The synoptic problem and the triplelink model

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The synoptic problem and the triple-link model

• Hypotheses about the relationships among the
  synoptic gospels

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The synoptic gospels

• Matthew (Mt), Mark (Mk) and Luke (Lk)
• Written in the second half of the first century
  (in Greek)
• From oral and/or written sources
• Originally written on scrolls
• The earliest surviving manuscripts from the third
  and fourth centuries are in codex form

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The Codex Sinaiticus
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Pericopes (sections)

• Triple tradition
• Double tradition (mainly Mt and Lk, e.g., Sermon
  on the Mount material)
• Single tradition (e.g., birth and infancy
  narratives of Mt and Lk)
• Variations in the order of pericopes

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The texts of the pericopes vary from gospel to
gospel

• Published synopses gospels laid out in parallel
  columns for comparison of pericope texts
• Note that there are variations in the text among
  the manuscripts and from one modern edition to
  the next of the New Testament in Greek

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The synoptic problem

• How do we account for the complex patterns of
  agreement and disagreement between the synoptic
  gospels?
• The Griesbach hypothesis?
• The two-source hypothesis (Q)?
• The Farrer theory?
• Other theories?

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The Augustinian hypothesis(so-called)
Mt
Lk
Mk
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Johann Jakob Griesbach(1745-1812)

• 1774-45 Critical edition of the New Testament
• 1776 Greek Gospel Synopsis of Matthew, Mark and
  Luke
• 1789-90 Dissertation the gospel of Mark has
  been extracted from Matthew and Luke

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The Griesbach hypothesis
Mt
Mk
Lk
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The two-source hypothesis
Q is the hypothetical source that accounts for
the large quantity of Mt-Lk double tradition
material that is absent from Mk.
Mt
Q
Lk
Mk
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The Farrer theory
Mk
Lk
Mt
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Counting verbal agreements

• The numbers of common occurrences in the same
  section of material of the same Greek word in the
  same grammatical form
• Data from Honoré (1968),Tyson and Longstaff
  (1978)
• Data aggregated over all the triple tradition and
  double tradition pericopes

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Counts of verbal agreements, aggregated over
triple and double tradition
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The triple-link model (Honoré)
A
C
z
x
y
B
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(A, B, C) any permutation of (Mt, Mk, Lk).
x the probability that a given word in Gospel A
is transmitted unaltered to Gospel B.
y the probability that a given word in Gospel B
is transmitted unaltered to Gospel C.
z the probability that a given word in Gospel A
is transmitted unaltered directly to Gospel C.
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A the event that a given word is in Gospel A
B the event that a given word is in Gospel B
C the event that a given word is in Gospel C
C1 the event that a given word is in Gospel C and
has been transmitted via Gospel B
C2 the event that a given word is in Gospel C and
has been transmitted directly from Gospel A
A the event that a given word is in Gospel A
According to the triple-link model, any word that
Gospel C has in common with either Gospel A or
Gospel B has been transmitted to Gospel C from
either Gospel A or Gospel B.
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x Pr(BA)
y Pr(C1B)
z Pr(C2A)
x is evaluated directly as a relative frequency,
the ratio of the number of words that are in both
Gospel A and Gospel B to the number of words that
are in Gospel A.
(Other conditional probabilities involving A, B
and C may be evaluated in a similar way.)
Additional assumptions have to be made in order
to evaluate y and z.
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Honorés three conditional independence
assumptions

• Given that a word is in Gospel A, the event that
  it is transmitted to Gospel B and the event that
  it is transmitted directly from Gospel A to
  Gospel C are independent.
• Given that a word is in Gospel B, the event that
  it is in Gospel A and the event that it is
  transmitted from Gospel B to Gospel C are
  independent.
• Given that a word is in Gospel A and Gospel B,
  the event C1 that it is transmitted from Gospel B
  to Gospel C and the event C2 that it is
  transmitted directly from Gospel A to Gospel C
  are independent.

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Using Honorés conditional independence
assumptions, we obtain the following formulae,
which we use to evaluate z and then y.
Pr(B?CA)
z
Pr(BA)
Pr(CB) - z Pr(AB)
y
1 - z Pr(AB)
We find also the formulae that were given by
Honoré
Pr(B?CA) xy xz - xyz
Pr(CA) z xy - xyz
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An additional criterionfor consideration
x gt max(y,z)
Lk-Mk-Mt and Mk-Lk-Mt would be ruled out
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Honorés assumptions modified

• Given that a word is in Gospel A, the event that
  it is transmitted to Gospel B and the event that
  it is transmitted directly from Gospel A to
  Gospel C are independent.
• Given that a word is in Gospel B, the event that
  it is in Gospel A and the event that it is
  transmitted from Gospel B to Gospel C are
  independent.
• The event C1 that a word is transmitted from
  Gospel B to Gospel C and the event C2 that it is
  transmitted directly from Gospel A to Gospel C
  are mutually exclusive.

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Using the modified assumptions, we obtain the
followingformulae, which we use to evaluate z
and then y.
Pr(B?CA)
z
Pr(BA)
y Pr(CB) - z Pr(AB)
The formula for y is simpler than before.We find
also the following simpler formulae
Pr(B?CA) x(y z)
Pr(CA) xy z
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Macro or micro level?
Biblical scholars tend to study in detail the
text of individualpericopes in order to support
their favoured synoptic model.Should we attempt
to fit the triple-link model to
individualpericopes, especially those from the
triple tradition,(the micro level) and to
examine in detail how the model worksfor each
pericope?When we attempt to do so, it turns out
that there is greatvariation from pericope to
pericope in how well the model fitsand in which
permutation A-B-C give the best fit.
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The importance of oral tradition
Synoptic models tend to assume that the close
similarities between the gospels are to be
explained by the evangelists use of written
sources. In recent years there has been a
renewed focus on the role oforal performance in
the transmission of stories about Jesusand his
teaching, e.g., Dunn (2003), Bauckham
(2006).The gospel writers may have had the
texts of the earliergospels available to them,
but they would also have beenfamiliar with
traditions transmitted by oral performance.
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Indications of oral tradition
Should our models somehow explicitly take account
of therole of oral transmission? Where the
different versions of a pericope are very
similar to each other, word for word, this
suggests literary dependence. Where the
relationship is looser, this may suggest the use
of oral traditions.
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More nuanced ways of measuring agreement?
The counting of exact verbal agreements, counting
only words having exactly the same grammatical
form, is a simple, yet crude way of measuring
agreement between texts. We might consider
counting the same words even if they have a
different ending. We might consider counting
synonyms. We might take into account word order
or, more generally, in some way, the grammatical
and narrative structure of the text. (Tyson and
Longstaff give data on some aspects of this.)