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Re: Request: help with Colwell's quantitative analysis

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  • Robert B. Waltz
    ... Let s start with the rates of agreement. I m going to refer to Table I (page 60 in Colwell s book) and give the data for B as Colwell gives it: 75 TR 61
    Message 1 of 18 , May 1, 1997
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      On Thu, 1 May 1997, "Perry L. Stepp" <plstepp@...> wrote:

      >Help!
      >
      >I'm looking at Colwell and Tune's article on quantitative analysis ("Method
      >in Establishing Quantitative Relationships between Text-Types of New
      >Testament Manuscripts," 56ff in Colwell, *Studies in Methodology in Textual
      >Criticism of the New Testament*). It occured to me, as I read the article,
      >that I'm not totally clear on part of the method. I thought I understood
      >it, but now I'm wondering.
      >
      >Colwell says: "the quantitative definition of a text-type is a group of
      >manuscripts that agree more than 70 per cent of the time and is separated
      >by a gap of about 10 per cent from its neighbors" (59). I'm fine with the
      >70 percent agreement, but I'm not sure how to discern the 10 percent gap.
      >Looking at the percentages, how does one use the 10 percent gap to
      >delineate one group from another? What am I missing?
      >
      >If anyone out there has a copy of Colwell's *Studies* and is willing to
      >explain the 10 percent gap (preferably via reference to Colwell's charts),
      >I'd *really* appreciate it.

      Let's start with the rates of agreement. I'm going to refer to Table I
      (page 60 in Colwell's book) and give the data for B as Colwell gives it:

      75 TR
      61 p45
      69 p66
      73 p66**
      92 p75
      79 Aleph
      83 Aleph**
      73 A
      73 A**
      53 D
      77 W
      78 W**
      65 Theta
      81 Psi
      74 Omega
      67 Cr
      71 565

      Now let's sort that in ascending order of agreement:

      53 D
      61 p45
      65 Theta
      67 Cr
      69 p66
      71 565
      73 A
      73 A**
      73 p66**
      74 Omega
      75 TR
      77 W
      78 W**
      79 Aleph
      81 Psi
      83 Aleph**
      92 p75

      Now I'm going to add in the separations -- that is, the distance between
      the percentage agreement between the current manuscript and the next one
      in the list

      53 D 8
      61 p45 4
      65 Theta 2
      67 Cr 2
      69 p66 2
      71 565 2
      73 A 0
      73 A** 0
      73 p66** 1
      74 Omega 1
      75 TR 2
      77 W 1
      78 W** 1
      79 Aleph 2
      81 Psi 2
      83 Aleph** 9
      92 p75 -

      Looking at these separations, there largest of these is 9 (between
      Aleph** and p75). If that were 10%, instead of 9%, it would be a
      10% gap and meet Colwell's definition. If we ignore Aleph**, though,
      as a text that may never have existed, we get a separation of 11 points
      (*not* percentage points) between p75 and Psi, so that at least
      would would constitute a gap. (Does this mean that p75 and B form
      a text-type all on their own? Well, not exactly.)

      That's what Colwell and Tune mean by the "gap." Now for the flies
      in the ointment. (This is where I reveal the truth about the defects
      in Colwell and Tune, so all you people who think I can't get anything
      right can go back to sleep now. We're going to do some mathematical
      thinking here.)

      I'm quoting my web page, from the Text-Types article, section
      "Definition of a Text-type":

      It was not until the mid-Twentieth century that E.C. Colwell offered the first
      balanced definition of a text-type.[*1] In one essay he gave a qualitative
      definition ("A Text-type is the largest group of sources which can be
      generally identified").[2] He adds the important qualification, "This
      definition is a definition of a text-type as a *group of manuscripts*
      [emphasis mine], not... a list of readings." Five years later, in an
      influential essay, Colwell went further. He attempted a quantitative
      definition. (Indeed, his method is frequently called the "quantitative method"
      -- a name that makes me cringe, since any statistical method is a
      "quantitative method.") His statement on the subject is perhaps the most-
      quoted statement on genealogy since Hort's time:

      "This suggest that the quantitative definition of a text-type is a group of
      manuscripts that agree more than 70 per cent of the time and is separated by a
      gap of about ten percent from its neighbors."[3]

      Colwell deserves immense credit for offering this definition (as well as for
      his other methodological studies; he is perhaps the greatest worker in this
      field in the twentieth century). This definition has the advantages of being
      clear, precise, and usable. Unfortunately, in the author's experience, it does
      not work. (It strikes me as almost tragic that Colwell's most-frequently-cited
      comment on text-types is also one of the few that is not entirely correct.
      It's worth noting that he rarely if ever refers back to this criterion.)

      There are two reasons for this. First, the percentage of agreements between
      manuscripts is entirely dependent on the sample. Second, the "gap" which
      Colwell refers to disappears when working with mixed manuscripts. Let us offer
      examples.[*4]

      To take the first point first, consider the relationship between B/03 and
      Aleph/01 in chapter 2 of Colossians. The two manuscripts agree in only two of
      the seven variations cited in GNT4, or 29%. If we take the 29 variants cited
      in NA27 (excluding conjectures), we find that they agree in 18 of 29, or 62%.
      If we turn to the Munster Institute's New Testament "Auf Papyrus," and examine
      the variants supported by two or more uncials (excluding orthographic
      variants), we find that the two agree in 32 of 47, or 68%. But if we turn to
      the editia minor of Tischendorf8, we find agreement in 19 of 32 non-
      orthographic variants, or 59%. Even if we throw out the small GNT sample, we
      still have almost a ten percent variation between the three remaining sample
      sets, all of which form large and reasonable bases for comparison. Which one
      should we use in deciding whether B and Aleph belong to the same text-type?
      The 68% number, which places them on the fringe of qualifying? The 59% number,
      which isn't even close? Or something else?

      All told, Aleph and B have 25 disagreements in this chapter (though some are
      scribal errors, usually in Aleph). How do we decide how many variants to
      spread these 25 differences out over to determine if there is 70% agreement?

      A thought-experiment about mixed minuscules should be sufficient to
      demonstrate the non-existence of the "gap." Suppose X is an unmixed
      manuscript, Y is copied from X with five percent Byzantine admixture, Z is
      copied from Y with another 5% admixture, and so on. It follows that X can
      never have a ten percent gap; that space is occupied by Y, Z, and so on down
      the line. If that is not proof enough, one can present a concrete example
      based on B in the Gospels. Using a large (990 reading) sample and 39 Greek
      manuscripts, I found two documents (2427 and p75) which, in their particular
      areas, agreed with B over 80% of the time. Below this was a gap -- but most
      manuscripts that are considered to belong with B (including Aleph, L, 33, and
      892) are on the far side of the gap![*5] The next-closest manuscript was
      Xi/040 in Luke, at 68%. From there down to the final manuscript in the list
      (D/05, with 30% overall agreement), there was no gap larger than eight
      percentage points (and even this gap would have been filled had I included the
      Coptic versions).

      The median gap among non-Byzantine manuscripts was one, and even the
      arithmetic mean ("average") was under two. Colwell's "gaps" will simply not
      exist in large manuscript samples.

      There is also a problem with the conceptual model of the Colwell system. Take
      a manuscript like L/019 of the gospels. It has a significant Byzantine
      component -- large enough that it will likely fail Colwell's 70% criterion.
      But -- where it is non-Byzantine -- it stands very close to B/03, and is one
      of the closest allies of that manuscript. Should we not be able to recognize L
      as a degenerate relative of B, and use it on that basis?

      Some would propose to address the problem by adjusting the numbers. This may
      work in some cases, but cannot be guaranteed; any statistic will be dependent
      on its sample. It is possible that we could assign percentages if we could
      produce a "representative" list of variants -- but what is a "representative"
      variant reading?

      **** Footnotes: ****

      1. Indeed, Colwell was one of the first to plead exclusively for the use of
      the word "text-type" in this context. See Colwell, Studies in Methodology, p.
      9.

      2. Ibid.

      3. Ernest C. Colwell and Ernest W. Tune, "Method in Establishing Quantitative
      Relationships between Text-Types of New Testament Manuscripts," reprinted in
      Studies in Methodology, p. 59.

      4. Ironically, it was Colwell himself who first pointed out the defect in his
      method -- four years before he proposed his definition! In "Method in Locating
      a Newly-Discovered Manuscript" (Studies in Methodology, page 33), he wrote
      "Weak members of a Text-type may contain no more of the total content of a
      text-type than strong members of some other text-type may contain. The
      comparison in total agreements of one manuscript with another manuscript has
      little significance beyond that of confirmation, and then only if the
      agreement is large enough to be distinctive."

      5. If someone objects that comparisons across the gospel corpus are not valid,
      let me simply add that I examined individual books, and even sections of
      books, and the results were the same within the margin for error. At times the
      leading manuscripts (especially W) shifted slightly, but the general picture
      never did. So I present overal statistics because they are simpler.

      -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-

      Robert B. Waltz
      waltzmn@...

      Want more loudmouthed opinions about textual criticism?
      Try my web page: http://www.skypoint.com/~waltzmn
      (A site inspired by the Encyclopedia of NT Textual Criticism)
    • Professor L.W. Hurtado
      A few rjoinder notes to Waltz s piece on Colwell and quantitative approaches. 1) Waltz cites figures from *Table 1* on p. 60 of Colwell, _Methodology_, which
      Message 2 of 18 , May 2, 1997
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        A few rjoinder notes to Waltz's piece on Colwell and quantitative
        approaches.
        1) Waltz cites figures from *Table 1* on p. 60 of Colwell,
        _Methodology_, which includes *singular* readings, which are (as
        Colwell explains in the essay) not useful for identifying
        *relationships*. Thus, Table 2 on the same page refines the numbers
        by including only those variation units where the tested mss exhibit
        agreement of at least two of them. There the separation becomes
        clearer. This exclusion of singular readings is an important
        feature. By definition, singular readings don't attest
        relationships
        2) One ofthe ways Colwell's method has been refined subsequently (by
        e.g., Fee and yours truly) is to insist that identification of mss
        relationships cannot safely be done in samples (and in the essay from
        which the tables come and in which Colwell sketches the basics of his
        method, he cites figures for John 11, a sample only), and that we
        have to take measurements (a) across a whole NT writing, and (b)
        chapter by chapter. If we do this, we can detect "block-mixture"
        (as, e.g., Fee did in Aleph in John, and as I confirmed in W in
        Mark).
        Where the "mixture" is not block-mixture but simply the apparent
        influence of one textual tradition upon another or the drift of a
        textual tradition towards another, the percentages of agreement will
        suggest what is going on *if you include relevant witnesses from
        sufficient major groups to measure comparative agreements (as, e.g.,
        I attempted with ref. to W in Mark, showing that as the W-P45-Fam 13
        tradition progresses it becomes more closely allied with the
        "Byzantine" type mss witnesses.

        L. W. Hurtado
        University of Edinburgh,
        New College
        Mound Place
        Edinburgh, Scotland EH1 2LX
        Phone: 0131-650-8920
        Fax: 0131-650-6579
        E-mail: L.Hurtado@...
      • Robert B. Waltz
        ... OK, I ll concede that one. I just took the first table I saw. That affects the list of manuscripts, but does not affect the meaning. I thought of doing my
        Message 3 of 18 , May 2, 1997
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          On Fri, 2 May 1997, "Professor L.W. Hurtado" <hurtadol@...> wrote:

          >A few rjoinder notes to Waltz's piece on Colwell and quantitative
          >approaches.
          >1) Waltz cites figures from *Table 1* on p. 60 of Colwell,
          >_Methodology_, which includes *singular* readings, which are (as
          >Colwell explains in the essay) not useful for identifying
          >*relationships*. Thus, Table 2 on the same page refines the numbers
          >by including only those variation units where the tested mss exhibit
          >agreement of at least two of them. There the separation becomes
          >clearer. This exclusion of singular readings is an important
          >feature. By definition, singular readings don't attest
          >relationships

          OK, I'll concede that one. I just took the first table I saw.
          That affects the list of manuscripts, but does not affect the
          meaning. I thought of doing my example with fudged numbers. I
          suppose I should have done so.

          The list supplied *did* demonstrate one point, though: how
          few gaps actually exist. Mixture (not block mixture, *mixture*)
          fills most of them in.

