source unknown to us and perhaps never written down” (p. 52). I would add that they may also derive from very different and unwritten sources, consistent with Thesleff’s account.

Keyser is right to point out that chronological researchers typically err in presenting more exact detail than their subject matter allows, violating Aristotle’s dictum (NE 1.3.1). Ledger and Thesleff are guilty. But anyone who has struggled with the order of Plato’s dialogues over a long period is likely to commit the same error; one’s insights, if they be insights, eventually come to exceed one’s ability to argue for them persuasively, and the sometimes irresistible temptation is to suggest what one cannot prove. This is no less true for those who examine the minutiae—E. R. Dodds stretching a little beyond his reach in his chronological remarks about the Gorgias—than for those like Ledger and Thesleff who seek the grand design. Since comfortable certainties are so often so trivial or so stale, I cannot wholly fault authors who enliven academic debate by putting their heads on the block from time to time. Besides, in this case their substantial contributions have earned them room to hypothesize, and both responsibly call attention to their suggestions and speculations as such.

A relatively minor point: rarely are books of such similar numbers of pages so different in length: Ledger’s is produced in easy to read type with wide margins and ample spacing for its nearly seventy figures and tables, some of which occupy several pages; there is a smattering of typographical errors, most annoying when they appear in tables that are (some of them) oriented upside down. Thesleff’s volume, by comparison, has undergone compression in the editorial process; reduced type is used not only for footnotes but for the stylometric conspectus, tables, running comparisons of argumentation, and the bibliography, producing a cadence of page after page of prose and notes, densely packed. While there are many typographical errors, there are no more than in other foreign presses; and the occasional cross-reference goes astray, but the wonder is that there are hundreds that do not. Both books have indices detailed enough to be very useful.

I began by saying that important issues may be obscured by details, yet I have dealt more with details than with grand schemes. I now offer Table 1 as a corrective, facilitating comparison of the incompatible findings of Ledger and Thesleff (those who know the traditional sequence will see at a glance that neither author provides corroboration for it).[20] A stunning dispute occurs over the size of the Platonic corpus: whereas Ledger increases the canon to thirty-five dialogues and letters (over Guthrie’s twenty-seven), Thesleff accepts only fourteen as univocally Plato’s, excluding seven of Ledger’s earliest eight dialogues.[21] Equally noteworthy is the stark difference among their accounts of Plato’s early career. Tradition has Plato beginning to write soon after Socrates’s death and in reaction to it. Although not without precedent, Ledger puts the Lysis before 399;[22] and Thesleff puts the final forms of all the dialogues, except the Apology, after the Academy’s foundation in 387. These decisions reflect widely divergent and highly significant views of Plato’s, for lack of a better word, ‘mission’. Ledger’s Plato is the consummate writer, beginning early in life, pressing on at a relatively constant rate through tragedy or success, acting alone in the production of a corpus coherent for all its breadth and depth. Thesleff’s Plato is above all the leader of an academic community, dialectical rather than doctrinaire, dabbling like some of his contemporaries with λόγοι σωκρατικοί until the establishment of the Academy provides him with philosophical collaborators and the impetus for a new genre, the dramatic prose dialogue, later practiced by other members of his community, sometimes under the master’s name. The Plato of the tradition is the passionate philosopher, compelled by grief at the death of his mentor to write a group of memorial pieces, later emerging from misery se consolatus philosophia, increasingly developing, elaborating and refining philosophical theories of his own and transmitting his doctrines to students, meanwhile suffering disappointments that hardened him in old age. If oysters had a Plato, he’d look like an oyster?

The chronology of the Platonic dialogues has never been so spectacularly at issue, never have the positions been so widely diverse, never have such disparate methods been brought to bear on the texts, as now. These books, poles apart, are well worth reading.[23]

Table 1. Chronologies Incorporating Absolute Dates[24]

NOTES

[1] Paul Keyser, BMCR 1991.07.03 and BMCR 1992.01.12.

[2] Thesleff excerpted and elaborated his book in an article, “Platonic Chronology,” for the widely available journal, Phronesis 34:1 (1989), 1-26. The unfortunate result is that several of the conclusions argued minutely in the book appear nude in the article, leading at least one otherwise judicious author, Jacob Howland (“Re-reading Plato: The Problem of Platonic Chronology,” Phoenix 45:3, 1991), to underestimate much of the power of Thesleff’s position.

