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2.1. The genealogy, if known, would make evaluation easy even in a contaminated tradition. Suppose that the manuscripts disagree. If we can find a common ancestor for the group that attest one reading, and at the same time a path bypassing that ancestor can be traced from each member of the (or a) rival group back to the original, the former reading is attributable to error in that ancestor. Every group can be tested thus against every other, and unless every reading is found attributable to error, the original (or rather the oldest recoverable) reading will be identified.

Now the only way to know that a group of manuscripts share an ancestor on which the remaining manuscripts are not wholly dependent is to have caught that group in an exclusive error elsewhere. Open traditions, however, exhibit a multitude of two-way splits (to go no farther), mostly rare or even unique. Over Cyprian's De Unitate, for example, there are 346 passages where the eighteen manuscripts collated by M. Bévenot survive and divide into two groups; these show no less than 198 different agreement patterns, of which 164 occur just once.[15] Many agreement patterns among the indeterminate passages occur in no determinate passage; none of their constituent groups, therefore, will have been observed in exclusive error. Such patterns cannot be illuminated by the partial genealogy derivable from the determinate passages. Among four manuscripts ABCD, for example, suppose that we detect unique errors in each, as well as some common errors in AB and some in CD. The stemma of fig. 4a results. Suppose in addition an indeterminate split AD:BC. According to fig. 4a, AD have no common source but the original, nor do BC; but in fact either AD or BC must have a common source, as one of the readings must be wrong.[16] The existing genealogy does not

aid evaluation here. On the contrary, an evaluation would fill out the genealogy: if we decided after all that AD were correct, we would ascribe to BC a common source (which fig. 4b takes simply as B); if we preferred to follow BC, we would link AD.

It may be noted that the same apparatus criticus admits more than one genealogy in an open tradition (§1.2). Suppose four manuscripts EFGH, each bearing unique errors, and suppose further some common errors in EF, some in GH, some in EH, some in FG. We might infer fig. 5a. However, the links E-H and F-G could be differently orientated (fig. 5b). Or, instead of ascribing common error to "intrastemmatic" contamination, we should perhaps ascribe common freedom from error to an "extrastemmatic" source (i.e. a lost source not derived from the latest common ancestor of the extant manuscripts);[17] in fig. 5c, μ accounts for the shared errors both of GH and of EF (which had no access to μ to correct λ's errors). In an open tradition it is not always obvious which of the alternative pedigrees has the dubious advantage of being the simplest.

2.2. For a genealogical approach to evaluation, then, one determinate specimen of every attested two-way split is prerequisite. Dom H. Quentin, however, claimed that a full genealogy could be constructed with far less information. He argued that if three manuscripts were related in any of the ways shown in fig. 6, the outer pair (AC) would never agree against

the intermediary (B).[18] All the diagrams comprise the same enchainment, variously orientated. Quentin supposed conversely that if the number of agreements of two manuscripts (AC) against a third (B) were zero, the three were related according to one or other of the diagrams in fig. 6 and stood in the enchainment A-B-C. On comparing by threes all the manuscripts of a tradition, Quentin expected to discover enough zeros to form the complete enchainment, which would merely require orientation. Conflation would be revealed through the last case in fig. 6, though in fact zero agreement in AC against B will occur only in the atypical case where B simply amalgamates AC and never errs.

Now in all six cases in fig. 6, at least one of the three manuscripts derives directly from another. It follows that if, after standard practice,[19] every manuscript which derives from another extant manuscript is eliminated, the remaining manuscripts will exhibit no zeros at all. Yet Quentin did obtain zeros, by restricting the field of variants. Suppose three independent descendants of one ancestor. Before the count begins, the number of agreements of any pair against the remaining manuscript is of course zero. If the text is long enough, all three manuscripts will eventually err and all three zeros will be breached. However, if the text is so short that one of the manuscripts did not err, a spurious zero will remain. Quentin used short texts, and further increased the likelihood of the survival of a zero by eliminating readings which "attirent l'attention des copistes".[20] He also regarded a low figure as a quasi-zero, equivalent to zero; but in fact a quasi-zero may result not only from intermediacy (e.g. if the two outer manuscripts occasionally agree by coincidence) but also from wholly different relationships.[21]

Quentin also eliminated unique readings. Any manuscript standing at the end of a branch was thereby replaced by the nearest extant manuscript

or branch-point; in fig. 7b, for example, a should show A's text apart from A's unique readings. Once an enchainment was established between these surrogates, the manuscripts themselves could be shown branching off it. For example, the enchainment Hub-Bern-Anic-Theo, reached after the removal of unique readings, was modified to fig. 7a

(Mémoire, p. 257). With this adaptation, Quentin's method detects zeros in a wider range of enchainments but by no means in all. In fig. 7b, A without its unique readings becomes a, as does B; C becomes β, and so on; but no zero reveals the relations between αβγδ.