          > 2) One ofthe ways Colwell's method has been refined subsequently (by
          >e.g., Fee and yours truly) is to insist that identification of mss
          >relationships cannot safely be done in samples (and in the essay from
          >which the tables come and in which Colwell sketches the basics of his
          >method, he cites figures for John 11, a sample only), and that we
          >have to take measurements (a) across a whole NT writing, and (b)
          >chapter by chapter. If we do this, we can detect "block-mixture"
          >(as, e.g., Fee did in Aleph in John, and as I confirmed in W in
          >Mark).

          True, but not relevant to the definition of the gap. :-)

          >Where the "mixture" is not block-mixture but simply the apparent
          >influence of one textual tradition upon another or the drift of a
          >textual tradition towards another, the percentages of agreement will
          >suggest what is going on *if you include relevant witnesses from
          >sufficient major groups to measure comparative agreements (as, e.g.,
          >I attempted with ref. to W in Mark, showing that as the W-P45-Fam 13
          >tradition progresses it becomes more closely allied with the
          >"Byzantine" type mss witnesses.

          Agreed. However, I interpret this differently (not your results,
          but the meaning of the situation).

          To examine text-types in their entirety means that we must
          examine *all* the witnesses, not just the "good" ones. This
          includes the mixed witnesses. This means, almost certainly,
          that there *will be* no gaps, even if a text-type exists.

          Allow me to give an example. I admit that this is based on
          a sample, not on the entire Gospel corpus, but it is based on
          a 990 reading corpus, so it should be representative assuming
          it is possible to take a representative sample in the Gospels.
          (By no means an assured point, and that could invalidate all
          studies -- including Hurtado's -- done so far.)

          Below is a sorted list of agreements with Aleph in those 990
          readings. I've omitted the papyri as incomplete and W as block-mixed.

          % MS "Gap"
          35 D 0
          35 E 0
          35 G 0
          35 N 0
          35 Omega 0
          35 U 1
          36 A 0
          36 Gamma 0
          36 K 0
          36 M 0
          36 Pi 1
          37 1424 0
          37 565 0
          37 700 0
          37 fam 13 1
          38 1010 0
          38 1506 1
          39 1071 0
          39 Theta 1
          40 X 3
          43 1342 0
          43 fam 1 2
          45 1241 4
          49 579 1
          50 33 2
          52 892 0
          52 C 7
          59 B 1
          60 L

          Notice that the largest gap in this list is 7, and the median gap is --
          ahem! -- *zero*. And that's based on fewer than thirty manuscripts and
          no versions. Throw in the Coptic versions and our largest gap shrinks to
          four. Throw in every Greek manuscript I studied (I admit this is bad
          technique) and the gap shrinks to *three*. In other words, there *is no
          gap.*

          I would also note that the highest rate of agreement observed is 60%.
          This obviously is much lower than Colwell's 70% threshold. This demonstrates
          another point: *Statistics depend upon their sample.* Even if we use
          some fixed rule such as "all variants supported by at least two manuscripts,"
          you will still have variations in your sample depending on what manuscript
          base you use.

          You can't assign some number here and expect it to work in every case.

          Please, people, study statistics before you use Colwell!

          Let me also stress that I am not attacking Colwell. I think he was
          the greatest textual thinker of his generation. My article on
          text-types quotes him more than any other. It is simply his misfortune
          that his one major mistake is the thing that so many scholars have
          latched onto as if it were gospel. It is, in fact, a statement with
          inadequate statistical foundations.

          -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-

          Robert B. Waltz
          waltzmn@...

          Want more loudmouthed opinions about textual criticism?
          Try my web page: http://www.skypoint.com/~waltzmn
          (A site inspired by the Encyclopedia of NT Textual Criticism)
        • Professor L.W. Hurtado
          Well, a few more response are called for by Waltz s latest. 1) Sure, the number counts will depend upon the mss selected for the exercise. That s why it s
          Message 4 of 18 , May 2, 1997
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            Well, a few more response are called for by Waltz's latest.
            1) Sure, the number counts will depend upon the mss selected for the
            exercise. That's why it's essential to the method to choose an
            adequate list of all relevant witnesses, relevant to determining
            which group mss belong to. This doesn't affect the validity of the
            method.
            2) I fail to see how my work is invalidated if samples are invalid.
            I didn't use samples, but collated across the whole of Mark.
            3) I quite agree with Waltz (and said previously the same) that there
            is nothing "magical" (his term; mine was "transcendent") about
            Colwell's numbers. Their beauty is that they were arrived at
            *inductively* by beginning with counting agreements of mss and seeing
            what happened. So, with all due respect to Waltz on statistics, one
            really doesn't have to be a stats techie to use the method, and I've
            seen no stats argument showing otherwise.
            4) I do want to know from Waltz the basis for his own numbers in his
            last posting. Agreements of this or that ms with Aleph at 990
            variation units . . .? What is the basis for determining the
            variation units? Mere counts of agreements of this ms with that one
            mean nothing *unless the counts are set within some meaningful
            context*. That is why in the Colwell method all counts are so
            carefully defined: e.g., the agreement of any two mss is seen in the
            context of the agreement of all other possible pairs (hence the grids
            of percentages, not merely a single row of numbers without a
            context).

            L. W. Hurtado
            University of Edinburgh,
            New College
            Mound Place
            Edinburgh, Scotland EH1 2LX
            Phone: 0131-650-8920
            Fax: 0131-650-6579
            E-mail: L.Hurtado@...
          • Professor L.W. Hurtado
            ... Excellent advice! Let s watch the beams as well as the motes, Bob! Waltz asks: How do you ... Bob. We have to start somewhere right? So, in Colwell s
            Message 5 of 18 , May 2, 1997
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              Waltz writes:
              > Here we go again. Please, people, read what I say, not what you
              > think I'm arguing against.

              Excellent advice! Let's watch the beams as well as the motes, Bob!


              Waltz asks: How do you
              > know, before you've done the work, which manuscripts are
              > significant?
              Bob. We have to start somewhere right? So, in Colwell's method, we
              start with what we *think* we know, and test it to see if our
              knowledge is correct. So, we start with the important mss witnesses
              we *think* are reps of what we *think* are major groups. Then we
              collate them & the counts will indicate whether they hang together in
              groups or not, how much they diverge etc., provided that (a) you have
              enough witnesses to detect what you're looking for (e.g., alignment
              with *major* groups, or whatever), and (b) provided you've used
              enough text and variation units to represent something.
              >
              > You cannot assume the solution.

              Uh, right. the method involves testing assumptions, Bob.
              I complained:
              > >2) I fail to see how my work is invalidated if samples are invalid.
              > >I didn't use samples, but collated across the whole of Mark.
              >
              > Simply false. You collated across the whole of Mark for readings
              > supported by at least two of the group p45 Aleph A B D W Theta f13
              > 565 TR. That *is* a sample. You may say that it includes at least
              > two witnesses from the Alexandrian, Byzantine, and "Caesarean"
              > text-types. Probably true, but you don't know that. (Robinson
              > will tell you that neither the TR nor A is a perfectly Byzantine
              > witness.) And where is the second "Western" witness?

              Bob, in TC "samples" normally mean sample bits, chapters, etc.
              Second, I collated *all* of Mark, noting *all* variations among *all*
              witnesses chosen, and counted *all* variation-units that were
              *meaningful* -- i.e., where it was possible to measure *agreements*
              of the witnesses.
              I don't know (nor does Robinson) what a "perfect" Byz witness would
              be. I used what are considered sufficiently good representatives of
              both earlier and later stages of the Byz text-type. And D is the
              only Greek witness in Mark--not something I can do anything about.
              In any case, I know of nobody who suggests that D in Mark is *not* a
              major "Wstern" witness.

              > You are once again assuming the solution. And you also ignore
              > the possibility of mixture (not block mixture, mixture). Both
              > the Alexandrian and Byzantine texts are represented by only
              > two witnesses. Suppose one is mixed for a particular reading.
              > Out it goes from your sample.
              Once again, Bob, we all make assumptions, and the aim is to test
              them, which is *precisely what the method aims to offer*. Moreover,
              I don't "ignore mixture" (by which I presume you mean mss influenced
              by more than one tradition/tendency, etc.). E.g., I point out that
              Fam 13 shows a drift toward the Byz text-type--precisely the
              "mixture" (your term) you claim I ignore. I've pointed this out
              earlier today, but you seem stronger on making charges than paying
              attention!
              As to your last sentence in the quote above, I'm not sure what you
              mean. All readings/variants that are supported by any two of the
              reps chosen are used whatever their complexion ("mixed" or not).
              >
              > You have used a sampling technique, merely one that uses a
              > very large sample. A large enough sample, I confess, that it
              > probably makes up for its methodoligical bias -- but only if
              > sampling works. (It probably does -- but can you prove it to
              > me?)
              You're simply not using "sample" in any meaningful way, but I can't
              stop you if you want to do so. And could you justify such pejorative
              language as "methodological bias"?
              >
              > Then consider the possibility of an undiscovered text-type.
              > With this sample, you cannot find it.

              Uh, Bob. I *did* make some discoveries. (1) W & P45 are *not* part
              of the "Caesarean" text-type, and (2) do seem to form agreement
              sufficient to make them look like a somewhat distinctive group. So,
              the method does in principle allow for what you deny.

              > I agree, anyone can use the method. So what? That doesn't make it
              > valid. I am not criticising your use of the method. I am criticising
              > the method itself.
              Again, Bob, take your own advice about careful reading of others.
              You've plainly distorted my point, which was that the method doesn't
              involve fancy, techie stats stuff, just empirical measurements and
              testings of hypotheses.
              You say:
              > Hurtado
              > is saying that I can't critique the design because he (Hurtado)
              > knows how to drive the car!

              You've lost me again, Bob. I didn't say you *couldn't* criticize
              anything. I said your criticisms aren't impressive because they miss
              the marks.

              I asked:
              > >4) I do want to know from Waltz the basis for his own numbers in his
              > >last posting. Agreements of this or that ms with Aleph at 990
              > >variation units . . .? What is the basis for determining the
              > >variation units? Mere counts of agreements of this ms with that one
              > >mean nothing *unless the counts are set within some meaningful
              > >context*.
              Waltz replies:
              > I gave a sample to demonstrate a point. The point was demonstrated:
              > There was no 10% gap. You are the one who says that I can use any
              > set of manuscripts, and therefore any sampling method, I want.
              > Therefore my results are valid. Q.E.D.

              This is getting tiresome, Bob. I did *not* say "any set of mss", for
              heaven's sake! I said chosen mss thought to represent major groups.
              I asked for the things that might make your figures meaningful and
              you again distort my words and dodge the question. Not good, Bob.

              Waltz goes on:
              > I simply state that there *is no* perfect method. And -- since
              > there is no method that adequately captures lists of variants --
              > we cannot treat the 70% number as magic.
              Who said "perfect" and what would that be, Bob? The aim is a method
              that is appropriate to the question and that stands up to competent
              analysis & criticism. Thus far, the refined Colwell method meets
              these criteria, but publish your results and lets see. And no one
              said "magic", either. Just pragmatic and verifiable.

              > Nor can we count
              > on the gap in all cases, since there are always mixed manuscripts
              > floating around. The inclusion or exclusion of such a manuscript
              > (in Mark, L would be a good example) will determine whether or
              > not the gap exists.
              Yup. There are mss that seem to lie between major groups . . . as
              the Colwell method will demonstrate, and as it will even allow one to
              portray quantitatively in a meaningful way by comparison with the
              quantitative agreements of mss of the group that are solid reps of
              it. If the "gap" is not very large, then the method shows . . . just
              what you refer to. What's the problem?

              L. W. Hurtado
              University of Edinburgh,
              New College
              Mound Place
              Edinburgh, Scotland EH1 2LX
              Phone: 0131-650-8920
              Fax: 0131-650-6579
              E-mail: L.Hurtado@...
            • James R. Adair
              I personally have found the debate between Hurtado and Waltz to be interesting, especially when matters of substance and theory are emphasized and personal
              Message 6 of 18 , May 2, 1997
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                I personally have found the debate between Hurtado and Waltz to be
                interesting, especially when matters of substance and theory are
                emphasized and personal comments are not. Let me ask the two antagonists
                (and anyone else who wants to respond) about a few specific points that I
                see coming out of this debate.

