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[Synoptic-L] Proof (?) that 222 was not written by Luke

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  • David Inglis
    All, I m trying to put together some solid arguments for various conclusions based on Dave Gentile s data. Because I go any further, please could I ask anyone
    Message 1 of 26 , Jan 25, 2002
      All,

      I'm trying to put together some solid arguments for various conclusions
      based on Dave Gentile's data. Because I go any further, please could I ask
      anyone who is interested to find holes in the following reasoning. Note:
      In the descriptions below Mt, Mk, and Lk represent the synoptists who
      created the Gospels of Matthew, Mark, and Luke respectively.



      Four categories contain words common to either two or all three of the
      Gospels. These are 222, 220, 202, and 022. Starting with 222, this
      contains triple tradition words that appear in Matthew, Mark, and Luke.
      Assuming that these common words were not all independently selected by Mt,
      Mk, and Lk, then these words all came from the same source (which I'm going
      to call T). This could be one or more documents that all three synoptists
      copied from, or could be a document created by one synoptist (from an
      unknown number of sources) that was then copied independently by the other
      two, or one synoptist copied from another who copied from the third who
      copied from T.

      In order to determine which of the above might be the case, it's worth
      looking at whether any sondergut material (200, 020, 002) correlates with
      222, on the basis that if one of the synoptists created 222, then we should
      expect the style of 222 to be similar to that of one of the sonderguts.
      However, none of 222, 200, 020, or 002 actually correlate each other,
      therefore providing no support for the idea that any two of them came from
      the same source.

      Each of the sondergut categories has a negative correlation with the other
      two (suggesting different sources for all three), so is it possible to say
      that the 200, 020, and 002 categories are representative of the styles of
      Mt, Mk, and Lk respectively? Suppose that the sources of 200, 020, and 002
      are M, K, and L respectively. Now, is it possible to have a common source
      for 200 and 002 (i.e. M and L are parts of the same source), when 200-002 is
      strongly negative? By definition, 200, 020, and 002 do not have equivalents
      in other synoptics, and so we have no way of knowing how much editing they
      may have undergone. As a result, it is possible that (for example) M and L
      are parts of the same source, and that either or both M and L have been
      heavily edited by Mt and Lk to create 200 and 002, causing 200-002 to be
      negative.

      Extending this idea to K, then M, K, and L might all be parts of the same
      source, even though the styles of 200, 020, and 002 are all different.
      Also, we can't tell purely from this data whether any of 200, 020, and 002
      are representative of the styles of Mt, Mk, and Lk respectively, or whether
      one is part of a common source that the other two edited to their own
      styles, or whether they all edited a common source. One thing we can say is
      that either T is not the same source as M, K, and L, or Mt, Mk, and Lk all
      edited this common source sufficiently to remove all positive correlations
      among 222, 200, 020, and 002. In fact, because 222-002 is one of the
      strongest negative correlations, then if T and L were part of the same
      source (T/L), then Lk (for some reason) obliterated the style of this common
      source when creating 002 from it.

      Now, if T and L were the same, we would have to explain why Lk included
      1,493 unedited words of T/L material in 222, but made very heavy changes in
      other parts of T/L, resulting in the 5,755 words of material that he alone
      included in 002. Of course, 222 is only that part of T that Lk used in
      unedited form. He also edited T to create the 1710 words of 112, and
      because 112 contains Lk's changes to T, the style of 112 reflects Lk's
      choices. Therefore, as would be expected, 222-112 is strongly negative.

      However, 002-112 is very strongly positive, and hence their styles are very
      similar. Now, we are supposing that 002 contains a mixture of T/L words
      plus Lk's own edits. So, 002 should look like a combination of 222
      (exclusively T words), and 112 (exclusively Lk's words). However, 222-112
      is strongly negative (T/L words don't look like Lk's words), but 002-112 is
      positive (T/L words plus Lk's words look like Lk's words). The only
      conclusion to be drawn from this is that the proportion of T/L words in 002
      (if any) is so small that it has no effect on the style of 002, and
      therefore 002 is (almost) entirely Lk's own words. The only reasonable
      conclusions to be drawn from this are:

