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Re: [Synoptic-L] Kloppenborg on the MAs (was Re: Incontovertible evidence?)

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  • Zeba Crook
    ... This is an interesting question, and one which ultimately shows the subjectiveness of our respective responses to the data -- how serious an anomaly are
    Message 1 of 8 , Jul 8, 2001
      Mark Goodacre wrote:

      > Kloppenborg is right that one often has to deal with anomalies
      > when working with hypotheses. I suppose the question ultimately
      > becomes one of the scope of the anomalies under discussion. In
      > the case of the 2ST, I remain concerned about the scope of the
      > Minor Agreements as anomalies, over against the lack of (in my
      > opinion!) any anomalies on the Farrer theory.

      This is an interesting question, and one which ultimately shows the
      subjectiveness of our respective responses to the data -- how serious an
      anomaly are the MAs? Farmer (and others no doubt) objected to the
      atomisation of the data, that is the breaking up the MAs into different and
      smaller groups, because this lessened the impact of their sheer number.
      Personally, however, I think it only makes sense to do this. So many of the
      MAs are completely inconsequential. Take for instance, in the Baptism of
      Jesus, Mt and Lk changing Mk's EIS of the dove to EPI. Mk's EIS simply does
      not make sense (though I'm sure the defenders of Mark's artistry will rush
      to his defense). It is not in the slightest alarming that Mt and Lk would
      independently cringe at the image of such a collision. It is only right
      that we remove from the MAs list such agreements which can be so easily
      accounted for.

      Now I totally agree that this will leave a number of MAs which are quite
      serious and difficult to account for (i.e., "Who struck you?" and I think
      maybe there are 6-7 others?), but these are far fewer in number than all of
      them put together.

      Zeb

      ***

      Zeba Antonin Crook (Ph.D. Cand)
      University of St. Michael's College
      Faculty of Theology
      81 St. Mary Street
      Toronto, Ontario, Canada
      M5S 1J4

      (416) 964-8629
      http://www.chass.utoronto.ca/~zcrook/



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    • Zeba Crook
      ... Now it s time for me to display my complete ignorance about probabilities and statistics, but it seems as unfair to me that you require the MAs to become
      Message 2 of 8 , Jul 9, 2001
        David Gentile wrote:

        > According to the laws of probability, the odds of all 10 being corrected the
        > same way, are now:
        > .9*.9*.9*.9*.9*.9*.9*.9*.9*.9 = .349. Thus even 10 examples of independent,
        > easy to explain MAs would still make complete independent use of Mark more
        > unlikely than not. Now given that there are very many MAs and many are far
        > less likely than 90% probable, I reach the conclusion that complete
        > independent use of Mark by Luke and Matthew is astronomically unlikely.
        >

        Now it's time for me to display my complete ignorance about probabilities and
        statistics, but it seems as unfair to me that you require the MAs to become
        successively and exponentially more unlikely as the divide and conquer approach
        seems to you. Intuitively it strikes me as erroneous to say that Mt and Lk are
        exponentially less likely to have made 10 identical corrections that they are to
        have made one. How do we measure this? We are dealing with humans and
        literature, which are not as random and consistent as flipping coins or rolling
        a dice. I'm saying you were making this analogy, but I have to think, how many
        options were there for Mt and Lk to fix Mk's EIS of the dove? If there were no
        or very very few other options, then the fact that Mt and Lk agree independently
        is not as noteworthy as it is in other lengthier cases. I guess the question
        is, when we are dealing with creative minds, social and literary influences
        (like the LXX, for example), personal style and taste, etc etc, how do we
        measure probabilities like this in a meaningful way?

        Zeb

        ***

        Zeba Antonin Crook (Ph.D. Cand)
        University of St. Michael's College
        Faculty of Theology
        81 St. Mary Street
        Toronto, Ontario, Canada
        M5S 1J4

        (416) 964-8629
        http://www.chass.utoronto.ca/~zcrook/



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      • Michael Grondin
        ... D. Gentile specifies 10 *independent* corrections, which I read as meaning 10 corrections of different words. This would rule out them being *identical*.
        Message 3 of 8 , Jul 9, 2001
          Zeba Crook wrote:
          >Intuitively it strikes me as erroneous to say that Mt and Lk are
          >exponentially less likely to have made 10 identical corrections
          >tha[n] they are to have made one.