                (1) Is the existence of a gap of about 10% between groups of witnesses
                really a useful measurement? I can see measuring levels of agreement
                (whether 70% or some other number), but surely manuscripts can always be
                chosen in such a way as to eliminate any substantial gap in levels of
                agreement. Maybe the gap could be redefined in a manner similar to this:
                if one group of mss agrees with one another in 70% of readings, and
                another group of mss likewise agrees among its members in 70% of _its_
                readings, _and_ there is a gap of 10% between any two members of one
                groups vs. the other, _then_ we can identify two different text-types.
                Such a definition would seem to eliminate mixed mss from consideration
                _when determining text-types_ (i.e., not entirely from consideration).

                (2) The 70% agreement has often been questioned. Other than the Byzantine
                and Alexandrian witnesses, does any other group show a 70% level of
                agreement anywhere in the NT? What level of agreement is there among the
                OL witnesses (eliminating D from the Western group)? Bob, what level of
                agreement is there in the groups you identify in Paul?

                (3) What exactly do levels of agreement tell us? They say that mss are
                very similar, but is that really the same thing as saying that they are
                genetically related (as a group)? Does discovery of text-types tell us
                more about where patterns of reading originated or more about where they
                ended up? One way to increase the level of agreement, of course, is to
                correct a ms from another ms, so levels of agreement may not say much
                about historical origin. As an analogy, consider the English language.
                Because of the Norman invasion of England, Modern English contains many,
                many words of French origin. Nevertheless, at its root, it is a Germanic
                language. Using statistical sampling, would we call Modern English a
                member of the Germanic or the Romance text-type (or would we say it's
                mixed?)?

                (4) The word "sample" is being used differently by Hurtado and Waltz, it
                seems to me. Hurtado says, "Bob, in TC 'samples' normally mean sample
                bits, chapters, etc. Second, I collated *all* of Mark, noting *all*
                variations among *all* witnesses chosen, and counted *all* variation-units
                that were *meaningful* -- i.e., where it was possible to measure
                *agreements* of the witnesses." It appears to me that Larry is using
                the word "sample" in a way commonly used in TC circles, whereas Bob is
                using a more formal mathematical (statistical) definition. I think that
                TCers will have to bow to math in this case. Even if "samples" normally
                mean "sample bits, chapters, etc." in TC circles, it is clear that this
                terminology is weak and should be changed to agree with the more rigorous
                math definition, especially when TCers are dealing with statistics.
                Despite the "alls" of Hurtado's study, there is a sample: in the choice of
                manuscripts. It may be a good sample, but it's still a sample.

                I'd be interested to see what Larry and Bob (and others) have to say about
                these points.

                Jimmy Adair
                Manager of Information Technology Services, Scholars Press
                and
                Managing Editor of TELA, the Scholars Press World Wide Web Site
                ---------------> http://scholar.cc.emory.edu <-----------------
              • Robert B. Waltz
                Here we go again. Please, people, read what I say, not what you think I m arguing against. Specifically to Hurtado: I am *not* attacking your study. In fact, I
                Message 7 of 18 , May 2, 1997
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                  Here we go again. Please, people, read what I say, not what you
                  think I'm arguing against. Specifically to Hurtado: I am *not*
                  attacking your study. In fact, I have quoted it -- and even
                  derived an interesting idea from it (could the so-called
                  "Caesarean" text actually be a true branch of the "Western" text,
                  and D an abberation?). I am attacking the method that Colwell
                  described in one essay and, as best I can tell, *never used again*....

                  On Fri, 2 May 1997, "Professor L.W. Hurtado" <hurtadol@...> wrote:

                  >Well, a few more response are called for by Waltz's latest.
                  >1) Sure, the number counts will depend upon the mss selected for the
                  >exercise. That's why it's essential to the method to choose an
                  >adequate list of all relevant witnesses, relevant to determining
                  >which group mss belong to. This doesn't affect the validity of the
                  >method.

                  Of *course* it affects the validity of the method. How do you
                  know, before you've done the work, which manuscripts are
                  significant?

                  You cannot assume the solution.

                  >2) I fail to see how my work is invalidated if samples are invalid.
                  >I didn't use samples, but collated across the whole of Mark.

                  Simply false. You collated across the whole of Mark for readings
                  supported by at least two of the group p45 Aleph A B D W Theta f13
                  565 TR. That *is* a sample. You may say that it includes at least
                  two witnesses from the Alexandrian, Byzantine, and "Caesarean"
                  text-types. Probably true, but you don't know that. (Robinson
                  will tell you that neither the TR nor A is a perfectly Byzantine
                  witness.) And where is the second "Western" witness?

                  You are once again assuming the solution. And you also ignore
                  the possibility of mixture (not block mixture, mixture). Both
                  the Alexandrian and Byzantine texts are represented by only
                  two witnesses. Suppose one is mixed for a particular reading.
                  Out it goes from your sample.

                  You have used a sampling technique, merely one that uses a
                  very large sample. A large enough sample, I confess, that it
                  probably makes up for its methodoligical bias -- but only if
                  sampling works. (It probably does -- but can you prove it to
                  me?)

                  Then consider the possibility of an undiscovered text-type.
                  With this sample, you cannot find it.

                  >3) I quite agree with Waltz (and said previously the same) that there
                  >is nothing "magical" (his term; mine was "transcendent") about
                  >Colwell's numbers. Their beauty is that they were arrived at
                  >*inductively* by beginning with counting agreements of mss and seeing
                  >what happened. So, with all due respect to Waltz on statistics, one
                  >really doesn't have to be a stats techie to use the method, and I've
                  >seen no stats argument showing otherwise.

                  I agree, anyone can use the method. So what? That doesn't make it
                  valid. I am not criticising your use of the method. I am criticising
                  the method itself.

                  I'll give an analogy. I know how to drive an automobile, and I
                  assume Hurtado does also. Does that make me competent to design
                  an automobile? Or repair one? Hardly. Nor would I want to critique
                  its design.

                  I am critiquing the design of Colwell's automobile -- which, as
                  someone with mathematical training, I have at least some skill
                  to do (not much, but more, at least, than Colwell had). Hurtado
                  is saying that I can't critique the design because he (Hurtado)
                  knows how to drive the car!

                  >4) I do want to know from Waltz the basis for his own numbers in his
                  >last posting. Agreements of this or that ms with Aleph at 990
                  >variation units . . .? What is the basis for determining the
                  >variation units? Mere counts of agreements of this ms with that one
                  >mean nothing *unless the counts are set within some meaningful
                  >context*. That is why in the Colwell method all counts are so
                  >carefully defined: e.g., the agreement of any two mss is seen in the
                  >context of the agreement of all other possible pairs (hence the grids
                  >of percentages, not merely a single row of numbers without a
                  >context).

                  I gave a sample to demonstrate a point. The point was demonstrated:
                  There was no 10% gap. You are the one who says that I can use any
                  set of manuscripts, and therefore any sampling method, I want.
                  Therefore my results are valid. Q.E.D.

                  And before anyone attacks that, I agree, the result I just stated
                  is not valid. But it demonstrates the importance of knowing what
                  one is sampling.

                  If one wishes to know the list of readings involved, it starts with
                  the variants found in the apparatus of GNT. I supplemented this with
                  a filter to find variants roughly every ten verses. (I say "roughly"
                  because I too required two witnesses to support each reading, and I
                  also had to take variants for which I could learn the readings of
                  all the witnesses.) If someone wants a list of readings, I will
                  offer them.

                  I concede that this is not a perfect method. It is biased toward
                  readings where B and Aleph divide, because those are the readings
                  that puzzled the editors of GNT. (This is one of the reasons
                  why I added my 400+ arbitrary readings.) This probably lowers
                  the overall list of agreements.

                  I simply state that there *is no* perfect method. And -- since
                  there is no method that adequately captures lists of variants --
                  we cannot treat the 70% number as magic. Nor can we count
                  on the gap in all cases, since there are always mixed manuscripts
                  floating around. The inclusion or exclusion of such a manuscript
                  (in Mark, L would be a good example) will determine whether or
                  not the gap exists.

                  I will repeat -- again -- my example from Colossians 2.

                  In this chapter, Aleph and B disagree 25 times. Spread over how many
                  readings? (Particularly since eight of those readings have no other
                  uncial support.)

                  If we take readings which are supported by two or more uncials,
                  then the two agree in 32 of 47, or 68%. But if we take readings
                  found in the Nestle apparatus, we get 62%. If we take Tischendorf's
                  minor eighth edition, we get 59%.

                  Can someone tell me which of those numbers is "right," and why?

                  And, BTW, does this mean B and Aleph don't belong to the same
                  text-type in Colossians 2? (I say yes, but not many people seem
                  to agree with me. And even I say it for other reasons....)

                  -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-

                  Robert B. Waltz
                  waltzmn@...

                  Want more loudmouthed opinions about textual criticism?
                  Try my web page: http://www.skypoint.com/~waltzmn
                  (A site inspired by the Encyclopedia of NT Textual Criticism)
                • Robert B. Waltz
                  TCers -- Hurtado and I have gotten into what is obviously a very nasty debate. He is either not understanding or refusing to read what I say, and evidently he
                  Message 8 of 18 , May 2, 1997
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                    TCers --

                    Hurtado and I have gotten into what is obviously a very nasty debate.
                    He is either not understanding or refusing to read what I say, and
                    evidently he feels that I am doing the same. What is more, it appears
                    to me that we are re-hashing arguments that have been said many
                    times before.

                    I could rebut Hurtado's post, but I'm not going to convince
                    him. And he won't convince me. (After all, I'm right and he's
                    wrong. :-)

                    The question is, is anyone else listening? Is there any point
                    in attempting a rebuttal? I doubt it -- but if anyone wants
                    us to keep flailing away at our respective viewpoints, let me know.
                    Otherwise, I will spare my blood pressure (and perhaps yours)
                    and let this thread die.

                    -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-

                    Robert B. Waltz
                    waltzmn@...

                    Want more loudmouthed opinions about textual criticism?
                    Try my web page: http://www.skypoint.com/~waltzmn
                    (A site inspired by the Encyclopedia of NT Textual Criticism)
                  • Robert B. Waltz
                    On Fri, 2 May 1997, James R. Adair ... I must apologise for my part in that. I will admit that the recent unpleasantness
                    Message 9 of 18 , May 2, 1997
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                      On Fri, 2 May 1997, "James R. Adair" <jadair@...>
                      wrote:

                      >I personally have found the debate between Hurtado and Waltz to be
                      >interesting, especially when matters of substance and theory are
                      >emphasized and personal comments are not.

                      I must apologise for my part in that. I will admit that the recent
                      unpleasantness about Academic Imperialism made me rather thin-skinned,
                      since I am one who does not have university credentials in TC.

                      >Let me ask the two antagonists
                      >(and anyone else who wants to respond) about a few specific points that I
                      >see coming out of this debate.

                      Nice to see something I can answer easily.

                      >(1) Is the existence of a gap of about 10% between groups of witnesses
                      >really a useful measurement? I can see measuring levels of agreement
                      >(whether 70% or some other number), but surely manuscripts can always be
                      >chosen in such a way as to eliminate any substantial gap in levels of
                      >agreement.

                      That is my contention. Surprisingly, I do think there is value
                      in the concept of the "gap" -- but I don't believe it can be applied
                      rigidly. In a large enough sample set, a gap of only a few percentage
                      points can be significant.

                      Also, I think it more useful to apply the gap to classified agreements
                      than to overall percentages of agreement. I offer as an example 630
                      in the Paulines. In my overall table of agreements, its closest relative
                      is L (77%). That's because 630 has suffered heavy Byzantine correction.

                      However, if we look at 630's handful of near-singular readings, we
                      find that it shares no fewer than 6 with 1739. Other than 1739 and
                      its obvious relative 1881, the next highest rate of near-singulars
                      is 3 with B and 2 with p46. So *there* we see a gap of significance.

                      By combining these facts, we come to the conclusion (borne out
                      by other data) that 630 is a heavily mixed manuscript, more Byzantine
                      than anything else, but with a strong infusion of family 1739
                      readings (in fact, family 1739 readings outnumber Byzantine readings
                      in Romans-Galatians; after that, 630 is effectively purely Byzantine).

                      >Maybe the gap could be redefined in a manner similar to this:
                      >if one group of mss agrees with one another in 70% of readings, and
                      >another group of mss likewise agrees among its members in 70% of _its_
                      >readings, _and_ there is a gap of 10% between any two members of one
                      >groups vs. the other, _then_ we can identify two different text-types.
                      >Such a definition would seem to eliminate mixed mss from consideration
                      >_when determining text-types_ (i.e., not entirely from consideration).

