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.
