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3. History-free approaches

3.1. Diagrams that resemble but do not constitute stemmata result from cluster analysis. Here an index of similarity (or conversely of distance) between every possible pair of manuscripts is required. Initially each manuscript constitutes a "group" of one. The two groups most similar according to the index are amalgamated, and this step is repeated until there is but one group, comprising all the manuscripts. The obvious


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index of similarity is the number of agreements, but, as Patricia Galloway explains, other indices exist and, where two groups each comprise many manuscripts, there is more than one way of defining the index between the groups in terms of the indices between the constituent manuscripts.[35] The resulting diagrams, unlike stemmata, cannot show one manuscript above another, or a branching into three or more lines, and many cluster analysts rightly distinguish them from stemmata.[36]

A. Kleinlogel, however, after a complex argument based on lattice algebra,[37] proposes that we provisionally select the original reading in every variant passage, and thence count, for every manuscript pair AB:

s=no. of variant passages where AB are correct
t=no. of places where A is correct and B errs
u=no. of places where B is correct and A errs
v=no. of places where AB err together
Three-way splits may be left aside. A similarity index which will supposedly reveal the stemma through cluster analysis is
τ = cos [π sqroottu/sqroottu + sqrootsv]
Yet in a simple example this method gives the wrong stemma. In fig. 11a,
α erred five times, and so on, and all forty-five errors arise in separate places. For all pairs we tabulate:


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AB  10  20  10  0.00 
AC  25  10  0.35 
AD  25  15  -1.00 
BC  10  25  -0.35 
BD  10  30  -1.00 
CD  30  10  -1.00 
Cluster analysis yields fig. 11b, which falsifies the history, and also the evaluation: if β and D erred simultaneously, whence a three-way split AB:C:D, with C alone correct, fig. 11b would wrongly condemn C's reading.[38]

Other investigators propose similarity indices not involving the distinction between true and false readings, apply cluster analysis, and call the results stemmata. Were this valid, one could obtain a stemma on the basis of mere similarity, without ever deciding between readings[39] — which is absurd, since, without the notion of error, one cannot even draw a stemma for two manuscripts AB, showing whether A derives from B or B from A or both from a lost source. The distinction, already stressed by Greg (see n. 3, p. 59) between similarity and historical relationship is illustrated by fig. 12a: AD are the most similar pair, but not the most

closely related, and cluster analysis yields the very different tree of fig. 12b. Yet P. Tombeur (loc. cit., see n. 36), and V. Wendland[40] attempted to found stemmata on the number of agreements as a similarity index.

Similar but more elaborate is P. Malvaux's treatment of fifteen manuscripts of Theodoret of Cyrrhus.[41] Five groups were immediately apparent from the apparatus criticus, each departing unanimously on between


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nine and eighty occasions from the agreement of the others. Together these groups covered all fifteen manuscripts (AYZ; BR; CFHP; ENT; GQW). Malvaux posited for each group an ancestor responsible for its distinctive readings, and a more distant ancestor free of them. To study the relations between those remoter ancestors, Malvaux discarded unique readings and the distinctive readings of the five groups, on the ground that they originated subsequently.[42] The disagreements between the extant manuscripts were counted over the reduced field of variants. Cluster analysis linked most closely AYZ and BR, between which the fewest disagreements occur, and then linked the two with ENT; meanwhile CFHP were linked with GQW; hence the main lines of fig. 13a. The contrary findings of his collaborator the philologist
P. Canivet, however, imposed the contamination line. Canivet produced no common error in CFHPGQW, and found in CFHP alone some readings that were undoubtedly correct.[43] This situation is better explained by fig. 13b, which rests on Canivet's findings plus Froger's method applied to the agreement patterns.[44] It rehabilitates one "séduisante" reading that Canivet abandoned in deference to the stemma (p. 405)[45] and accommodates 403 of the 447 variants reported (out of a total of 585). In any event, as Canivet concluded (p. 413), this is not a particularly contaminated tradition.

In yet another approach that excluded the criterion of error, Carmélia Opsomer-Halleux counted for each manuscript pair the number of


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common departures from the text of the majority, and on that index founded a stemma.[46] But the majority need not be correct; an error may have infected a fertile family. The notion of error cannot be sidestepped.

3.2. Some investigators find similarities informative, even though they yield no genealogy. J. G. Griffith has used them to arrange the manuscripts in a spectrum, i.e. a sequence in which manuscripts that are similar textually stand close together.[47] In a study of Juvenal's Satires, the sincerest witnesses came out at one end and the most interpolated at the other. The textual worth of a manuscript could thus be inferred from its position along the spectrum. Between eight spectra for different sections of the Satires, Griffith found some variation, which indicated shifts of allegiance, as he confirmed by traditional methods. Within each spectrum groups were discerned which showed especially high similarity figures among themselves. In a second study, covering fourteen or fifteen manuscripts over four samples from Luke and John, the spectra did not prove interpretable as scales of textual purity. The groups, however, followed accepted divisions, appearing in the order: Byzantine, Caesarean, Alexandrian, Western.