                      Personally I see a lot of merit in this idea. It makes analysis a lot
                      harder, but the concept is good.

                      It does leave one problem: It leaves us stuck if we have to investigate
                      a text-type which no longer exists in pure form in any manuscript.
                      Which, sadly, puts us back where we started in my last argument with
                      Hurtado: the advocates of the "Caesarean" text explicitly defined it
                      in terms of readings mined from mixed manuscripts.

                      Still, if you'll allow me to fudge those numbers a little, depending
                      on the sample, I could live with this idea.

                      >(2) The 70% agreement has often been questioned. Other than the Byzantine
                      >and Alexandrian witnesses, does any other group show a 70% level of
                      >agreement anywhere in the NT? What level of agreement is there among the
                      >OL witnesses (eliminating D from the Western group)? Bob, what level of
                      >agreement is there in the groups you identify in Paul?

                      I'll give as much data here as I can type in half an hour. (BTW -- if
                      some of the numbers don't agree, blame the fact that I'm retyping all
                      this. If there's an inconsistency, tell me and I'll check it.)

                      *************************************

                      Gospels: If we omit D, and people are willing to live with my samples,
                      the "European" Latins (a, b, ff2) seem to agree about 70-80% of the
                      time. (By comparison, they agree with D about 60-65% of the time,
                      and with D about 35% of the time. They agree with k about 55% of the
                      time.)

                      *************************************

                      I have no good data for Acts.

                      *************************************

                      I'm going to annotate the data for Paul. :-)

                      *************************************

                      p46/B type:
                      p46: Closest relative is B, 62% of the time. Next closest is 1739, 56% of
                      the time. p46 and B also have 34 near-singular agreements, as opposed to
                      14 between p46 and Aleph, 21 between p46 and D, 16 between p46 and 1739.
                      B: Closest relative is actually the Sahidic, 68% of the time. After that,
                      it's about a wash between 1739 (64%) and p46 (62%). Aleph is at 57%,
                      D at 42%. But p46 remains the clear winner in near-singulars (34, to
                      26 for the Sahidic and 18 for 1739).

                      Alexandrian text:
                      Aleph: Closest relative is A, 76%. Outside Romans (where 33 is Byzantine),
                      33 takes the prize at about 77%. C agrees 76% , 1506 72%, the
                      Bohairic 73%. The fragmentary I gets the prize where it exists, 80%.
                      For comparison, B agrees with Aleph 57%, D agrees 47%, 1739 agrees 63%.
                      A: Closest is C at 77%, followed by Aleph at 76. With B, 53%; with D,
                      47%; with 1739, 62%
                      C: Closest is A, 77%, followed by Aleph, 76%. With B, 51%; with D,
                      48%; with 1739, 63%.
                      33: Closest is Aleph, 69%. A C follow at 65% (exclude Romans and all
                      these numbers go up by about 7-8 points). With B, 54%; with D, 48%;
                      with 1739, 61%.

                      "Western" text:
                      D: Closest relative , not surprisingly, is d, 84%. Next are F G, 72%,
                      then the other Old Latins in the 60-70% range. With B, 42%; with
                      Aleph, 47%; with 1739, 47%.
                      G: Other than, of course, F f, the closest relatives are D d, 72%.
                      With B, 41%; with Aleph, 46%; with 1739, 47%.

                      As a typical example of the Byzantine text, we note that K L
                      agree 91% of the time.

                      Family 1739:
                      0243 and 1739 agree 96% of the time. (I hope soon to study this
                      relationship in detail.)
                      6 agrees with 1739 64% of the time (compared to 69% with L), but
                      has 19 near-singular agreements. (Next on the near-singular list,
                      other than 424** with 18 and 1881 with 12, is B with 10)
                      The corrections in 424 go with 1739 91% of the time, and of 424**'s
                      26 near-singulars, 20, or 77%, are shared by 1739. (This is
                      extraordinary, since in the typical manuscript at least a third
                      of the near-singulars are errors.)
                      1881 agrees with 1739 77% of the time.
                      1739 itself agrees with p46 56% of the time, with B 64% of the time,
                      with Aleph 63% of the time, with D 47% of the time.

                      *************************************

                      Now to the Catholics. Here I'll just make a table.

                      p72 Aleph A B C K 33 323 614 1241 1739 2495
                      p72 - 38 43 66 45 21 41 47 39 48 51 39
                      Aleph 38 - 60 48 54 37 57 50 45 51 60 46
                      A 43 60 - 44 57 35 79 55 52 60 66 50
                      B 66 48 44 - 49 20 46 44 32 48 56 36
                      C 45 54 57 49 - 42 56 60 51 57 70 51
                      K 21 37 35 20 42 - 38 47 52 38 34 48
                      33 41 57 79 46 56 38 - 59 58 59 67 54
                      323 47 50 55 44 60 47 59 - 50 71 78 50
                      614 39 45 52 32 51 52 58 50 - 47 52 82
                      1241 48 51 60 48 57 38 59 71 47 - 80 49
                      1739 51 60 66 56 70 34 67 78 52 80 - 50
                      2495 39 46 50 36 51 48 54 50 82 49 50 -

                      *************************************

                      To summarize (and I'm using some additional data not offered here):

                      In the Gospels, we find that the "Western" group falls on the ragged
                      edge of the 70% rule -- so close to the edge that the sample might
                      tip things one way or the other. There is a huge "gap" between
                      "Western" and non-Western, though.

                      In Paul, the Alexandrian, "Western," and Family 1739 texts all
                      meet the 70% rule for their stronger members, though some of the
                      weaker ones fail. p46 and B *don't* make it, though they are clearly
                      akin. In Paul, for my sample, 60% might be a better threshold.
                      BTW -- if you observe, 1739 seems to agree with all three of
                      the other text-types more than they agree with each other.
                      This is the basis for my belief that it forms its own text-type.

                      In the Catholics, we find 80% agreement between the members of
                      family 2138 (614 630 1505 1611 1799 2138 2412 2495, etc.), with
                      subgroups breaking the 90% mark. The members of family 1739
                      (C 323 945 1241 1881 2298) gnerally exceed this mark with respect
                      to 1739 though not to each other. There is a group within the
                      Alexandrian text (A Psi 33 81 436 bo etc.) which exceeds the 70%
                      threshold, but neither Aleph nor p72/B are part of it. There
                      probably needs to be work done on the Alexandrian text in the
                      Catholics. (It may well be that p72/B are a separate text-type.)

                      N.B.
                      One thing that I think is worth noting is that, in the Catholics,
                      1241 agrees with 1739 80% of the time, and C agrees with 1739 70%
                      of the time. But 1241 and C agree only 57% of the time. Interesting,
                      huh? This ought to tell us something (I'm not sure what yet, but
                      it's one of those reasons why I'm concerned with the statistical
                      nature of variants).

                      >(3) What exactly do levels of agreement tell us? They say that mss are
                      >very similar, but is that really the same thing as saying that they are
                      >genetically related (as a group)?

                      To give a great answer, I say, "Yes and no." That is, a high rate of
                      agreement means that they have something in common -- but it may
                      be just a bunch of Byzantine mixture.

                      In my view, a manuscript (call it X) that is 80% Byzantine and
                      20% something else has value only in the 20% that's something
                      else. If we want to examine the Byzantine text, we have plenty
                      of purely Byzantine manuscripts to look at. For simplicity,
                      let's say that X had a Byzantine ancestor B and a less-Byzantine
                      ancestor O. Now it may be that a lot of X's Byzantine readings
                      came from O; we can't tell.

                      But it doesn't matter. I will freely concede to Hurtado, Colwell
                      and Tune, et al that X is more closely related to B and the
                      Byzantine text than to O and something else. However, I don't
                      see that it matters. Since we don't care about the Byzantine
                      text (given how many good examples we have), our interest is
                      in the small relationship with O.

                      >Does discovery of text-types tell us
                      >more about where patterns of reading originated or more about where they
                      >ended up? One way to increase the level of agreement, of course, is to
                      >correct a ms from another ms, so levels of agreement may not say much
                      >about historical origin.

                      Entirely agreed, from where I sit. See above.

                      >As an analogy, consider the English language.
                      >Because of the Norman invasion of England, Modern English contains many,
                      >many words of French origin. Nevertheless, at its root, it is a Germanic
                      >language. Using statistical sampling, would we call Modern English a
                      >member of the Germanic or the Romance text-type (or would we say it's
                      >mixed?)?

                      Depends on the sampling method. :-)

                      If we sampled grammatically, or based on words in common use, we'd
                      say it's a Germanic language. If we look at a dictionary, where
                      obscure Latin-derived words predominate, we'd say it's a Romance
                      language.

                      In my view, the Grammar is simplified Germanic, the vocabulary is
                      mixed. I don't know what one would call the result.

                      >(4) The word "sample" is being used differently by Hurtado and Waltz, it
                      >seems to me. Hurtado says, "Bob, in TC 'samples' normally mean sample
                      >bits, chapters, etc. Second, I collated *all* of Mark, noting *all*
                      >variations among *all* witnesses chosen, and counted *all* variation-units
                      >that were *meaningful* -- i.e., where it was possible to measure
                      >*agreements* of the witnesses." It appears to me that Larry is using
                      >the word "sample" in a way commonly used in TC circles, whereas Bob is
                      >using a more formal mathematical (statistical) definition. I think that
                      >TCers will have to bow to math in this case. Even if "samples" normally
                      >mean "sample bits, chapters, etc." in TC circles, it is clear that this
                      >terminology is weak and should be changed to agree with the more rigorous
                      >math definition, especially when TCers are dealing with statistics.
                      >Despite the "alls" of Hurtado's study, there is a sample: in the choice of
                      >manuscripts. It may be a good sample, but it's still a sample.

                      Thanks for pointing out the difference in language. You're right, I was
                      using the mathematical sense -- and not even thinking of other meanings.

                      Naturally, I vote for the mathematical use. :-)

                      >I'd be interested to see what Larry and Bob (and others) have to say about
                      >these points.

                      I hope this clarifies things. If not, well, I'll try again next week
                      some time. :-)

                      Thanks for both the conciliatory words and the curiosity.

                      -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-

                      Robert B. Waltz
                      waltzmn@...

                      Want more loudmouthed opinions about textual criticism?
                      Try my web page: http://www.skypoint.com/~waltzmn
                      (A site inspired by the Encyclopedia of NT Textual Criticism)
                    • Bart Ehrman
                      ... Mr. Waltz: is it still the case that you haven t actually read any of my stuff? I completely agree that our models have to be mathematically based,
                      Message 10 of 18 , May 4, 1997
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                        On Sun, 4 May 1997, Robert B. Waltz wrote:
                        >
                        > If we are to make mathematical analysis of TC a truly respectable
                        > discipline, we must create a greater degree of rigour. Now I know that
                        > not everyone wants to do this (witness my exchange with Ehrman about
                        > the Comprehensive Profile Method. I say that profiles should be created
                        > by mechanical means. He says that human beings should create them.
                        > There is no "right" answer here; it's just that one way is rigourous
                        > and the other is not). All I am saying is that such rigour is required
                        > from proper mathematical analysis. Results must be repeatable!

                        Mr. Waltz: is it still the case that you haven't actually read any of
                        my stuff?

                        I completely agree that our models have to be mathematically based,
                        repeatable, and rigourous. I thought that was why I developed the
                        comprehensive profile method in the first place. If you have suggestions
                        about the method itself, I really would like to hear them, since there are
                        several doctoral dissertations being written right now that are using it,
                        and refinements could prove quite useful (Vincent Broman's comments have
                        been extremely helpful; I have to say that I prefer his approach of
                        offering suggestions of a method that he has read and understand to
                        your approach of criticizing a method you haven't even examined; but
                        maybe it's a matter of taste).

                        With respect to our disagreement, it is not over either rigor or
                        repeatability. It's over how one *decides* what constitutes a variant or
                        not and how one goes about using these variants to classify manuscripts.
                        The points you're raising over that issue are precisely what is at stake,
                        in part because they show that the decision cannot be made mechanically
                        until you, a subjective being, actually *make* these decisions. I.e.,
                        it's wrong to say that I think human beings "should" make decisions; I
                        think humans *have* to make them. There is no choice about the matter.
                        The question about whether they are rigourous or not in doing so is
                        altogether different. (BTW, your point that binary agreements always
                        create a Byzantine vs. a non-Byzantine reading of course is obviously
                        false, so I wonder what you're thinking of. Could you tell me, by the
                        way, if you've evaluated yet the standard criticism of the earlier methods
                        of establishin a Caesarean text by considering only those variants that
                        differ from the Byzantine text? To most of us, this criticism is
                        absolutely valid, and based precisely on a rigorous set of
                        considerations.)