      1 L (the source of 002) is Lk
      2 T (the source of 222) is not Lk

      Dave Inglis
      david@...
      3538 O'Connor Drive
      Lafayette, CA, USA



      Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
      List Owner: Synoptic-L-Owner@...
    • Brian E. Wilson
      Dave Inglis wrote -- ... Dave, To make your argument solid, do you not need to define correlation ? You say that each of the sondergut categories has a
      Message 2 of 26 , Jan 26, 2002
        Dave Inglis wrote --
        >
        >I'm trying to put together some solid arguments for various
        >conclusions based on Dave Gentile's data. Be[fore] I go any further,
        >please could I ask anyone who is interested to find holes in the
        >following reasoning. ...
        >
        >Each of the sondergut categories has a negative correlation with the
        >other two (suggesting different sources for all three)...
        >
        >Therefore, as would be expected, 222-112 is strongly negative. ...
        >
        >However, 002-112 is very strongly positive, and hence ...
        >
        Dave,
        To make your argument solid, do you not need to define
        "correlation"? You say that "each of the sondergut categories has a
        negative correlation with the other two", but various people on this
        List have already argued that the infamous 200-020 is not a correlation
        in any meaningful sense of the word. The absolute value of r is as low
        as 0.03402, and p has an extraordinarily large value of over a half,
        indicating that the value of r is in any case more likely than not to be
        the consequence of mere chance.

        Equally, what about defining what a "strongly" negative, or positive,
        correlation is? According to the contributions of scientist to this
        List, in physics, for instance, a result with a value of r less than
        0.7 would be regarded as useless. Yet the value of r for 222-112 which
        you describe as "strongly negative" is less than 0.5 .

        Similarly with "very strongly" positive, or negative. Should not this be
        r with a value greater than 0.9 ? The value for r for 002-112, which you
        cnnsider "very strongly positive" is only just over 0.5 , at 0.52023 .

        In my opinion, it is beyond reasonable doubt that there is some sort of
        documentary relationship between the synoptic gospels. The similarities
        of wording and order of material (which go much further than those
        considered in Dave Gentile's tables of results) show beyond reasonable
        doubt that, in the case of each pair of synoptic gospels, either one is
        the documentary descendant of the other, or both are documentary
        descendants of either the remaining synoptic gospel or a hypothetical
        documentary source. I think it is unreasonable not to accept this
        "General Documentary Hypothesis". I would suggest that, as far as
        tracing particular documentary linkages, however, Dave Gentile's results
        cannot take us beyond this. Dave's results contain no clear indications
        of any particular documentary linkage in a specified direction between
        any two synoptic gospels, or between a synoptic gospel and any posited
        hypothetical source. I would suggest the one clear indication his
        results give us is that each synoptist redacted his source material in
        his own way. If, separately from Dave's results, we posit a synoptic
        documentary hypothesis, then the correlations results can be used to
        investigate more fully how each synoptist did redact his source material
        under that documentary hypothesis. For instance, under the Griesbach
        Hypothesis, it can be more fully investigated how Mark redacted Luke,
        whereas under the Farrer Hypothesis, it can be seen more clearly how
        Luke redacted Mark, and so on.

        Best wishes,
        BRIAN WILSON

        >HOMEPAGE http://www.twonh.demon.co.uk/

        Rev B.E.Wilson,10 York Close,Godmanchester,Huntingdon,Cambs,PE29 2EB,UK
        > "What can be said at all can be said clearly; and whereof one cannot
        > speak thereof one must be silent." Ludwig Wittgenstein, "Tractatus".
        _

        Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
        List Owner: Synoptic-L-Owner@...
      • Ron Price
        ... Dave, A commendable idea. ... But here we already run into a problem, for it appears from this statement that you must be using the data in which a (0,0)
        Message 3 of 26 , Jan 26, 2002
          David Inglis wrote:

          >I'm trying to put together some solid arguments for various conclusions
          >based on Dave Gentile's data.

          Dave,
          A commendable idea.

          >Each of the sondergut categories has a negative correlation with the other
          >two

          But here we already run into a problem, for it appears from this
          statement that you must be using the data in which a (0,0) result counts
          towards the confidence level. If this is so, and if this is indeed the
          way Dave Gentile's last set of results have been arrived at, then some
          of the confidence levels are artificially inflated (as Stephen Carlson
          pointed out) and therefore unreliable.
          I think you mentioned the possibility of adjusting the cut-off to
          around 0.00000000001. This miniscule figure seems to reflect a highly
          artificial situation. Admittedly I also suggested tightening the cut-off
          value, but on second thoughts this wouldn't be right because it would
          not make enough allowance for comparisons having a very large number of
          (0,0)s, but on the other hand it would tend to unduly penalize
          comparisons having very few of them.