          D. Gentile specifies 10 *independent* corrections, which I read as meaning
          10 corrections of different words. This would rule out them being
          *identical*. But there is a flaw in Gentile's algorithm. It considers only
          MA's, and not any cases wherein Mt and Lk both apparently correct Mk, but
          in different ways. If there was one of those to every nine where they
          correct Mk in the same way, then the stipulated individual probability of
          90% would be maintained for the entire set of ten, because the one would
          "take up the exponential slack" of the nine, so to speak.

          Mike Grondin

          The Coptic Gospel of Thomas, saying-by-saying
          http://www.geocities.com/mwgrondin/sayings.htm

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        • Michael Grondin
          Zeba- I see now that I misunderstood what you meant by identical corrections . In any case, your intuitions are sound. The reason why Dave is led to the
          Message 4 of 8 , Jul 9, 2001
            Zeba-

            I see now that I misunderstood what you meant by "identical corrections".
            In any case, your intuitions are sound. The reason why Dave is led to the
            erroneous conclusion that "complete independent use of Mark by Luke and
            Matthew is astronomically unlikely" is that the selection of data for his
            algorithm (as well as the algorithm itself) *makes it so*. And the reason
            it makes it so, is that, by concentrating exclusively on the MA's, it
            includes *no* cases of divergent correction, hence the product of the
            probability of coincident corrections (i.e., cases where Mk and Lk correct
            Mt in the same way) inevitably approaches zero. In other words, what's
            going on is that data which would go to prove independence are being
            unwittingly excluded in advance. No wonder, then, that the methodologically
            predetermined conclusion of this statistical argument is "no independence"!
            Which is not to say that the conclusion is false - only that one can't get
            to it that way.

            If a simple multiplication of probabilities won't do it, what might a sound
            algorithm look like? For starters, let n = the number of cases wherein
            either Mt or Lk correct a grammatical error in Mk. Then let m = the number
            of coincident (i.e., "identical") corrections between Mt and Lk. The degree
            of coincidence between Mt and Lk (with respect to correcting Mk) would then
            be m/n. (Ex: if Mt and Lk agree on 9 out of 10 corrections to Mt, but
            correct the 10th in a different way, then m/n = 90%). This degree of
            coincidence (DC) would then be compared with a "control figure" (CF; say,
            90%) which would represent the expected results given *any* two independent
            corrections of Mk. If DC turns out to be significantly less than or greater
            than CF, then probabilistic conclusions could be drawn - altho I'm not
            entirely sure what those would be, given the number of alternative
            scenarios we're working with. (It might also be noted that, even without
            examining the data, the likelihood that DC would be significantly higher
            than a CF of 90% is slim - whatever one wants to make of that.)

            Mike


            The Coptic Gospel of Thomas, saying-by-saying
            http://www.geocities.com/mwgrondin/sayings.htm

            Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
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          • David Gentile
            Mike, You are indeed correct that the number of times they make changes, but don t agree must be considered. A similar statistical oversight lead to the
            Message 5 of 8 , Jul 9, 2001
              Mike,
              You are indeed correct that the number of times they make changes, but
              don't agree must be considered. A similar statistical oversight lead to the
              space-shuttle explosion. NASA looked only at the temperature at launch on
              days with previous o-ring problems. No significant pattern was found. Had
              they looked at all launches, the fact that cold days caused o-ring problems
              would have be obvious.

              My argument was specifically directed against throwing out some of the data.

              To address your point. Let's say we estimate, on average, that the authors
              would have a 10% chance of making the same change, each time they make a
              change, and that in reality we find they make the same change 30% of the
              time. Lets say we have 1000 opportunities for MAs.
              What do the probabilities look like now?
              It turns out that if the real chances are about 30/70 that there would be
              about a 2.7% chance of exactly 300 MAs in our specific case, a slightly less
              chance of exactly 299 or 301, etc. So we would expect something close to 300
              MAs.

              But if the probability was really 10/90, then the chance of 300 MAs in 1000
              changes is about 10 to the power of 68 to 1 against.

              So with the many MAs/opportunities the percentage expected and found
              would have to be in fairly close agreement for independence to be
              reasonable.

              In many of the MAs it seems quite a bit more unlikely than likely that the
              exact same word would be chosen, so I would still maintain that complete
              independence is extremely unlikely. At the very least, one would need to
              appeal to a strong well maintained oral tradition for the agreements, I
              think.
              But even that seems unsatisfactory to me.

              I've previously argued on this list that just by examining the apparent
              doublets in Mark, and nothing else, and seeing which ones appear in Mt and
              Lk/ (2 in both, 2 in Lk/1 in Mt, 2 in Lk/none in Mt, etc.) it is possible to
              rule out Mt and Lk independently using Mk with 98% confidence.