                        -- Bart D. Ehrman, University of North Carolina at Chapel Hill
                      • Robert B. Waltz
                        TCers -- In the last week or so, I ve gotten several requests for information on the use of statistics in TC. In one sense, that s good; it means I ve been
                        Message 11 of 18 , May 4, 1997
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                          TCers --

                          In the last week or so, I've gotten several requests for information on
                          the use of statistics in TC. In one sense, that's good; it means I've
                          been getting you thinking. But I haven't been much help in my replies.
                          Given that the questions keep coming in, I think I have to try to give
                          something of an overview of *why*.

                          The basic question that has been asked is, "What is a good mathematical
                          reference for TCers?" As far as I know, there is none. If there were,
                          I would be quoting it, rather than stumbling along looking for methods
                          of my own.

                          Now I'll admit that there could be a great reference out there somewhere.
                          But I doubt it. And the reason that I doubt it is that we haven't even laid
                          all the groundwork.

                          To give an example: In the last few decades, we've done a great deal to
                          define what constitutes a "variant." Epp and Fee are among the big names
                          here. They've given us a nomenclature both for the variants themsleves
                          and for their nature. What they haven't given us is a rigid system for
                          determining the scope of variants. And the latter is vital.

                          Consider this: In Larry Richards's statistical analysis of the Catholic
                          Epistles, he goes to great lengths to make all his variants binary
                          (that is, to have *two and only two* readings). As I recall (and I'm
                          not checking this), he had only four ternary variants (those with
                          three readings) in his whole set of a hundred and some.

                          By contrast, about 25% of the variants in the apparatus of UBS/GNT
                          are ternary (or of even higher order).

                          Does this matter? You bet it does! If all variants are binary, then
                          in general we can say that, for any variant, one reading is Byzantine
                          and one reading is non-Byzantine. This means that, if two manuscripts
                          both have the non-Byzantine reading here, then they automatically
                          agree. In other words, agreement in non-Byzantine readings is meaningless;
                          every manuscript -- even one that is purely Byzantine -- will have 100%
                          agreement with every other in non-Byzantine readings.

                          But it's worth remembering that Lake, Streeter, et al *defined* the
                          "Caesarean" text in terms of the non-Byzantine readings. If all variants
                          are binary, then *all* manuscripts become "Caesarean" under this definition.
                          Whereas, if many of our variants are ternary, there are two non-Byzantine
                          readings, and agreement in non-Byzantines becomes a meaningful statistic.

                          Is anyone prepared to state that the existence or non-existence of a
                          text-type depends entirely on how many readings we allow at a variant?
                          Seems pretty silly to me....

                          If we are to make mathematical analysis of TC a truly respectable
                          discipline, we must create a greater degree of rigour. Now I know that
                          not everyone wants to do this (witness my exchange with Ehrman about
                          the Comprehensive Profile Method. I say that profiles should be created
                          by mechanical means. He says that human beings should create them.
                          There is no "right" answer here; it's just that one way is rigourous
                          and the other is not). All I am saying is that such rigour is required
                          from proper mathematical analysis. Results must be repeatable!

                          Another problem with recommending a math text or reference to TCers
                          is the level of math required. I don't know about your colleges,
                          but my school offered two statistics courses -- one, called "Statistics,"
                          was taught by the economics department, and had no prerequisites.
                          The math department offering was called "Probability and Statistics,"
                          and had as prerequisites multi-variable calculus and linear algebra.

                          Now I'll tell you the truth: the Economics version of the course was
                          more "useful." They taught you a lot more things. In Probs & Stats,
                          we didn't even learn such basic tools as chi-square testing. Instead,
                          we studied possible outcomes, probability distributions -- and
                          where and when one can apply various methods. The Economics class
                          never taught that. And it's a real lack. Those economic students
                          frequently applied tests and formulas to results where they simply
                          didn't apply. But I frankly don't know how to *tell* people how
                          to apply the tests until they've reached the level of mathematical
                          maturity implied by four semesters of calculus, linear algebra, etc.
                          (There may be a way; I just don't know it. :-)

                          To show how much work there is to be done, I will point out that,
                          in the six or so years since I first started applying statistics
                          to textual criticism, I have refined my methods five times. And
                          I *still* don't have a method that lets me plug in a collation
                          and have the computer read off the text-type of the resulting
                          manuscript. I have a lot more data than I used to, and it's all
                          very pretty, but it isn't rigorous. (And, I fear, I'm about used
                          up. I'm 35, and mathematicians stop having ideas at 30. So somebody
                          else will likely have to take up the torch.)

                          This brings up another point. I may, at some point, have said that
                          Colwell and Tune and/or Hurtado are wrong in their definition of a
                          text-type. I should not say that. Their methods are faithful to
                          their definition.

                          But note that word: "Definition." They have *postulated* the
                          definition of a text-type (70% agreement, 10% gap). That is, they
                          have said that "this is what we mean by a text-type."

                          That is a legitimate mathematical method. They could, for all
                          it matters mathematically, define text-types in terms of the
                          color of ink used in the manuscript. This is logically consistent.
                          It's just that the results wouldn't match what we instinctively
                          think of as a text-type.

                          The informal definition of a text-type is "the loosest grouping
                          of manuscripts between which some degree of relationship can be
                          discerned." Now I say that, due to mixture, this definition
                          contradicts the Colwell/Tune definition. Allow me enough manuscripts,
                          and I will show you a set in which there are no 10% gaps.

                          That is the reason why I did, and do, reject the Colwell definition.
                          I've spent the last several years trying to find a definition which
                          more or less conforms with what we already knew, without shutting
                          us off from new discoveries. And I am the first to admit that I
                          have failed. I believe I have constructed an accurate picture of
                          the text-types in Paul and the Catholics -- but I also admit
                          that this is based on my informal analysis of the statistics
                          I produce, not on the statistics themselves.

                          The Colwell/Tune definition carries with it two seemingly
                          unnoticed corollaries:

                          1. A text-type can only exist if it has a pure representative
                          2. A sufficiently mixed text cannot belong to a text-type.

                          I personally reject this. By this definition, the Alexandrian
                          text did not exist in the Gospels until B and Aleph became known!

                          I would postulate something different:

                          1. Text-types exist.
                          2. Text-types need not have a pure representative.

                          On that basis I have stumbled around (and stumbled is the right word!)
                          looking for a mathematical rule that will let me prove the existence
                          of text-types.

                          I hope that is a decent summary of the situation. We can't just go
                          out and call on mathematicians to help us out. If we ever want TC
                          to be a rigorous subject (and I say *if*, because some do *not*
                          want it to become one), we need to get our house in order. Get
                          our definitions straight, study the nature of variants so that
                          we know what tests we can apply. If we do that, then maybe finally
                          we can write the textbook that everybody wants.

                          All right, the voice yapping in the wilderness will now stop yapping
                          for a bit. :-)


                          -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-

                          Robert B. Waltz
                          waltzmn@...

                          Want more loudmouthed opinions about textual criticism?
                          Try my web page: http://www.skypoint.com/~waltzmn
                          (A site inspired by the Encyclopedia of NT Textual Criticism)
                        • Robert B. Waltz
                          ... To answer the question: Yes, I have read various things you have written. But to answer the *implied* question: No, I haven t gotten to the article on the
                          Message 12 of 18 , May 4, 1997
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                            On Sun, 4 May 1997, Bart Ehrman <behrman@...> wrote:

                            >On Sun, 4 May 1997, Robert B. Waltz wrote:
                            >>
                            >> If we are to make mathematical analysis of TC a truly respectable
                            >> discipline, we must create a greater degree of rigour. Now I know that
                            >> not everyone wants to do this (witness my exchange with Ehrman about
                            >> the Comprehensive Profile Method. I say that profiles should be created
                            >> by mechanical means. He says that human beings should create them.
                            >> There is no "right" answer here; it's just that one way is rigourous
                            >> and the other is not). All I am saying is that such rigour is required
                            >> from proper mathematical analysis. Results must be repeatable!
                            >
                            > Mr. Waltz: is it still the case that you haven't actually read any of
                            >my stuff?

                            To answer the question: Yes, I have read various things you have written.
                            But to answer the *implied* question: No, I haven't gotten to the article
                            on the Comprehensive Profile method. I admit that this is something I
                            need to do -- but it hardly affects my discussion of the Colwell/Tune
                            definition.

                            [ ... ]

                            > With respect to our disagreement, it is not over either rigor or
                            >repeatability. It's over how one *decides* what constitutes a variant or
                            >not and how one goes about using these variants to classify manuscripts.
                            >The points you're raising over that issue are precisely what is at stake,
                            >in part because they show that the decision cannot be made mechanically
                            >until you, a subjective being, actually *make* these decisions. I.e.,
                            >it's wrong to say that I think human beings "should" make decisions; I
                            >think humans *have* to make them. There is no choice about the matter.

                            In part I agree. But human beings are always subjective, and should
                            be kept *out* of the process as long as possible. (Sez I.) So I
                            prefer to use the computer to do every bit of the work it possibly
                            can. There may be methodological bias in my programming -- but at
                            least that bias will affect all manuscripts equally.

                            >The question about whether they are rigourous or not in doing so is
                            >altogether different.

                            I will try to be charitable and assume that we are using "rigour" in
                            different ways. So what in the world do you mean if you do not mean
                            something that can be done absolutely mechanically? (This excludes,
                            of course, the meaning in mathematical logic -- but even I don't
                            see any way to apply mathematical logic to TC.)

                            >(BTW, your point that binary agreements always
                            >create a Byzantine vs. a non-Byzantine reading of course is obviously
                            >false, so I wonder what you're thinking of.

                            What? Assume that, at some point of variation, there are two readings,
                            A and B. That is what I mean by a binary variant.

                            If this is true, then there are only two possibilities: Either the
                            Byzantine text is split (which can happen, of course, but is not
                            especially common), or one of the readings is Byzantine and the
                            other is not. For simplicity, let's say that reading B is Byzantine
                            and A is not. Together so far?

                            Now take two manuscripts, X and Y. Since, *by definition of a binary
                            variant*, they can only have reading A or reading B here, there are
                            four possible results:

                            1. X reads A, Y reads A -- Comment: This is the only case where both are
                            Non-Byzantine. And X and Y agree.
                            2. X reads A, Y reads B -- Comment: Y is Byzantine, so this is not a
                            case where both are non-Byzantine.
                            3. X reads B, Y reads A -- Comment: X is Byzantine, so this is not a
                            case where both are non-Byzantine.
                            4. X reads B, Y reads B -- Comment: Both Byzantine, so this is not a
                            case where both are non-Byzantine.

                            In other words, *if all readinngs are binary*, then wherever two manuscripts
                            are non-Byzantine, they agree.

                            Q.E.D.

                            This does not admit of argument. If you wish to prove this statement untrue,
                            you must attack the premise that all readings are binary. I do not say that
                            all readings are binary, only that, if they are, then agreement in
                            non-Byzantines is meaningless.

                            Or were we disagreeing about what "agreement in non-Byzantines" means?

                            >Could you tell me, by the
                            >way, if you've evaluated yet the standard criticism of the earlier methods
                            >of establishin a Caesarean text by considering only those variants that
                            >differ from the Byzantine text? To most of us, this criticism is
                            >absolutely valid, and based precisely on a rigorous set of
                            >considerations.)

                            I'm not sure I understand the question. Are you asking, "have I examined
                            the Lake/Blake/New/Streeter system of defining the 'Caesarean' text in
                            terms of its divergences from the Byzantine text?"?

                            If so, the answer is that I have not repeated the experiment that they
                            undertook, so I do not know if the "Caesarean" text exists. I have suspicions,
                            but no final answer.

                            However, I have no objection, in theory, to their method. They applied it
                            incorrectly (the TR is *not* the Byzantine text), and of course they
                            applied it circularly. That means that they needed better application of
                            their method, not a better method.