A spectrum can be viewed as a one-dimensional map where the distance between successive manuscripts is not quantified. Griffith and others have experimented with maps in two or even more dimensions. Each manuscript is represented by a point on the map, such that the distances between points reflect the degrees of textual divergence between the corresponding manuscripts. Manuscript maps were first proposed by the monks of Solesmes, in their edition of the neumic text of the Roman Gradual.[48] These maps bore obvious but not total resemblance to geographical maps of provenance of the manuscripts, and facilitated the comparison of textual with political and linguistic affinity. The map also served to divide into eighteen clusters the four-hundred-odd manuscripts collated, and whichever reading was attested by the majority of these clusters prevailed.[49] Despite the obvious risk that an


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error might have infected the majority, this evaluative policy was as reasonable as any, for one can hardly detect errors in a neumic text.

While the monks of Solesmes drew their maps freehand, other investigators use factor analysis. D. Najock[50] and F. G. Berghaus (op. cit., see n. 36, pp. 102 f, 110) analysed thus the tradition of Old English glosses on the Psalter, obtaining maps which demarcated clearly the two classes distinguished by conventional methods. Again, the main accepted groupings of New Testament manuscripts were confirmed, with some fresh insights, in J. Duplacy's map.[51] In a map compiled by P. Monat of nine manuscripts of Lactantius' Divinae Institutiones IV, the manuscripts located to the 'west' carried a longer version of the whole work, and those to the 'east' a shorter version, both attributed to the author; the oldest manuscripts appeared in the 'south'; Monat concluded (p. 322) that any reading attested jointly by the most 'southwesterly' manuscript and the most 'southeasterly' should prevail.[52] Griffith's maps of passages from Horace, Juvenal, the Gospels and Aeschylus confirmed and refined earlier groupings, while variation between results from passages by one author suggested shifts in the textual history.[53]

The deficiency of all these approaches, including cluster analysis, is that the main aims of textual criticism—an evaluative policy and a history—are not attained. Admittedly, into one spectrum series (Juvenal) and one map (Lactantius) the notion of error, or at least priority, was readily imported, and led to an evaluative policy; but the contrasting performance of the remaining spectra and maps casts doubt even on those evaluative policies which intuitively emerge.[54] Many interesting results remain, especially the groupings, and the differences in transmission between different sections of one work or between different types of variant (e.g. whether they involve a whole word or not) (Galloway, see n. 35, pp. 4 ff).


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3.3. We turn finally to approaches that involve no genealogies or other diagrams. M. Bévenot set forth a principle applicable to any tradition, however contaminated: a reading attested by two manuscripts never or seldom caught erring together prevails over a reading that lacks such attestation (op. cit., see n. 15, pp. 133 ff, 147 ff). In his edition of Cyprian's De Unitate, Bévenot had set up a 'Resultant Text' presenting at each point his choice of reading on intrinsic grounds. He then counted, for each manuscript pair, their agreements in readings not accepted for the Resultant Text. The pairs showing the lowest totals were termed "opposed". He identified some instances of three mutually opposed manuscripts, and argued that their shared readings were almost certainly correct. Using this principle to check the text, he found that triply opposed manuscripts hardly ever agreed in a reading earlier rejected; but this confirmation of his original choice of readings is suspect, since the underlying statistics of agreement in error themselves depend on that choice. More soundly, he applied his results from the De Unitate to another Cyprianic treatise, the De Lapsis, whose textual history could be presumed identical. He had meanwhile noted in the De Unitate a group (which he later called a 'team') of four mutually opposed manuscripts, and, in the evaluation of variants in the De Lapsis, "the agreement of any three of the four almost invariably carried the day."[55]

M. L. West too counts common errors within every manuscript pair, to identify manuscripts that never err together when the truth anywhere survives.[56] Like Bévenot again, he constructs a 'team', but better defines it as the smallest group to contain all the ancient readings anywhere preserved. Bévenot's formulation (minimum agreement in false readings) might have admitted a group of manuscripts that were deficient, or exhibited separate errors, in places where the truth survived elsewhere. West's team does not rest on his statistics of common error. Instead, he lists all identifiable ancient readings.[57] Any manuscript that uniquely preserves such readings is adopted. Any ancient reading attested by the existing team members is struck from the list, and whichever manuscript contains the most of the remaining readings joins the team. The procedures in the last sentence are repeated until the list is exhausted.


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The approach of Bévenot and West seems the most promising. It is logically sound and attacks directly the goal of evaluation. It reduces the bulk of the apparatus criticus, and the labour of collation in works whose history may be presumed identical. It does not, however, yield a textual history.[58] The evaluative policy is clear, but only when the team is unanimous. Unfortunately it is often divided; in the De Unitate, for example, Bévenot's team of four (aepY) is divided in some twenty passages in Ch. 1 alone. Bévenot, as stated, would follow the majority, but this is to ignore the common phenomenon of unique preservation.[59] West is silent; but if the approach is indecisive wherever the team divides, its role in evaluation is limited indeed. The following sections ask whether these gaps can be filled.