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4. The inductive approach to evaluation

4.1. In an open tradition, the agreement patterns are too confused to illuminate directly the history and evaluation, but the principle of opposed pairs (§3.3) remains valid. To develop the argument we require what will be termed the bipolar assumption.

If we collate many manuscripts, we can identify a relatively small 'team' of manuscripts which together attest all the good readings anywhere preserved (§3.3). Let us now define the team differently as the smallest set of manuscripts never to exhibit a common error when the truth anywhere survives.[60] Team members may on that account be termed 'poles'. What determines the size of such a team? A team of one results, of course, if only one manuscript is collated or is the source of all the others. Any other uncontaminated tradition yields a team of two, or rather many alternative teams. Any pair independently derived from the archetype form a team, and every manuscript belongs to at least one team. Fig. 3a, for example, yields eight teams (AD, AE, BD, CE, . . .). On the original definition, multiple splits could extend the team: in fig. 3a, if in one place xz erred separately, in another yz erred separately, and in a third w erred, we should need a team of three, namely (1) C or G, (2) A or B, and (3) D or E. With the modified definition all eight teams stand, and team size depends not on scribal behaviour but on genealogy alone.[61]

A group of manuscripts can suffer some contamination but still have just two poles. If one manuscript (γ in fig. 14a) adopts good readings from a lost extrastemmatic source (§2.1), then any original team (i.e. a team that would have been valid had no contamination occurred) not containing that manuscript or a descendant thereof is eliminated. In fig. 14a, only the teams AC and AD would survive. Two lines of extrastemmatic contamination, however, might eliminate all the original teams

(e.g. if the lines led to B and γ), and result in a team of three. As for intrastemmatic contamination, if one member of an original team (or an ancestor thereof) transfers error to the other member (or an ancestor thereof) the team is invalidated; but as long as one team stands (AC in fig. 14b) the tradition remains bipolar.

Consider a team of three members ABC. Each is on occasion correct against the agreement of the other two. There are many possible pedigrees, all rather complex, which could bring this about. In fig. 15a, each

pair shares a source and thence errors, but the only source common to all three manuscripts is the original. In fig. 15b, some of B's errors mar BC but not A (thanks to a), some of C's reach A but arose after B, some of α's reach AB but not C (thanks to β). In fig. 15c, B consulted λ in some passages where ω was corrupt, C consulted λ in other such passages, and A is sound where BC bear β's errors. Teams of four or more betoken even more complicated genealogies. If such intricacy seems far-fetched, one need only recall that in the Aeschylean triad the question is whether the team numbers eleven or twenty.[62]

Evidently not every tradition is bipolar. Moreover, even if the set of all manuscripts collated is bipolar, not every sub-group is necessarily so: for example, the group ωλβABC (all for a moment supposed extant) in fig. 15c is bipolar, but the sub-group ABC is not. Nevertheless, the assumption that manuscript groups are bipolar is far less restrictive than that of total absence of contamination.

4.2. The method here proposed begins with a list of the determinate two-way splits. Hence the errors in every manuscript and the errors common to every manuscript pair are counted. Multiple splits are excluded from the list, since manuscripts which elsewhere err together may there err separately and cause anomalies, as in fig. 16. Suppose that β and D

each erred, so that BC show one error and D another; it would be misleading to ascribe one common error to BC and none to BD or CD and thereby suggest an exclusive relationship between BC.[63] In any case multiple splits are rare, if each independent point of variation, however great or small, is separated. Thus the readings to you I tell: to you I say: I say to you entail two variations: word order and tell/say. Similarly composed: composing: reposing comprises two variations: comp-/rep- and -ed/-ing. The readings amorous AB: loving CD: lufand EF yield two variations: (1) amorous/[loving] AB:CDEF, and (2) loving/lufand CD:EF (with AB unavailable). Some multiple splits (e.g. say:tell:sing) are, however, irresoluble.[64] The criterion of independence is usually easy to apply; for example, see and hear: hear and see yield not two independent variations, but one. (Contrast Dearing, see n. 29, p. 32.)

An error unique to any manuscript cannot affect the totals of shared errors, and as for the error total for that manuscript, all that matters (cf. §4.3) is whether unique errors occur or not. Unique errors can (rather than must) therefore be excluded, though their carriers should be noted. Unique preservation of the original reading, however, does affect the error totals, and any variant for which this possibility exists must remain.

Probable cases of coincidence in error or successful conjecture should be excluded, since the figures are intended for extrapolation to indeterminate passages, where such non-genealogical causes of common error are not especially liable to generate the same agreement patterns.