                            Let me try asking the question from the other direction: Do you insist
                            that a text-type can only exist if there is a pure representative of the
                            type? Because I will readily concede that there are no surviving pure
                            representatives of the "Caesarean" text. All of them, from Theta on
                            down, are mixed (if they form a text at all). But if you cannot examine
                            manuscripts at the points where they are free of Byzantine mixture,
                            how can you examine that lost text?

                            ***

                            Let me make another observation on this exchange. Those who are
                            neutrals (lucky you :-) will observe that I keep being attacked
                            at *the same points.* Usually it's where I have questioned a common
                            assumption, but not always.

                            The one thing that is universal is that we are debating over
                            postulates. Colwell, or Ehrman, or Hurtado, are offering postulates.
                            (You don't think Colwell postulated his definition? Consider how
                            he "derived" it. He looked at one small set of data, offered
                            some numbers -- and by some amazing process those numbers have
                            become gospel, accepted without proof by very many TCers.)

                            So I would ask a question: What is wrong with trying alternate
                            postulates? I can't give a TC analogy -- but I can state one
                            thing with certainty: Mathematics has always gotten richer when
                            it has tried using different postulates.

                            -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-

                            Robert B. Waltz
                            waltzmn@...

                            Want more loudmouthed opinions about textual criticism?
                            Try my web page: http://www.skypoint.com/~waltzmn
                            (A site inspired by the Encyclopedia of NT Textual Criticism)
                          • Professor L.W. Hurtado
                            As Jimmy Adair and a couple of others think they found some value in the exchanges Bob Waltz and I had late last week, and as substantive matters continue to
                            Message 13 of 18 , May 5, 1997
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                              As Jimmy Adair and a couple of others think they found some value in
                              the exchanges Bob Waltz and I had late last week, and as substantive
                              matters continue to be on the table, I hope I shall be permitted
                              patience for another contribution. (And Bob, I never saw our
                              exchanges as shouting matches, at least on my end.)
                              Adair highlights some interesting matters. Also, in his response to
                              Adair and in his subsequent posting Waltz makes a number of
                              statements that require some clarification in my view, merely to be
                              able to understand what he means before I can evaluate them. Let me
                              try to be concise and itemize matters.
                              1.) It bears remembering what Colwell (and Tune) were up to in the
                              two or three relevant essays in Colwell's _Methodology_ collection in
                              which the % matters come up. Colwell posits that the only
                              helpful definition of "text-Type" is "a group of manuscripts, not .
                              . . a list of readings" (Colwell, _Methodology_, p. 9). That is
                              essential to understand the quantitative method he tried to develop.
                              We're trying to group mss so that we can then proceed toward a
                              history of the NT text. In order to do this, we can apply the
                              Colwell-Tune quantitative approach, and in this approach they offered
                              as a *quantitative* definition of a text-type (i.e., group of mss),
                              70% or more agreement in point of variation where any two of the
                              leading witnesses of all known major groups share a variant across a
                              significant body of text (in my view the collation has to be book by
                              book across whole books).
                              As I've stated the reason for the 70% figure is simply that when they
                              did this exercise in their sample, and when Fee carried out his
                              exercise in John and when I did mine in Mark, we found that the major
                              reps. of Hort's "Neutral" type and of the "Byzantine" type agreed at
                              this level and their agreement was separated from agreement with
                              major reps of other text types by 10% or more. These figures might
                              well be modified, if one changes the nature of the experiment to ask
                              other questions, but that would say nothing about the usefulness of
                              the figures *for the purpose at hand*--viz. to group mss into
                              text-types and to then see where and whether new mss fit with any of
                              these groups.
                              Thus, when Waltz says that we can introduce enough mss to make the
                              "gap" of agreement much smaller, this is misleading. One might well
                              introduce mss that are "weak" members of a text-type/group and
                              the agreement of these mss with the text-type of which they are
                              weak members would *not* be separated as distinctly from their level
                              of agreement with members of other text-types. But the validity
                              of the 10% "gap" and the 70% agreement observation is that these
                              figures are functional quantitative definitions of the behavior of
                              *major/good reps. of text-types when collated with major/good reps.
                              of all other known text-types*. Thus, that weaker members of the
                              text-type might not exhibit this behavior is very interesting, almost
                              predictable, but not relevant for the validity of the definition of
                              strong members of a text-type, at least a text-type like the Neutral
                              and Byzantine ones.
                              2.) There has been some confusion over the word "sample". Given that
                              we cannot collate all known Greek mss, we have to chose well certain
                              representative mss for any such exercise. I suppose one could call
                              such reps "samples", but "samples" in at least some social science
                              exercises can involve *random* sampling, and when you're choosing
                              particular mss because they are already thought to be leading reps.
                              of groups this is hardly "sampling".
                              Moreover, when the purpose is to measure the agreements of mss (a)
                              where the mss collated vary, and (b) where their variations enable us
                              to say anything about agreements with one another, then if we count
                              all such places how is this a "sample"? I suppose one could think of
                              such variation units as "samples" in the sense that they are not
                              every word/phrase in the NT, but only places where the text varies.
                              But, again, "sample" implies a portion of the relevant data. But if
                              all the relevant data is counted, how is it only a sample?
                              Waltz cites critically L. Richardson's study of the Johannines, and I
                              too have strong reservations about R's approach, which, N.B. is *not*
                              the sort of application of quantitative analysis that Fee and I have
                              practiced and advocated.
                              3) With respect (sincere, though my patience
                              wears thin at times), Waltz makes several statements that either seem
                              to me incorrect or else not comprehensible to me.--He allgeses as
                              what he calls corollaries of the Colwell-Tune method (a) that a
                              text-type can exist only if it has a pure representative, and (b)
                              that a sufficiently mixed ms can't belong to a text-type. Both are
                              incorrect allegations. To repeat: per Colwell, a text-type is a
                              group of mss that can be shown to belong together in some objective
                              way (i.e., open for others to examine and test). No pure rep is
                              required, only that a group of mss exhibit sufficiently strong
                              agreement to indicate that they are a group. Mixed mss may show up
                              as weaker members of such a group, or a group of "mixed" mss. might
                              exhibit sufficient agreement to form a group. I really don't see
                              where Waltz gets these corollaries, for the studies done using and
                              adapting the Colwell-Tune approach demonstrate my statements.--Waltz
                              alleges that Fee & Epp haven't given us "a rigid system for
                              determining the scope of variants", and Waltz regards this as
                              "vital". I'd really like Waltz to specify what in the impressively
                              cogent discussions in chaps. 3-4 of the recent Epp/Fee _Studies in
                              The Theory & MEthod_ volume he takes issue with, and where in these
                              discussions he finds mis-steps or omissions. E.g., the "recommended
                              definitions & limitations" on Epp/Fee pp. 57-61 are fairly explicit
                              and precise. Can you improve on these paragraphs, Mr. Waltz? If so,
                              please specify.--Waltz criticizes the Colwell-Tune quantitative
                              definition (70%, etc.) as contrary to "what we instinctively think of
                              as a text-type". "Instinctively"??? Given that some have used
                              text-type to = a "pattern of readings" and others (my preference) an
                              identifiable major group of mss distinguisable from other major
                              groups, where does instinct come in?--Mr. Waltz quite commendably
                              wants "mathematical analysis" in NT TC to be "a truly respectable
                              discipline" and calls for "a greater degree of rigour". I therefore
                              fail to understand how it is an advance to list mere numbers of
                              agreements of two mss in "non-Byzantine" readings. And I simply
                              don't know what his tables of numbers and percentages mean. Mere
                              numbers and percentages mean nothing without a context. Percentages
                              of what? Numbers of what? Mr. Waltz earlier mentioned counting
                              variantion units from N/A27, but I didn't catch the details. Could
                              you please give us a simple statement of what it is you do, as
                              scientifically clear as possible? Merely stating alleged results
                              without the scientific notation of process is near useless.
                              --What do you mean by seeking to "apply the gap to classified
                              agreements"?
                              --What do you mean by "near-singular readings"?
                              --How is it rigorous or meaningful to make a judgment about mss
                              relationships based on a handfull of readings (as in Waltz's list of
                              6 agreements of 630 with this or that ms)?

                              Finally, as I've stated earlier (and demonstrated in my study of the
                              Codex W) quantitative analysis is only the *first step* in grouping
                              mss and in analysing their relationships. It has to be complemented
                              with analysis of the specific readings shared by mss. No one has
                              suggested that I know of that quantitative agreement alone is more
                              than a rough measurement and one with heuristic value.
                              L. W. Hurtado
                              University of Edinburgh,
                              New College
                              Mound Place
                              Edinburgh, Scotland EH1 2LX
                              Phone: 0131-650-8920
                              Fax: 0131-650-6579
                              E-mail: L.Hurtado@...
                            • Robert B. Waltz
                              On Mon, 5 May 1997, Professor L.W. Hurtado ... If you read my web page, you ll note that I quote that statement too. Although this,
                              Message 14 of 18 , May 5, 1997
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                                On Mon, 5 May 1997, "Professor L.W. Hurtado" <hurtadol@...>
                                wrote, in part:

                                >Adair highlights some interesting matters. Also, in his response to
                                >Adair and in his subsequent posting Waltz makes a number of
                                >statements that require some clarification in my view, merely to be
                                >able to understand what he means before I can evaluate them. Let me
                                >try to be concise and itemize matters.
                                >1.) It bears remembering what Colwell (and Tune) were up to in the
                                >two or three relevant essays in Colwell's _Methodology_ collection in
                                >which the % matters come up. Colwell posits that the only
                                >helpful definition of "text-Type" is "a group of manuscripts, not .
                                >. . a list of readings" (Colwell, _Methodology_, p. 9).

                                If you read my web page, you'll note that I quote that statement too.

                                Although this, too, is something that might be worthy of discussion.
                                Is a text-type a group of readings or a group of manuscripts?
                                If it is a group of manuscripts, how do we determine which manuscripts
                                belong except by looking at some list of readings? And if it is a
                                list of readings, how do we choose the readings except by looking
                                at the manuscripts containing them?

                                I wonder, therefore, if we can separate manuscripts and readings.
                                (I'm not being dogmatic here; I just don't know. Thoughts, anyone?)

                                >That is
                                >essential to understand the quantitative method he tried to develop.
                                >We're trying to group mss so that we can then proceed toward a
                                >history of the NT text.

                                With which goal I hearily agree -- probably more heartily than most
                                on this list, since I don't trust internal evidence if I don't have
                                to.

                                >In order to do this, we can apply the
                                >Colwell-Tune quantitative approach, and in this approach they offered
                                >as a *quantitative* definition of a text-type (i.e., group of mss),
                                >70% or more agreement in point of variation where any two of the
                                >leading witnesses of all known major groups share a variant across a
                                >significant body of text

                                Notice that I said in my last post that this is a consistent method.
                                I just don't think it produces quite the results we want. Also, it
                                really *does* assume the solution. It's all very well to say that
                                we need to start somewhere. Believe me, I know the need! My
                                database defaults to comparing limited lists of manuscripts.

                                But we need to make our assumptions as few as possible. If we just
                                keep *assuming* that this witness or that is "the best," we can
                                never tell if something else is better.

                                >(in my view the collation has to be book by
                                >book across whole books).

                                I agree in part with that last. That is, one has to be alert for
                                block mixture.

                                However, complete collation of all manuscripts is simply not possible
                                at this time. So if we are to study all manuscripts, we must use a
                                sampling technique. (Note that I am not saying this is *good*; I'm
                                saying this is *necessary.*) This means that we may not have enough
                                data points, especially for short books, to produce detailed results
                                book-by-book. To get more statistical accuracy, we need to check
                                book-by-book for block mixture, and then -- if possible -- study
                                results for an entire corpus. Only that way can we involve enough
                                readings to be certain our results are reliable.

                                >As I've stated the reason for the 70% figure is simply that when they
                                >did this exercise in their sample, and when Fee carried out his
                                >exercise in John and when I did mine in Mark, we found that the major
                                >reps. of Hort's "Neutral" type and of the "Byzantine" type agreed at
                                >this level and their agreement was separated from agreement with
                                >major reps of other text types by 10% or more. These figures might
                                >well be modified, if one changes the nature of the experiment to ask
                                >other questions, but that would say nothing about the usefulness of
                                >the figures *for the purpose at hand*--viz. to group mss into
                                >text-types and to then see where and whether new mss fit with any of
                                >these groups.