The variants therefore had to be kept few. One of Quentin's genealogies rested on a passage of under 250 words—hardly long enough for every copyist to have committed an error meeting Quentin's conditions. All his analyses involve fewer than 100 variants and he considered twenty sometime sufficient (Essais, pp. 124, 65). Those who took larger samples of the same works found no zeros. For example, whereas Quentin used 91 variants from the Vulgate Octateuch (Mémoire, p. 328), Dom J. Chapman found, on the basis of some two thousand from Genesis and Exodus alone, that "comparison by threes will no longer produce zeros".[22] Again, the zeros which Quentin found on the basis of a sample from the Lai de l'Ombre were breached elsewhere, as Bédier noted (Romania, LIV [1928], 328). Similarly a test on hundreds of variants in Mark yielded "but one zero line among eighty-four groups of three manuscripts".[23]

Quentin's approach has been continued by G. P. Zarri, who uses even fewer variants. In a section of some one hundred lines of the Chanson de Roland he reduced the field to just thirteen, by eliminating on the suspicion of polygenesis the variants that prevented the appearance of the requisite zeros.[24] Another study concerned a text so tiny that Zarri found

too many zeros: the Copa in the Appendix Vergiliana, comprising thirty-eight lines, yielded sixteen admissible variants among six manuscripts, and no less than fourteen zero lines among the twenty groups of three manuscripts.[25] His rules for combining the lines of intermediacy are questionable. For example, in fig. 8a he expects a zero in C against BE,

among many others. In fact, however, two manuscripts will not show zero agreement against a third if a path exists between the two manuscripts—other than a path leading downwards from both—which bypasses the third. Some agreements of BE against C are therefore expected, where C innovates and E follows D. Again he wrongly supposes that the pattern of zeros allows a convergent enchainment to be re-orientated. Fig. 8b will exhibit one zero, namely in BD against A; if B is instead placed uppermost, the only zero now stands in AC against B.[26]

2.3. Instead of a contaminated genealogy, some are content to reconstruct an outline stemma on which every manuscript is derived from its main source alone. One method is to list the two-way splits in decreasing order of frequency until we meet one that is inconsistent (§1.1) with some predecessor.[27] If contamination is slight, this selection will include most passages, and a stemma accounting for them follows through the methods of Maas and Froger. Where contamination is more extensive, different procedures are proposed by P. Buneman,[28] V.A. Dearing,[29] D. Najock[30] and E. Poole[31] for selecting variants on which to base a tree that traces

main sources. In this situation, however, the cumulative neglect of subsidiary sources, which in some cases might be almost as important as the main sources, compromises both the historical and evaluative functions of the tree.

In open traditions, it may be impossible to identify any genealogy of main sources as the correct one. A single apparatus criticus admits many equally plausible histories, which may differ even if secondary sources are overlooked. For illustration, suppose three manuscripts ABC which err together five times; let each manuscript also bear ten unique errors; in five more places, A alone is correct, and, in seven more places, C alone. One possible genealogy is fig. 9a:ω committed five errors, and so on, while B adopted seven of a's errors and five of β's and added ten of its own. B thus departed from α in 15-7+5+10=23 places, and from β in 8-5+7+10=20 places. Hence its main source is β, and the genealogy of main sources is fig. 9b. However, the genealogy of fig. 9c equally fits the

facts. Here A used λ to avoid five of γ's errors and one of δ's, but accepted two of λ's errors and added eight of its own. As A departs from λ twenty-five times and from δ only sixteen times, its main source is δ, whence the tree of fig. 9d. Now any procedure to recover a divergent tree from the apparatus criticus will yield either (b), which is false if (c) is the true history, or (d), which is false if (a) is the true history. The tree yielded by any particular procedure can therefore be no more than one out of many possible genealogies of main sources.

Evaluation can be falsified by disregard of subsidiary sources. Fig. 9b implies that AB's agreements are correct, but they may in fact be errors inherited from the neglected a; similarly fig. 9d gives unwarranted priority to BC's shared readings. Again, as shown in §2.1, contradictions result if the stemma is applied to evaluate variants discarded in its construction as inconsistent. If fig. 4b were the true genealogy, with C following β more often than B, and the stemma of fig. 4a were recovered, then in the splits AD:BC, resulting from C's secondary use of B, the stemma could not decide priority. Such discarded variants would abound, in open traditions. The first chapter (about 160 words) of Cyprian's

De Unitate yields, for the eighteen manuscripts abBDeGhHJkmOp-PRTWY, the following five splits, among others:[32]

1. DHJkP: rell. (induimur)
2. bhHmpRT: rell. (subruendis)
3. GhHJmpRT: rell. (grassatur)
4. DhJmT:GY: rell. (crudelitate)
5. aJHT: rell. (conatus)

Of these five, no stemma could accommodate more than one. Generally, no stemma can provide an evaluative policy in a seriously contaminated tradition. V.A. Dearing's application of stemmata to evaluation require the discarded variants to be "treated as something different from what they really are" (see n. 29, pp. 87 ff.). The present writer has elsewhere criticised in detail the logic of Dearing's approach to history and evaluation. A model tradition, representing in miniature two parallel families that influence each other (fig. 10a), supplied a test: Dearing's procedures yielded a quite different tree (fig. 10b) and led to the wrong choice of reading in 44% of passages.[33] Dearing replies that a test problem which

contradicts his method involves different assumptions on textual transmission, and that a tradition which violates his own assumptions is not "likely to occur in real life";[34] but real life seems more varied than Dearing allows. He further objects that, in any case, "hypothetical cases are always hypothetical"—rather as if the manufacturer of a drug which in experiments on rats proved fatal protested that rats were merely rats.