              One specific oddity, is that when Mt keeps both halves from Mk, Lk keeps
              none, far less that would be expected, based on Lk behavior when Matthew has
              only 1, or neither.

              The inference I make from that is that Matthew had 2 sources for triple
              tradition, and so did Luke, and only 1 was shared, and the shared one was
              not Mark.
              (a very long jump if I were basing the idea only on that evidence)

              This is a good test of independence since the bits are from all over Mark.
              This test by itself could be faulted, but when considered as part of the
              wider picture of
              MAs it adds up to non-independence.

              Thanks,

              Dave Gentile
              Riverside, Illinois
              847-286-3624

              -------------------------------------------------------------------------
              "When you have eliminated the impossible,
              whatever remains, however improbable, must be the truth."
              - Sherlock Holmes,
              in The Sign of Four, by Sir Arthur Conan Doyle.

              "Why sometimes I've believed as many as
              six impossible things before breakfast."
              - The Red Queen,
              in Through the Looking Glass, by Lewis Carroll


              > Zeba-
              >
              > I see now that I misunderstood what you meant by "identical corrections".
              > In any case, your intuitions are sound. The reason why Dave is led to the
              > erroneous conclusion that "complete independent use of Mark by Luke and
              > Matthew is astronomically unlikely" is that the selection of data for his
              > algorithm (as well as the algorithm itself) *makes it so*. And the reason
              > it makes it so, is that, by concentrating exclusively on the MA's, it
              > includes *no* cases of divergent correction, hence the product of the
              > probability of coincident corrections (i.e., cases where Mk and Lk correct
              > Mt in the same way) inevitably approaches zero. In other words, what's
              > going on is that data which would go to prove independence are being
              > unwittingly excluded in advance. No wonder, then, that the
              methodologically
              > predetermined conclusion of this statistical argument is "no
              independence"!
              > Which is not to say that the conclusion is false - only that one can't get
              > to it that way.
              >
              > If a simple multiplication of probabilities won't do it, what might a
              sound
              > algorithm look like? For starters, let n = the number of cases wherein
              > either Mt or Lk correct a grammatical error in Mk. Then let m = the number
              > of coincident (i.e., "identical") corrections between Mt and Lk. The
              degree
              > of coincidence between Mt and Lk (with respect to correcting Mk) would
              then
              > be m/n. (Ex: if Mt and Lk agree on 9 out of 10 corrections to Mt, but
              > correct the 10th in a different way, then m/n = 90%). This degree of
              > coincidence (DC) would then be compared with a "control figure" (CF; say,
              > 90%) which would represent the expected results given *any* two
              independent
              > corrections of Mk. If DC turns out to be significantly less than or
              greater
              > than CF, then probabilistic conclusions could be drawn - altho I'm not
              > entirely sure what those would be, given the number of alternative
              > scenarios we're working with. (It might also be noted that, even without
              > examining the data, the likelihood that DC would be significantly higher
              > than a CF of 90% is slim - whatever one wants to make of that.)
              >
              > Mike
              >
              >
              > The Coptic Gospel of Thomas, saying-by-saying
              > http://www.geocities.com/mwgrondin/sayings.htm
              >
              > Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
              > List Owner: Synoptic-L-Owner@...



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            • David Gentile
              One additional thing I forgot to mention. Yes, the MAs themselves must be looked at, and, yes, the changes that are not MAs must be looked at. But, in addition
              Message 6 of 8 , Jul 9, 2001
                One additional thing I forgot to mention.
                Yes, the MAs themselves must be looked at, and, yes, the changes that are
                not MAs must be looked at.
                But, in addition the places where no changes at all have been made must be
                considered too.
                In other words, given the number of changes Lk makes, and the number Mt
                makes, what is the chance that they would change the same thing must be
                considered first, then the chance that they would choose the same change.

                Thanks,

                Dave Gentile
                Riverside, IL
                847-286-3624

                -------------------------------------------------------------------------
                "When you have eliminated the impossible,
                whatever remains, however improbable, must be the truth."
                - Sherlock Holmes,
                in The Sign of Four, by Sir Arthur Conan Doyle.

                "Why sometimes I've believed as many as
                six impossible things before breakfast."
                - The Red Queen,
                in Through the Looking Glass, by Lewis Carroll

                >
                >


                Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
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              • Michael Grondin
                Dave- I m a little confused by your response to me, particularly when taken ... Unless I misunderstood your response to me, you would no longer wish to
                Message 7 of 8 , Jul 9, 2001
                  Dave-

                  I'm a little confused by your response to me, particularly when taken
                  together with what you wrote to Zeba about an hour earlier, in part:

                  > [If] the events are independent [then] the formula I used is correct.