                                I'm not saying that you didn't achieve these results. I'm saying the
                                value you find depends on the sample. In your system, based on variants
                                found in two or more witnesses in a group of less than a dozen, the
                                addition of even one more manuscript, depending on its nature, could
                                significantly alter your results.

                                >Thus, when Waltz says that we can introduce enough mss to make the
                                >"gap" of agreement much smaller, this is misleading. One might well
                                >introduce mss that are "weak" members of a text-type/group and
                                >the agreement of these mss with the text-type of which they are
                                >weak members would *not* be separated as distinctly from their level
                                >of agreement with members of other text-types. But the validity
                                >of the 10% "gap" and the 70% agreement observation is that these
                                >figures are functional quantitative definitions of the behavior of
                                >*major/good reps. of text-types when collated with major/good reps.
                                >of all other known text-types*.

                                Assume that to be true. It very well may be. It still leaves you
                                unable to assess mixed manuscripts. And I would claim that there
                                are several known text-types that exist *only* in mixed manuscripts.
                                The "Caesarean" text type, if it exists, is an example. The p46/B
                                type of Paul, if *it* exists, is an example.

                                And there is at least one undisputable example: Family 2138 in the
                                Catholics. This is a very large family (I've personally gathered
                                statistics for 614 630 1505 1611 1799 2138 2412 2495, and there
                                is evidence that there are many more.) On average, these manuscripts
                                agree with each other in about 70%-80% of the cases. But if we look
                                at the reading found in the majority of these manuscripts, they
                                all agree with that 80%-90% of the time. What's more, in my spot
                                checks, *every time they deviated,* it was in the direction of the
                                Byzantine reading. In other words, here is a group where the members
                                meet the Colwell definition, but even so can be shown to be slightly
                                mixed. It doesn't take much to see that only a little more Byzantine
                                mixture would have knocked the group below the Colwell threshold.
                                Does it cease to become a text-type just because the members are
                                a little more mixed? I don't see it that way.

                                >Thus, that weaker members of the
                                >text-type might not exhibit this behavior is very interesting, almost
                                >predictable,

                                More than predictable. A logical necessity.

                                >but not relevant for the validity of the definition of
                                >strong members of a text-type, at least a text-type like the Neutral
                                >and Byzantine ones.

                                But this is my key objection: I don't care about using *only* the
                                strong members of a text-type. Sure, it's nice where they are
                                available. But I refuse to write off the weak ones.

                                >2.) There has been some confusion over the word "sample". Given that
                                >we cannot collate all known Greek mss, we have to chose well certain
                                >representative mss for any such exercise.

                                I'm afraid I don't accept that, either. If you haven't studied all
                                manuscripts, how do you know which are representative? (This strikes
                                me as too obvious for words.)

                                Better to sample a large number of manuscripts than to know only
                                a handful in detail.

                                I'll give an example. There is a family in Paul consisting of 330, 451,
                                and 2492. (Incidentally, Maurice Robinson confirmed the relationship
                                between 330 and 451 in Acts.) This group seems to have an interesting
                                and independent text (though it's mostly Byzantine, and I don't know
                                if there was ever a pure non-Byzantine type behind it). If we insisted
                                on looking only at well-known, pure witnesses, we would never know that
                                this group exists.

                                >I suppose one could call
                                >such reps "samples", but "samples" in at least some social science
                                >exercises can involve *random* sampling, and when you're choosing
                                >particular mss because they are already thought to be leading reps.
                                >of groups this is hardly "sampling".

                                "Sample" as I have been using it applies not to manuscripts but
                                to readings. And sampling need not be random; a "sample" is just
                                a bunch of stuff. In certain instances one prefers a random sample.
                                However, I would point out that often one does *not* want a random
                                sample. Without going into details (all the more so since I don't
                                remember them), consider all the political polls that call up lists
                                of people carefully selected to meet certain characteristics.

                                Now this may sound like I'm agreeing with Hurtado and saying that one
                                should use selected manuscripts. I'm not. Remember, I use "sample" to
                                apply to readings. We may choose to select readings carefully (although
                                frankly I tried in my work on the gospels to select them randomly).
                                But I would strongly argue that we cannot selectively choose manuscripts.
                                When a pollster calls John Smith, it's because the pollster known that
                                John Smith is 35-50 years old, has two years of college, has two
                                children, etc. When we leave, say, manuscript 223 out of our calculations,
                                is it because we know its text? Much more likely it's because we *don't*
                                know its text. In other words, we are creating a biased sample without
                                even knowing the biases.

                                I have elsewhere said some rather unkind things about the Alands'
                                "manuscript categories" and "thousand readings." I still don't think
                                it's an adequate classification tool. But at least it lets us separate
                                the bulk of Byzantine manuscripts from the ones which are something
                                (it hardly matters *what*) else. I would maintain that this is where
                                we have to start.

                                [ ... ]

                                >Waltz cites critically L. Richardson's study of the Johannines, and I
                                >too have strong reservations about R's approach, which, N.B. is *not*
                                >the sort of application of quantitative analysis that Fee and I have
                                >practiced and advocated.

                                Agreed. It's a modified Claremont approach. And, actually, I agree
                                with many of Richards' results. I find the same three families
                                non-Byzantine families he does (though I use different and, I think,
                                more informative names: "Alexandrian," "family 1739," "family 2138").
                                My complaints with him are that his collations are inaccurate, that
                                "Mixed" is not a text-type, and that his three so-called Alexandrian
                                groups are actually separate text-types (surely this is obvious
                                in the case of Family 2138!)

                                > 3) With respect (sincere, though my patience
                                >wears thin at times), Waltz makes several statements that either seem
                                >to me incorrect or else not comprehensible to me.--He allgeses as
                                >what he calls corollaries of the Colwell-Tune method (a) that a
                                >text-type can exist only if it has a pure representative, and (b)
                                >that a sufficiently mixed ms can't belong to a text-type. Both are
                                >incorrect allegations.

                                Let's be clear: Not the Colwell-Tune *method*, the Colwell-Tune
                                *definition.*

                                I'm going to demonstrate my point very simply. I've done this before;
                                I hope (sorry, but I'm going to be acid here) you'll read it this
                                time.

                                Let's start with a pure manuscript of a text-type. Call it M.
                                Assume, without loss of generality (to put that in layman's terms,
                                the way I construct this example will work for any number of readings),
                                that there are six points of variation we might study. Number
                                them 1, 2, 3, 4, 5, 6 (how's that for original). At each of these
                                points let "A" represent the reading of M. Our alternate reading,
                                which we may consider to be the reading of the Byzantine text, is "B."

                                Make two copies of M; call them N and P. Initially, both N and
                                P have the same profile:

                                N P
                                --- ---
                                1. A A
                                2. A A
                                3. A A
                                4. A A
                                5. A A
                                6. A A

                                Now let's randomly mix three Byzantine readings into N and P. Let's
                                say that N receives Byzantine readings at 1, 3, and 4; P gets them
                                at 2, 3, and 5. So now our profile is:

                                N** P**
                                --- ---
                                1. B A
                                2. A B
                                3. B B
                                4. B A
                                5. A B
                                6. A A

                                Now copy N** (call the result Q) and P** (call that R). Then destroy
                                M, N, and P.

                                If we compare Q and R, they agree only twice: at 3 (where both are
                                Byzantine) and at 6 (where both have the original reading).

                                Now I say that Q and R still represent -- albeit badly -- the original
                                text-type of M. But they *do not* meet the Colwell definition, and
                                no manuscripts mixed in this manner can.

                                Try it yourself, with as many readings and as many Byzantine corruptions
                                as you like. If you don't want to do the math yourself, the article
                                on mathematics on my web page (see the section labelled "Probability")
                                will show you the expected degree of agreement between manuscripts
                                which have suffered various degrees of mixture.

                                [ ... ]

                                >Waltz
                                >alleges that Fee & Epp haven't given us "a rigid system for
                                >determining the scope of variants", and Waltz regards this as
                                >"vital". I'd really like Waltz to specify what in the impressively
                                >cogent discussions in chaps. 3-4 of the recent Epp/Fee _Studies in
                                >The Theory & MEthod_ volume he takes issue with, and where in these
                                >discussions he finds mis-steps or omissions.

                                You completely missed the point of what I was saying. What I was
                                out is that the way we set variants determines what statistical
                                analysis we can use. I showed why, too.

                                I pointed out that Epp & Fee made great progress in this area.
                                But their work was not related to statistical analysis, merely
                                to classification. We need to add the statistical element -- e.g.
                                do we insist on binary readings, etc.

                                Those who think I am denigrating Epp would be advised to read all
                                the various postings in which I have quoted Epp's opinions *against*
                                the orthodox views of textual critics.

                                [ ... ]

                                >Waltz criticizes the Colwell-Tune quantitative
                                >definition (70%, etc.) as contrary to "what we instinctively think of
                                >as a text-type". "Instinctively"??? Given that some have used
                                >text-type to = a "pattern of readings" and others (my preference) an
                                >identifiable major group of mss distinguisable from other major
                                >groups, where does instinct come in?

                                Plenty of people around here have said "I know a text-type when I
                                see one." Perhaps I mis-spoke; maybe some people on this list
                                don't have a feeling for text-types. The "instinctive" definition
                                is "the highest [loosest] degree of relationships between manuscripts
                                that we can perceive."

                                A lot of people have perceived the "Caesarean" text. Zuntz perceived
                                the p46/B text. Neither meets the Colwell definition. That must say
                                something.

                                [ ... ]

                                >And I simply
                                >don't know what his tables of numbers and percentages mean. Mere
                                >numbers and percentages mean nothing without a context. Percentages
                                >of what? Numbers of what? Mr. Waltz earlier mentioned counting
                                >variantion units from N/A27, but I didn't catch the details. Could
                                >you please give us a simple statement of what it is you do, as
                                >scientifically clear as possible? Merely stating alleged results
                                >without the scientific notation of process is near useless.

                                I *never once* mentioned "variantion units from N/A27" with respect
                                to my most recent table (for the Catholics). I did say the numbers
                                were precentages of agreement. I may not have said in the last post
                                that these were based on the variation units in GNT3 and T&T. But
                                I have stated that in the past. I've also put most of the details
                                on my web page.

                                >--What do you mean by seeking to "apply the gap to classified
                                >agreements"?

                                That depends on what system of classifications one uses. Ehrman
                                has one, I have another -- and we disapprove of each others'
                                methods. So I can't answer that categorically. But the idea
                                is that, for any given manuscript and any given statistic,
                                *other than overall agreements*, there will probably be a gap
                                how close it stands between its immediate relatives and how
                                it stands with respect to non-relatives. The size and nature
                                of that gap, however, are dependent on the statistic, the
                                manuscript, and the control manuscripts.

                                >--What do you mean by "near-singular readings"?

                                The technical definition is "a reading is near-singular if it is
                                supported by no more than x manuscripts of those being examined."
                                The number x will, of course, depend on the number of manuscripts
                                examined. I've been working with 30-50 manuscripts, and typically
                                use x=5 or x=6.

                                >--How is it rigorous or meaningful to make a judgment about mss
                                >relationships based on a handfull of readings (as in Waltz's list of
                                >6 agreements of 630 with this or that ms)?

                                Oh muses, I call on you to make people read what I say!

                                I used a sample of 550+ readings. In this set, 630 was found to
                                have a certain number of near-singular readings (19, I believe).
                                Of these 19, 6 agreed with 1739. No other manuscript had even
                                close to that many near-singular agreements.

                                ***

                                My apologies to all of you caught in the crossfire. I hope this
                                will be my last reply to Hurtado on this subject. If others of
                                you have questions, feel free to ask. I hope I will be able to
                                answer -- but I can't spend time like this repeating myself.
                                Sadly, I have a real job too....

                                -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-

                                Robert B. Waltz
                                waltzmn@...