          If it really is impractical to include the (0,x) and (x,0) results
          whilst excluding the (0,0) results, then surely we should either utilize
          an effective 'sample size' which ignores the (0,0) results when
          calculating the confidence level, or we should go back to the first set
          of A_W results.

          In any case I think you should have stated which set of Dave Gentile's
          data and what confidence level you are using.

          Ron Price

          Weston-on-Trent, Derby, UK

          e-mail: ron.price@...

          Web site: http://homepage.virgin.net/ron.price/index.htm

          Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
          List Owner: Synoptic-L-Owner@...
        • David Inglis
          ... other ... Whoops, my mistake. I don t need them to be negative, just to not show a correlation, and for this the non-zero data is fine. I ve been
          Message 4 of 26 , Jan 26, 2002
            Ron Price wrote:

            > Dave,
            > A commendable idea.
            >
            > >Each of the sondergut categories has a negative correlation with the
            other
            > >two
            >
            > But here we already run into a problem, for it appears from this
            > statement that you must be using the data in which a (0,0) result counts
            > towards the confidence level. If this is so, and if this is indeed the
            > way Dave Gentile's last set of results have been arrived at, then some
            > of the confidence levels are artificially inflated (as Stephen Carlson
            > pointed out) and therefore unreliable.

            Whoops, my mistake. I don't need them to be negative, just to not show a
            correlation, and for this the 'non-zero' data is fine. I've been looking at
            the 'zero' data a lot and mixed them up.

            > I think you mentioned the possibility of adjusting the cut-off to
            > around 0.00000000001. This miniscule figure seems to reflect a highly
            > artificial situation. Admittedly I also suggested tightening the cut-off
            > value, but on second thoughts this wouldn't be right because it would
            > not make enough allowance for comparisons having a very large number of
            > (0,0)s, but on the other hand it would tend to unduly penalize
            > comparisons having very few of them.

            If someone could suggest a good 'P' value to use with this data then I'd
            love to use it. Perhaps reducing the cut-off by either a factor of 10 or
            100 would be more reasonable?

            > If it really is impractical to include the (0,x) and (x,0) results
            > whilst excluding the (0,0) results, then surely we should either utilize
            > an effective 'sample size' which ignores the (0,0) results when
            > calculating the confidence level, or we should go back to the first set
            > of A_W results.
            >
            > In any case I think you should have stated which set of Dave Gentile's
            > data and what confidence level you are using.

            Yes, I should have. It's the 'non-zero' results, with P<=0.0003 (unless
            I've made other mistakes).

            > Ron Price
            >
            > Weston-on-Trent, Derby, UK
            >
            > e-mail: ron.price@...
            >
            > Web site: http://homepage.virgin.net/ron.price/index.htm
            >
            > Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
            > List Owner: Synoptic-L-Owner@...



            Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
            List Owner: Synoptic-L-Owner@...
          • David Inglis
            ... Yes. As I replied to Ron Price, I was (incorrectly) looking at the zeros data from Dave Gentile. However, as all I needed to show here was a lack of
            Message 5 of 26 , Jan 26, 2002
              Brian Wilson wrote:

              > Dave,
              > To make your argument solid, do you not need to define
              > "correlation"? You say that "each of the sondergut categories has a
              > negative correlation with the other two", but various people on this
              > List have already argued that the infamous 200-020 is not a correlation
              > in any meaningful sense of the word. The absolute value of r is as low
              > as 0.03402, and p has an extraordinarily large value of over a half,
              > indicating that the value of r is in any case more likely than not to be
              > the consequence of mere chance.

              Yes. As I replied to Ron Price, I was (incorrectly) looking at the 'zeros'
              data from Dave Gentile. However, as all I needed to show here was a lack of
              any correlation, then that's still OK with the earlier data.

              > Equally, what about defining what a "strongly" negative, or positive,
              > correlation is? According to the contributions of scientist to this
              > List, in physics, for instance, a result with a value of r less than
              > 0.7 would be regarded as useless. Yet the value of r for 222-112 which
              > you describe as "strongly negative" is less than 0.5 .
              >
              > Similarly with "very strongly" positive, or negative. Should not this be
              > r with a value greater than 0.9 ? The value for r for 002-112, which you
              > cnnsider "very strongly positive" is only just over 0.5 , at 0.52023 .

