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Re: Request: help with Colwell's quantitative analysis

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  • 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 1 of 18 , May 2, 1997
      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 2 of 18 , May 2, 1997
        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 3 of 18 , May 2, 1997
          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 4 of 18 , May 2, 1997
            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 5 of 18 , May 2, 1997
              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 6 of 18 , May 2, 1997
                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 7 of 18 , May 4, 1997
                  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 8 of 18 , May 4, 1997
                    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 9 of 18 , May 4, 1997
                      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 10 of 18 , May 5, 1997
                        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 11 of 18 , May 5, 1997
                          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 12 of 18 , May 6, 1997
                            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 13 of 18 , May 6, 1997
                              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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