                                Want more loudmouthed opinions about textual criticism?
                                Try my web page: http://www.skypoint.com/~waltzmn
                                (A site inspired by the Encyclopedia of NT Textual Criticism)
                              • Professor L.W. Hurtado
                                Thanks to Robt. Waltz for his response to my previous posting. I too hope that my previous postings have been sufficiently clear to make it possible to move
                                Message 15 of 18 , May 6, 1997
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                                  Thanks to Robt. Waltz for his response to my previous posting. I too
                                  hope that my previous postings have been sufficiently clear to make
                                  it possible to move on to other things now, with only the following
                                  brief clarifications:
                                  Waltz writes:
                                  > If it [a text-type] is a group of manuscripts, how do we determine
                                  > which manuscripts
                                  > belong except by looking at some list of readings? And if it is a
                                  > list of readings, how do we choose the readings except by looking
                                  > at the manuscripts containing them?
                                  If the question we seek to answer is whether a given selection of mss
                                  constitutes an identifiable group such as a "text-type", then we
                                  collate them across a large body of text counting their behavior at
                                  all points of variation, and then asssessing the count in comparison
                                  to the behavior of other manuscripts that can afford us what we think
                                  might be a valid analogy and/or contrast. Thus, we compare counts
                                  with counts, agreement of mss with agreement of other mss. It's
                                  *overall significantly high levels of agreements in variants* that is
                                  the crucial indicator of a text-group. Analysis of readings comes
                                  later, and enables us to say something about the *nature/quality* of
                                  the kind of readings "preferred" by a given group, and about the
                                  "mixture" or other factors that have influenced the text of the
                                  group.
                                  (And, by the way, "mixture", by which Waltz seems to assume always
                                  influence of one kind of ms upon another, is only *one* way that a
                                  ms might acquire kinds of readings. Scribes can quite independently
                                  have produced the same variants, e.g., harmonizations, stylistic
                                  improvements, etc., because they had same/similar tastes and
                                  concerns. This is why we have to go by *overall high numbers of
                                  agreements* and not merely small numbers of shared readings.)

                                  > Notice that I said in my last post that this is a consistent method.
                                  > I just don't think it produces quite the results we want. Also, it
                                  > really *does* assume the solution.

                                  > But we need to make our assumptions as few as possible. If we just
                                  > keep *assuming* that this witness or that is "the best," we can
                                  > never tell if something else is better.
                                  But, as Waltz will surely know, the essence of scientific work is to
                                  assume/hypothesize something *which we then devise a means of
                                  testing*. The Colwell-Tune type approach offers a means of testing
                                  whether mss are what we might have assumed. There's nothing wrong
                                  in assuming something so long as (a) you're aware of the assumption
                                  you're making, and (b) can devise a means of testing the assumption.
                                  Thus, if we assume that Codex W has sufficiently strong agreement
                                  with Theta and 565 to make it a "pre-Caesarean" witness, and then we
                                  conduct the exercise in Mark I conducted in my published study, the
                                  Colwell-Tune approach indicates that W does not in fact show anything
                                  approaching strong enough agreement to indicate any particular
                                  relationship twixt W and Theta in Mark. And when you then follow
                                  this up (as I did) with detailed analysis of the *particular
                                  readings* W and Theta do share, you find that even the *kinds* of
                                  shared readings are less likely to be the result of any direct
                                  relationship of the two mss.
                                  Of the Colwell-Tune approach Waltz writes:
                                  > I'm not saying that you didn't achieve these results. I'm saying the
                                  > value you find depends on the sample. In your system, based on variants
                                  > found in two or more witnesses in a group of less than a dozen, the
                                  > addition of even one more manuscript, depending on its nature, could
                                  > significantly alter your results.
                                  For what it's worth, for the published version of the study I did add
                                  another ms (565) to the original list (in the PhD thesis version),
                                  and the results were strengthened! I have always wanted since then
                                  to have the chance to run, say, L and 33 in Mark through this
                                  collation, to see if we can say anything more precise about how and
                                  whether they are in fact (as often thought) "weaker"
                                  Alexandrian/Neutrals in Mark, and if so what other affiliations they
                                  might have and/or what kind(s) of readings they may prefer. I do
                                  doubt that this would alter the evident & strong relationships show
                                  among primary Neutrals/Alexandrians and primary Byzantines. So, I
                                  rather doubt that it would "significantly alter results" in fact.
                                  But it might contribute to our grasp of the mss added.

                                  Waltz states (again and again!) that my approach:
                                  > . . . still leaves you
                                  > unable to assess mixed manuscripts. And I would claim that there
                                  > are several known text-types that exist *only* in mixed manuscripts.
                                  > The "Caesarean" text type, if it exists, is an example.
                                  But I *did* assess "mixed manuscipts" in Mark in my study, for
                                  example. I characterized in some precision and detail the "mixed"
                                  nature of the text of W and P45, and even Family 13, etc. Not by
                                  mere counting, but by then following up the counting with analysis of
                                  readings. The full method Fee and I have advocated involves *both*
                                  quantitative study *and* readings-analysis, the combination of which
                                  permits *identification* of "mixture (by quantitative study) *and
                                  characterization* of "mixture" (by analysis of readings identified in
                                  the countings). I've staed this more than once but Waltz seems not
                                  to have noticed. I hope this will be the last time necessary.
                                  Waltz writes:
                                  > But this is my key objection: I don't care about using *only* the
                                  > strong members of a text-type. Sure, it's nice where they are
                                  > available. But I refuse to write off the weak ones.

                                  Nor does anyone else "care about using *only* the strong members of a
                                  text-type" and urge us "to write off the weak ones". One tries to
                                  select good/strong reps of a text type *for the initial purposes of
                                  seeing if a new ms belongs to this or that group*. One might also
                                  use/select deliberately "mixed" or "weaker" members of a text-type to
                                  see if a new ms accords more closely with them or with the stronger
                                  members. No one's writing off anything. Where does this notion come
                                  from?

                                  To my pragmatic statement:
                                  > >2.) There has been some confusion over the word "sample". Given that
                                  > >we cannot collate all known Greek mss, we have to chose well certain
                                  > >representative mss for any such exercise.

                                  Waltz reponds:
                                  > I'm afraid I don't accept that, either. If you haven't studied all
                                  > manuscripts, how do you know which are representative? (This strikes
                                  > me as too obvious for words.)
                                  And I find it "too obvious for words" that Waltz is mistaken again.
                                  Once more: We *have* been studying mss for quite a while, and these
                                  studies may have been accurate or less than accurate in conclusions.
                                  So, we take what's been done and *TEST* the previous conclusions by
                                  some approach/method that will help tell us something. Which is what
                                  the Colwell-Tune approach was designed to assist. Which is what Fee
                                  did in John (correcting previous identification of Aleph, for
                                  example), which is what I did in Mark (correcting previous
                                  identification of W, P45, Fam. 13, etc.).

                                  > >Waltz
                                  > >alleges that Fee & Epp haven't given us "a rigid system for
                                  > >determining the scope of variants", and Waltz regards this as
                                  > >"vital". I'd really like Waltz to specify what in the impressively
                                  > >cogent discussions in chaps. 3-4 of the recent Epp/Fee _Studies in
                                  > >The Theory & MEthod_ volume he takes issue with, and where in these
                                  > >discussions he finds mis-steps or omissions.
                                  >
                                  > You completely missed the point of what I was saying. What I was
                                  > out is that the way we set variants determines what statistical
                                  > analysis we can use. I showed why, too.
                                  No, Waltz hasn't shown what he claims in his last sentence. And he
                                  hasn't specifically shown what's wrong/missing in the fairly clear
                                  definition of variants, variation-units, etc. that Epp offers.

                                  >
                                  > I pointed out that Epp & Fee made great progress in this area.
                                  > But their work was not related to statistical analysis, merely
                                  > to classification. We need to add the statistical element -- e.g.
                                  > do we insist on binary readings, etc.

                                  I've not seen from Waltz anything specifically as to what
                                  "statistical analysis" offers us.

                                  > A lot of people have perceived the "Caesarean" text. Zuntz perceived
                                  > the p46/B text. Neither meets the Colwell definition. That must say
                                  > something.
                                  Yup. It probably means that "Caesarean" text-type has to be
                                  re-thought or else has to be demonstrated as being anything like what
                                  we otherwise expect of agreement of mss alleged to belong to the same
                                  text-type. I'm satisfied that Theta & 565 show this kind of
                                  agreement (or approach it). So there's something in Mark of the
                                  period of these mss, and the Colwell-Tune approach helps us to see it
                                  in some objective terms.

                                  Waltz writes:
                                  > The technical definition is "a reading is near-singular if it is
                                  > supported by no more than x manuscripts of those being examined."
                                  > The number x will, of course, depend on the number of manuscripts
                                  > examined. I've been working with 30-50 manuscripts, and typically
                                  > use x=5 or x=6.
                                  I take it that "technical definition" here must be Waltz's, as I've
                                  never even come across the term before in nearly 30 yrs. of NT
                                  text-critical work. I've seen "sub-singular", but not this one. But
                                  then maybe I've missed it somewhere.

                                  So, for my part as well, I hope this final posting is final on the
                                  subject for me and has been helpful in clarifying some matters for
                                  others.

                                  L. W. Hurtado
                                  University of Edinburgh,
                                  New College
                                  Mound Place
                                  Edinburgh, Scotland EH1 2LX
                                  Phone: 0131-650-8920
                                  Fax: 0131-650-6579
                                  E-mail: L.Hurtado@...
                                • Robert B. Waltz
                                  I promised not to continue the debate with Hurtado, and I won t. If I haven t made my opinions clear by now, I probably am unable to do so. (E.g. I can t stop
                                  Message 16 of 18 , May 6, 1997
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                                    I promised not to continue the debate with Hurtado, and I won't. If I
                                    haven't made my opinions clear by now, I probably am unable to do so.
                                    (E.g. I can't stop using mathematical language, which I gather
                                    confuses certain people.)

                                    But there is one point that I thought I should clarify, since it may
                                    be that I *haven't* discussed this before.

                                    So here is the quote:

                                    >Waltz writes:
                                    >> The technical definition is "a reading is near-singular if it is
                                    >> supported by no more than x manuscripts of those being examined."
                                    >> The number x will, of course, depend on the number of manuscripts
                                    >> examined. I've been working with 30-50 manuscripts, and typically
                                    >> use x=5 or x=6.
                                    >I take it that "technical definition" here must be Waltz's, as I've
                                    >never even come across the term before in nearly 30 yrs. of NT
                                    >text-critical work. I've seen "sub-singular", but not this one. But
                                    >then maybe I've missed it somewhere.

                                    The definition is indeed mine. As far as I know, I am the first
                                    person to give a precise definition to the term "near-singular"
                                    (although it seems to me that I saw it used somewhere).

                                    It will be observed that a near-singular reading is not the same as
                                    subsingular reading (although all sub-singulars are near-singular,
                                    the reverse is not true). Subsingulars are usually defined as
                                    readings having support from only one significant document;
                                    a near-singular can have several strong supporters. The point
                                    is simply that it represents only a small fraction of the
                                    tradition.

                                    It will be observed that the concept only has meaning when one
                                    is studying a fairly large number of manuscripts (I wouldn't use
                                    it on a set of less than 25 mss).

                                    The goal of the concept is to find the characteristic readings
                                    of a text-type, without the inherent biases of having a human
                                    being look for them. It also has the mechanical advantage that
                                    such a near-singular profile can be computed on the fly. (To
                                    compute such a profile, on my slow database on my slow machine,
                                    takes about three minutes per 100 readings -- and that's while
                                    computing four other statistics as well. Even if the results
                                    are arguably not as good as Ehrman's profiles, I can probably
                                    find them for a hundred manuscripts in the time it takes a
                                    human being to do *one*.)

                                    The concept is largely equivalent to any previous system of
                                    classified agreements, going all the way back to Hutton's triple
                                    readings. However, it avoids Hutton's problem of assuming the
                                    solution. (And Hutton *clearly* assumed the solution; his system
                                    acknowledged only Alexandrian, Byzantine, and "Western" types.)

                                    It should be noted that near-singular agreements in and of themselves
                                    are not sufficient to classify manuscripts; we also need overall
                                    rates of agreement, and (sez I) at least one other statistic as
                                    well. (I prefer more). The reason for this should be obvious:
                                    While a distinctive manuscript like B will have many near-singular
                                    readings (over 100 in my set of 990 readings in the Gospels),
                                    many of the Byzantine manuscripts have none at all -- or if they
                                    do have one or two, they are often the result of error.

                                    Rates of agreement in near-singular readings are often low -- closely
                                    related manuscripts may agree no more than 30-40% of the time. But
                                    unrelated manuscripts will often have no near-singular agreements at
                                    all. So the statistic can be meaningful, and it is a good place to
                                    apply the concept of the "gap."

                                    Or so say I....

                                    Bob Waltz
                                    waltzmn@...
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