              In the first place, I need to be more careful with my terms. I don't think
              that 'strongly negative' and 'strongly positive' have any statistical
              meaning, so I shouldn't say this. Perhaps it would be better to just say
              'positive' or 'negative' and then actually quote the 'p' and 'r' values.
              Secondly, I too have a problem with the generally low absolute values of 'r'
              reported, even where 'p' is very small. I have been previously used to
              using mod r = 0.7 as my 'cut off', but here that doesn't seem to work. So,
              what's different?

              Well, as has been explained many, many, many times, there is a 'negative
              bias' in the design of the experiment. Because all our correlations are
              looking at 'frequency shifts' in comparison to an average, categories that
              are the result of independent documentary processes will tend to produce
              negative correlations because of word frequencies straddling the average.
              This effect is something I've been trying to eliminate, but so far with no
              success.

              Dave Gentile suggested all the correlations have a negative bias
              of -(1/(19-1)) = -0.0556, but I don't think this can be correct because it
              can't account for things like 221-112 = -0.52. On the other hand, just
              adding 0.52 to all results in order to make sure that none are negative is
              obviously wrong as well, because that would make 021-121 = 1.21! In my
              view, every correlation requires it's own unique positive adjustment, but
              I've no idea what the right value should be. Perhaps for now the correct
              thing to do is to use only the value of P to determine whether to ignore a
              result or not. If so, does the following work?

              1 If P<=0.0003 and r is positive then the two categories have a
              documentary relationship.
              2 If P<=0.0003 and r is negative then the two categories do not have a
              documentary relationship.
              3 Anything else means we just can't tell.

              If not, then PLEASE can someone (Stephen?) tell us how to determine what
              value of 'r' we should consider to be a 'cut off'. Is '0.3' a good value to
              use? What from I've read so far I don't believe anyone has suggested a
              specific value, but perhaps I've been misunderstanding what has been
              written.

              > In my opinion, it is beyond reasonable doubt that there is some sort of
              > documentary relationship between the synoptic gospels. The similarities
              > of wording and order of material (which go much further than those
              > considered in Dave Gentile's tables of results) show beyond reasonable
              > doubt that, in the case of each pair of synoptic gospels, either one is
              > the documentary descendant of the other, or both are documentary
              > descendants of either the remaining synoptic gospel or a hypothetical
              > documentary source. I think it is unreasonable not to accept this
              > "General Documentary Hypothesis".

              Generally accepted, except that you need to limit what you have written to
              just parts of the gospels. At the moment you are implying that 'whole
              gospels' are documentary descendants of something else, which is NOT
              supported by any results that I know of. If you had stated "either part of
              one is the documentary descendant of the other, or parts of both are
              documentary descendants of either the remaining synoptic gospel or a
              hypothetical documentary source" then I would have agreed with you.

              > I would suggest that, as far as
              > tracing particular documentary linkages, however, Dave Gentile's results
              > cannot take us beyond this.

              This is where we differ.

              > Dave's results contain no clear indications
              > of any particular documentary linkage in a specified direction between
              > any two synoptic gospels, or between a synoptic gospel and any posited
              > hypothetical source.

              In my posting I wasn't suggesting any 'direction' (e.g. chronology).

              > I would suggest the one clear indication his
              > results give us is that each synoptist redacted his source material in
              > his own way.

              I think we would have to assume this whatever the situation.

              Now, apart from the above, is there anything else in what I wrote regarding
              002 NOT being an edited part of the same source from which 222 was taken
              that doesn't hold up?

              Dave Inglis
              david@...
              3538 O'Connor Drive
              Lafayette, CA, USA



              Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
              List Owner: Synoptic-L-Owner@...
            • Brian E. Wilson
              Dave Inglis wrote -- ... Dave, With regard to number 1 above, 112-002 has r = 0.51917 and p
              Message 6 of 26 , Jan 27, 2002
                Dave Inglis wrote --
                >
                >does the following work?
                >1 If P<=0.0003 and r is positive then the two categories have a
                >documentary relationship.
                >2 If P<=0.0003 and r is negative then the two categories do not have a
                >documentary relationship.
                >3 Anything else means we just can't tell.
                >
                Dave,
                With regard to number 1 above, 112-002 has r = 0.51917 and
                p<0.0001, but I see no need to posit any documentary relationship
                between the passages containing these categories. The observed positive
                correlation can be accounted for as the result of Luke having overlaid
                his style on all the material in his gospel. The same argument applies
                to 112-012 with r = 0.32063 and p<0.0001 .