                  Unless I misunderstood your response to me, you would no longer wish to
                  maintain this, i.e., that your original formula (which involved the simple
                  multiplication of probabilities) was appropriate to the use to which it was
                  put. In the absence of further clarification, I'm going to assume that,
                  anyway - as well as that my own suggested formula is consistent with your
                  current thinking on the matter.

                  Regards,
                  Mike

                  The Coptic Gospel of Thomas, saying-by-saying
                  http://www.geocities.com/mwgrondin/sayings.htm

                  Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
                  List Owner: Synoptic-L-Owner@...
                • Mark Goodacre
                  ... Yes, Farrer also complained about the atomisation approach. I think one of my own concerns, which I tried to articulate in response to Tuckett in my
                  Message 8 of 8 , Jul 19, 2001
                    I wrote:

                    > > Kloppenborg is right that one often has to deal with anomalies
                    > > when working with hypotheses. I suppose the question ultimately
                    > > becomes one of the scope of the anomalies under discussion. In the
                    > > case of the 2ST, I remain concerned about the scope of the Minor
                    > > Agreements as anomalies, over against the lack of (in my opinion!)
                    > > any anomalies on the Farrer theory.

                    On 8 Jul 2001, at 23:15, Zeba Crook wrote:

                    > This is an interesting question, and one which ultimately shows the
                    > subjectiveness of our respective responses to the data -- how serious
                    > an anomaly are the MAs? Farmer (and others no doubt) objected to the
                    > atomisation of the data, that is the breaking up the MAs into
                    > different and smaller groups, because this lessened the impact of
                    > their sheer number. Personally, however, I think it only makes sense
                    > to do this. So many of the MAs are completely inconsequential.

                    Yes, Farrer also complained about the atomisation approach. I
                    think one of my own concerns, which I tried to articulate in
                    response to Tuckett in my "Fallacies" piece, is not so much the
                    atomisation *within* the category of MAs as the distinction
                    between so called Minor Agreements and so called Mark-Q
                    overlaps. In fact "Mark-Q overlap" is, one might say, just another
                    way of saying "major agreement", a way of categorising the data
                    that effectively detracts attention from the existence of a
                    continuum, from triple trad. with MAs to Mark-Q overlap to double-
                    tradition.

                    > Take
                    > for instance, in the Baptism of Jesus, Mt and Lk changing Mk's EIS of
                    > the dove to EPI. Mk's EIS simply does not make sense (though I'm sure
                    > the defenders of Mark's artistry will rush to his defense). It is not
                    > in the slightest alarming that Mt and Lk would independently cringe at
                    > the image of such a collision. It is only right that we remove from
                    > the MAs list such agreements which can be so easily accounted for.

                    I'm not sure if it's quite so easy to dispense with as you propose.
                    Of course if Matt. and Luke were writing independently of one
                    another, this is possible, perhaps even plausible; but it's not water-
                    tight. Codex Bezae has EIS for Luke here, so at least one scribe
                    didn't think it absurd to maintain the Marcan wording. Evang.
                    Ebion. has EIS too (Goulder argues for Christological reasons). My
                    point would be that even if it's, say, 90% likely that Luke might
                    independently have changed EIS to EPI, an accumulation of these
                    and more impressive cases would become troubling. I think that
                    this is Goulder's and Gundry's point using the example of Luke
                    9.22 -- the cumulative factor of clusters of MAs.

                    > Now I totally agree that this will leave a number of MAs which are
                    > quite serious and difficult to account for (i.e., "Who struck you?"
                    > and I think maybe there are 6-7 others?), but these are far fewer in
                    > number than all of them put together.

                    I think that there are probably at least 6-7 that the independent
                    redaction theory has really major difficulties with. Mark 14.65 is
                    indeed the most notorious because of the conjectural emendation
                    argument. But I wonder whether the very isolation of just a small
                    "rump" of difficult MAs by people like Goulder has in the end
                    played into Two-Source Theorists' hands. It generates the
                    impression that we are only talking about a handful of anomalies for
                    the 2ST and not a broader spectrum of evidence, in which the
                    "rump" of MAs are just the tip of the iceberg.

                    Thanks for the thoughtful post and apologies for the delayed
                    response.

                    Mark
                    -----------------------------
                    Dr Mark Goodacre mailto:M.S.Goodacre@...
                    Dept of Theology tel: +44 121 414 7512
                    University of Birmingham fax: +44 121 414 6866
                    Birmingham B15 2TT
                    United Kingdom

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