4.3. We obtain, then, a table of error totals. Each total can now be expressed as a percentage of the number of determinate passages. This yields the average number of errors observed per hundred variant passages. (The problem of missing readings is ignored for the moment.) It is now assumed that, over the indeterminate variants too, every manuscript or pair of manuscripts yields a similar percentage of errors. This assumption turns on the number and accuracy of our determinate variants, and ultimately on our critical judgment; compare assumption (vi) in §1.1.

At any indeterminate variant passage, the manuscripts divide into two or more groups. Even if such a group contains more than two manuscripts, its error percentage can still be defined as the average number of errors common to the group over a field of one hundred variants. The obvious course is, as before, to express the number of common errors detected in the group as a percentage of the total of determinate passages; but the results, at least for larger groups, may be unhelpful. In a tradition where scribes constantly compared sources in order to improve the text, readings that penetrated a good proportion of the extant tradition and yet can be confidently identified today as errors are rare. If (say) eight manuscripts agreed against ten in an indeterminate passage, it is all too likely that we could identify no instance of all the eight agreeing in error, nor of all the ten, and comparison of the two error percentages would be fruitless.

The error percentage for a larger group is instead estimated through the bipolar assumption. Of all the pairs that can be formed from the group, let the pair PQ (say) show the smallest error percentage. The error percentage for the entire group cannot be greater; PQ plus others cannot agree in error more often than PQ alone. Can the error percentage be smaller for the group than for PQ? Let us suppose the group bipolar. PQ are then poles: wherever PQ err together, the truth survives

nowhere in the group, which either shares PQ's error or is divided between two or more separate errors. The latter event being exceptional, most of PQ's shared errors will be common to the entire group, whose error percentage will approach that of PQ, the pair yielding the lowest percentage.

For a group comprising just one manuscript, the error percentage will have been tabulated; if the manuscript bears unique errors, one will note that the true figure is higher.

If the error percentage for the group attesting one variant reading is zero, that reading will prevail—unless a rival also shows zero, implying that our determinate variants formed an inadequate sample. If the error percentage for one group is low, and that for the rival group is far higher, say by a factor of four or more, that factor will indicate the odds in favour of the first reading, which of course prevails.[65] If there is no overwhelming imbalance between the error percentages, however, no decision is possible, as either group might well have erred.[66]

As the error percentages for groups depend on those for pairs, this procedure comes back to the principle of opposed pairs: a reading attested by a pair never caught agreeing in error prevails over a reading not attested by any such pair. The replacement of 'never' by 'relatively seldom' adds a probabilistic version of that principle.

4.4. Let us examine further the logical role of the bipolar assumption. Two different lists of variants, requiring two different critical policies, could yield the same array of error totals (and percentages). Suppose that among ABC the error totals are two for each individual and one for each pair. This would result not only (i) if each manuscript erred once alone and all three erred once together, but also (ii) if AB erred once against C, AC erred once against B, and BC erred once against A.[67] These possibilities lead to different genealogies (the former to fig. 17, the latter to such genealogies as fig. 15abc) and imply respectively that readings common to ABC might, or cannot, be errors. The bipolar assumption, reasoning

from constituent pairs to parent group, chooses whichever possibility posits the least contamination—here, the former.

The consequences if the assumption fails appear from fig. 18. Thirty-two determinate passages (excluding unique readings) reveal eight common errors in AB, ten in AC, twelve in BC and two in DE. These were inherited from the lost manuscripts λ, μ, ν and ξ respectively, unbeknown to the investigator. The bipolar assumption, however, would impute

eight common errors to ABC, and admit the genealogy of fig. 18b. Consider now a split ABC:DE. The smallest error percentage amongst ABC is 25%, yielded by AB (100% x 8/32), while DE show 61/4% (100% x 2/32). Our investigator would find odds of 4:1 (=25:61/4) in favour of DE's reading. In fact, however, the agreements of ABC must reproduce Ω, and the split ABC:DE indicates an error in DE.

4.5. To adjust for missing readings, the error total for any manuscript (or pair) should be expressed as a percentage not of the total of determinate passages, but of the number of determinate passages where the manuscript(s) is (are) available. Should this new denominator appear inadequate, the percentage must be treated cautiously or even discounted. Otherwise we might come to follow the agreement of a certain pair of manuscripts on the ground that they have never been caught in error

together, when in fact there was little opportunity of catching them, either because they hardly overlapped or because the critic lacked the knowledge to recognise many errors. The adequacy of any particular denominator can only be assessed by someone expert in the tradition.

With this revised definition, the error percentages can be tabulated and utilised as above to assess the credibility of the manuscript groups attesting the rival readings. The use of these procedures is illustrated in §6.