                With regard to number 2 above, 202-112 has r = -0.29366 and p<0.0001. I
                see no reason, however, why the 202 passages (the double tradition) and
                the 112 passages (the triple tradition), should not have been "Q" and
                Mark in the Fleddermann Hypothesis in which Mark is a documentary
                descendant of Q. The observed negative correlation could well be the
                result of Luke having followed the 202 words of Q (along with Matthew)
                but having supplied words of his own choosing in the triple tradition in
                the 112 words, the styles therefore being observably different and
                producing a negative correlation. The negative correlation does not rule
                out a documentary relationship, therefore.

                With regard to 3 above, I would simply omit the word "else", and say
                that we just can't tell any documentary particular documentary
                relationship from the correlations results observed. Of course the
                "General Documentary Hypothesis" is true, but no particular synoptic
                documentary hypothesis can be falsified or verified from the observed
                HHBC correlations. In this respect, the 2DH, FH, GH, 3SH, and so on, are
                safe.

                Best wishes,
                BRIAN WILSON

                >HOMEPAGE http://www.twonh.demon.co.uk/

                Rev B.E.Wilson,10 York Close,Godmanchester,Huntingdon,Cambs,PE29 2EB,UK
                > "What can be said at all can be said clearly; and whereof one cannot
                > speak thereof one must be silent." Ludwig Wittgenstein, "Tractatus".
                _

                Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
                List Owner: Synoptic-L-Owner@...
              • Brian E. Wilson
                Dave Inglis wrote -- ... Dave, A specific value has been suggested. Bruce Merrill wrote, some weeks ago, -- ... On this view, a cut off absolute value for r of
                Message 7 of 26 , Jan 27, 2002
                  Dave Inglis wrote --
                  >
                  >PLEASE can someone (Stephen?) tell us how to determine what value of
                  >'r' we should consider to be a 'cut off'. Is '0.3' a good value to
                  >use? What from I've read so far I don't believe anyone has suggested
                  >a specific value, but perhaps I've been misunderstanding what has been
                  >written.
                  >
                  Dave,
                  A specific value has been suggested. Bruce Merrill wrote, some
                  weeks ago, --
                  >
                  >There is no widely accepted objective definition of a "strong"
                  >correlation. A correlation of 0.7 explains only half the variability
                  >in the data (i.e., if r=0.7, r**2 =0.7**2 =0.49 or approximately
                  >half), so many researchers begin talking about meaningful
                  >correlations when the absolute value reaches 0.7, with strong
                  >correlations being somewhat greater than 0.7 (or strong negative
                  >correlations being somewhat less than -0.7).
                  >
                  On this view, a cut off absolute value for r of 0.3 is far too low. the
                  value only *begins* to be meaningful at 0.7 .

                  Best wishes,
                  BRIAN WILSON

                  >HOMEPAGE http://www.twonh.demon.co.uk/

                  Rev B.E.Wilson,10 York Close,Godmanchester,Huntingdon,Cambs,PE29 2EB,UK
                  > "What can be said at all can be said clearly; and whereof one cannot
                  > speak thereof one must be silent." Ludwig Wittgenstein, "Tractatus".
                  _

                  Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
                  List Owner: Synoptic-L-Owner@...
                • Ron Price
                  ... Dave, Thanks. But I m still torn between taking the results at face value then simply seeking explanations, and using my NT knowledge (which is of course
                  Message 8 of 26 , Jan 28, 2002
                    David Inglis wrote:

                    >[I'm using] the 'non-zero' results, with P<=0.0003

                    Dave,
                    Thanks.
                    But I'm still torn between taking the results at face value then
                    simply seeking explanations, and using my NT knowledge (which is of
                    course debatable) to shed light on the best technique.
                    It is rather curious that if we reject correlations with absolute
                    values <0.3, then arguably all the quirky results disappear. It would
                    even be possible then to dispense entirely with the P values (which
                    anyway correlate closely with the r values). The same thing is probably
                    true also with the second set of results (including the (0,0)s) if we
                    reject all ABS(r)<0.235. I just wonder if there might be some reason as
                    yet undiscovered why an r cut-off gives 'better' (at least more
                    consistent) results than a P cut-off. Perhaps the P calculation is
                    slightly flawed here. For it assumes each different word is independent
                    of all the others, whereas the usage of some of them might be related,
                    for example, EIPEN and AUTOIS; LEGW and hUMIN.