[3] Until the recent Socrates: Ironist and Moral Philosopher (Cambridge, 1991), Vlastos’s chronological arguments were presented in articles, and even the book relies to a large extent on readers’ having absorbed those arguments. Key are: “Classical Greek Political Thought: I. The Historical Socrates and Athenian Democracy,” Political Theory 11, 1983; and “Elenchus and Mathematics: A Turning-Point in Plato’s Philosophical Development,” American Journal of Philology 109, 1988. The most original contemporary contribution within an essentially Vlastosian framework is that of Charles H. Kahn (“Did Plato Write Socratic Dialogues?” Classical Quarterly 31:2, 1981; “Plato’s Methodology in the Laches,” Review of International Philosophy 40, 1986; and “On the Relative Date of the Gorgias and the Protagoras,” Oxford Studies in Ancient Philosophy 6, 1988; et al.). Kahn’s views have been criticized effectively, from two very different perspectives, by Mark L. McPherran, “Kahn on the Pre-middle Platonic Dialogues,” Oxford Studies in Ancient Philosophy 8, 1990, and Charles L. Griswold, Jr., “Unifying Plato: Charles Kahn on Platonic Prolepsis,” Ancient Philosophy 10, 1990.

[4] Ledger correctly points out that previous stylometricians in Platonic studies have eschewed the value of orthography, so Keyser’s professed intention “to establish the history correctly since Ledger does not” by devoting a whole page (p. 423 and nn. 1-7) to a small treasure of irrelevant orthographic work is misguided.

[5] For the first category (ALETS = 19 variables), all words containing the letters alpha-omega were counted, except that 6 letters that occur infrequently (beta, zeta, xi, phi, chi, psi) were lumped together to produce a number high enough to be useful statistically; for the second (BLETS = 9 variables), all words ending in alpha, epsilon, eta, iota, nu, omicron, sigma, upsilon, omegma (the only letters that end words in Greek) were counted; and for the third (CLETS = 9 variables), all words with alpha, delta, epsilon, eta, iota, omicron, tau, upsilon, omega in the penultimate position (again, the only possibilities in Greek) were counted. Accents and breathing marks were not considered. This procedure produced a total of 37 variables x 493 segments = 18,241 data points for the Platonic corpus, or rather about 90% of the corpus (letters and dialogues of fewer than 1000 words could not be included; and there were of course residual words after the division into 1000-word extracts).

[6] Originally, a subset of 320/702 segments was tested, and Ledger’s text describes those early experiments with the 1982 Statistical Analysis Systems in some detail; all 702 were subjected to analysis, and eight new methods tried on subsets, when the 1983 version of SAS appeared later.

[7] Keyser says dismissively, “of ten clusters, three are contaminated,” implying 30% error (p. 424)—but there were 55 segments, only three of which went astray (5.45% error). Along the way, Keyser intimates, by asking niggling questions (“…but which book?” “but which?”), that Ledger’s discussion is incomplete; in each case I had no trouble finding clear answers in the text in close proximity to the pages under discussion. Likewise, when Keyser says of Ledger, “he apparently used all 37 variables for this test: p. 47,” his term “apparently” insinuates that Ledger has not clearly specified how many variables he used; but Ledger provides the number explicitly at least nine times (pp. 40-51).

[8] It should be noted that the degree of accuracy obtained is directly related to the test applied; perfect accuracy (100%) between Plato and Xenophon, for example, can be achieved by varying the particular method of discriminant analysis (using the ‘within’ covariance matrix), but there were too few segments of the other authors for them to be included in this type of test (pp. 96-7 and nn. 3-4).

[9] The two most important variations were: a reduction in the number of variables, and the calculation of Mahanalobis distances (indicators of which dialogues are most like which others in style). Keyser objects that Ledger should have specified which variables were used, but this borders on the absurd; Ledger rightly explains exactly how the subset of variables was chosen—as useful a piece of information as a list, “CLET4 removed, CLET6 entered, ALET1 entered …”—particularly since this method does not prove pivotal in the work.

[10] Working with Mahanalobis distances, dialogue by dialogue (pp. 142-68), Ledger too often lowers his standard with respect to the 4.0-4.5 criterion he set initially to indicate authenticity, i.e. a spurious work must be no further from at least one uncontroversially genuine dialogue than 4.0-4.5 to be allowed into the canon. Yet Clitophon, for example, has no scores less than 6.2, and finds its way in anyway; Menexenus, though usually considered genuine, scores closer to a segment of Thucydides (because of genre?) than to its nearest Plato neighbor (Phaedrus at a too-high 5.71).

[11] Keyser’s treatment of Ledger’s ch. 9 (pp. 425-7), involves the following problems: (a) Keyser conflates the distinctions before-or-after, temporal proximity, and early-or-late—all of which are different—perhaps because Ledger is also rather sloppy with them, especially in labelling Table 9.2. (b) Keyser criticizes Ledger’s conclusions by dipping freely for evidence into sets of variables Ledger has eliminated for reasons that are provided; it’s a cheap shot because a reviewer is not obliged to justify the use of any particular set of variables. (c) Keyser objects that Ledger adheres to the statistical order of the middle dialogues in cases where the numerical differences among them are too small to matter; while it is true that Ledger might have decided to arrange such dialogues alphabetically, Ledger’s reason for keeping the sequence was simply that he had no arguments for changing most of it; where he had arguments, he changed the order. (d) Keyser’s language implies far more certainty in Ledger’s presentation than is warranted: when Keyser says, “Ledger is willing to announce such details as… ‘Crit. being cut short by Plato’s death'” (p. 427), the reader might profitably restore the rest of Ledger’s sentence to find its qualifiers, “nearly” and “suggesting” (p. 197)—something short of an announcement.

[12] Various statistics textbooks have been recommended to BMCR readers already. But for sheer clarity in the presentation of statistical concepts and their intelligent application, nothing surpasses the second edition of Statistics by David Freedman et al. (New York: Norton, 1991). Humanists who fear statistical analysis will be engaged by the prose and will feel at home with an emphasis on principle rather than number crunching.

[13] Even so, I think Keyser’s discussion of “statistical uncertainty (symbolised sigma)” and “the z-score” is a minor subterfuge implying that error was only glancingly treated, if not suppressed. Readers in search of Keyser’s ‘sigma’ should look under “standard deviation” in Ledger (and for “z-score” under “significance”); significance tests are routine in SAS.

[14] Thesleff almost always points to precedents in the literature for the positions he advocates, but these are often little more than suggestions in his predecessors’ works. His only truly important intellectual debts appear to be to the Tübingen school, although Thesleff’s use of the esoteric-exoteric distinction is more tempered than theirs, and to the unitarian approach of Paul Shorey (The Unity of Plato’s Thought, Chicago, 1903) et al.

[15] This particular view baffles me. Thesleff believes the reported dialogues, with their frames and their hints about the characters, were the more likely to have been used within the Academy, that the dramatic pieces were the ones published outside, probably for performance: “most of the dramatic pieces in Corpus Platonicum are very obviously not intended for performance in a closed circle only” (p. 63). But it seems to me that Academicians were less likely to have required such hints, which could as easily have been provided orally, and that if the dialogues were performed anywhere, it was most likely in the Academy itself—but the reader should look at the arguments (pp. 53-67).

[16] Thesleff argues that Speusippus was the likely author in the 370s, but I don’t believe his chief reason is sound: that Plato would not have felt “Socrates’ loyalty to the laws of Athens worth a particular, weighty and serious defence against what must have been his own conviction” (pp. 208-10). I think Plato was indeed inclined to write against his own conviction, that this is in fact what sets him apart from so many other philosophers as dialectical rather than doctrinaire.

[17] This section includes, apart from a great deal of information about Plato’s life and associates, a close examination of the dialogues and letters for references and allusions to his contemporaries and their works, to datable events, and to other dialogues; and a search of the works of Plato’s contemporaries for references and allusions to Plato or his works. The only datum that rankles (me) is the repeated insistence that Plato was shy.

[18] Thesleff’s previous book, Studies in the Styles of Plato (Helsinki, 1967) provides the foundation for this approach, but Thesleff has changed his views substantially over the years, and is careful to point out differences with his own former positions.

[19] Thesleff’s collaboration with K. Loimaranta, a statistician with whom he was working at least until 1981, came to an end sometime before the publication of Thesleff’s 1989 article in Phronesis where he says the results were statistically disappointing. Apparently, they did not publish their results. What interests me in the approach they were taking is that some dialogues were subdivided to test for effects of revision and/or possible dual authorship (e.g. Parmenides and Republic).

[20] Similar tables for Guthrie, Brandwood, Vlastos, and Kahn make clear a number of variations among the traditional account of Platonic chronology and those of Ledger and Thesleff My reason for excluding them (and for containing this review to these two authors) is that all the others date the dialogues relatively (e.g. early-middle-late); only Ledger and Thesleff are willing to commit to print a full set of absolute dates, though they both emphasize the far greater defensibility of their own relative sets. Comparing across such differences in approach would have introduced complications better left to a non-review forum.

[21] Ledger puts Lysis first while Thesleff puts it ninth (of fourteen); Thesleff puts Apology first while Ledger puts it fourteenth (of thirty-five).

[22] According to F. Ueberweg (Untersuchungen über die Echtheit und Zeitfolge Platonischer Schriften und über die Hauptmomente aus Plato’s Leben, Wien, 1861), Tennemann (1792) placed at least nine dialogues before 399, including Lysis. Others followed (Thesleff lists six such researchers) with variations on this view until at least 1862 with R. Schöne’s Über Platons Protagoras. Ein Beitrag zur Lösung der platonischen Frage (Leipzig).

[23] I am grateful to W. Levitan for his interest, enthusiasm, and criticism.

[24] Ledger: parentheses = dubia/spuria. Thesleff: superscripts = editions (Gorgias¹, Phaedrus¹, and Theatetus¹ being narrated dialogues, the others as described).

[25] According to Thesleff: “school accumulation” or “semi-authentic”: Clitophon (379); 370s: Crito, Laches, Alcibiades 1, Theages, Hippias Minor, Ion; 360s: Amatores, Eryxias, Euthyphro; Hippias Major (360); 350s: Epistles 2,3,4,6,8,13, Hipparchus, Sisyphus, Minos, Demodocus, De Virtute, De Justo; Epinomis (>347).