                    After yet another diversion, let's get back to the deductions from the
                    stated starting point.

                    > ..... One thing we can say is that
                    >either T [222] is not the same source as M, K, and L, or Mt, Mk, and Lk all
                    >edited this common source sufficiently to remove all positive correlations
                    >among 222, 200, 020, and 002.

                    I think it is a little dubious to make deductions from the absence of
                    correlations, in this case regarding 222-200 and 222-020. Surely it
                    would be safer to base our deductions on the positive and negative
                    correlations.

                    > ..... The only reasonable conclusions [from 002-112 positive; 222-002
                    negative; 222-112 negative] are:
                    >
                    >1 L (the source of 002) is Lk
                    >2 T (the source of 222) is not Lk

                    Agreed.

                    Ron Price

                    Weston-on-Trent, Derby, UK

                    e-mail: ron.price@...

                    Web site: http://homepage.virgin.net/ron.price/index.htm

                    Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
                    List Owner: Synoptic-L-Owner@...
                  • David Inglis
                    ... I ve just posted a lengthy explanation of why I think we can take values of r down to 0.3 (actually, slightly below that) as indicating strong
                    Message 9 of 26 , Jan 28, 2002
                      Ron Price wrote:

                      > It is rather curious that if we reject correlations with absolute
                      > values <0.3, then arguably all the quirky results disappear. It would
                      > even be possible then to dispense entirely with the P values (which
                      > anyway correlate closely with the r values).

                      I've just posted a lengthy explanation of why I think we can take values of
                      r down to 0.3 (actually, slightly below that) as indicating 'strong'
                      correlations, but as I'm not sure how rock-solid (if at all!) my argument
                      is, I'd rather stick to a P cut-off if I had to make a choice.

                      > The same thing is probably
                      > true also with the second set of results (including the (0,0)s) if we
                      > reject all ABS(r)<0.235. I just wonder if there might be some reason as
                      > yet undiscovered why an r cut-off gives 'better' (at least more
                      > consistent) results than a P cut-off. Perhaps the P calculation is
                      > slightly flawed here. For it assumes each different word is independent
                      > of all the others, whereas the usage of some of them might be related,
                      > for example, EIPEN and AUTOIS; LEGW and hUMIN.

                      I'm sure the usage IS related. After all, they have to obey the rules of
                      Greek semantics, and hence some word orderings will be common, and some will
                      never appear. How this affects P I've no idea.

                      > > ..... One thing we can say is that
                      > >either T [222] is not the same source as M, K, and L, or Mt, Mk, and Lk
                      all
                      > >edited this common source sufficiently to remove all positive
                      correlations
                      > >among 222, 200, 020, and 002.
                      >
                      > I think it is a little dubious to make deductions from the absence of
                      > correlations, in this case regarding 222-200 and 222-020. Surely it
                      > would be safer to base our deductions on the positive and negative
                      > correlations.

                      Generally, I agree with you. However, in this case I think I'm actually
                      stating a basic assumption, i.e. here's two explanations for a lack of a
                      positive correlation:

                      1 T is not the same as M, K, and L, or:
                      2 T was heavily edited during the production of M, K, and L.

                      It's probably better to state this up front, and perhaps expand on it. I'll
                      think about how best to do this.

                      > > ..... The only reasonable conclusions [from 002-112 positive; 222-002
                      > negative; 222-112 negative] are:
                      > >
                      > >1 L (the source of 002) is Lk
                      > >2 T (the source of 222) is not Lk
                      >
                      > Agreed.

                      Once I've got this pretty solid, I'll expand the logic to Matthew, and then
                      to Mark.

                      Dave Inglis
                      david@...
                      3538 O'Connor Drive
                      Lafayette, CA, USA



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                    • David Inglis
                      ... I shouldn t have included the word documentary . As you ve just shown, other kinds of relationships apply equally well. ... You are right. A negative
                      Message 10 of 26 , Jan 28, 2002
                        Brian Wilson wrote:

                        > Dave Inglis wrote --
                        > >
                        > >does the following work?
                        > >1 If P<=0.0003 and r is positive then the two categories have a
                        > >documentary relationship.
                        > >2 If P<=0.0003 and r is negative then the two categories do not have a
                        > >documentary relationship.
                        > >3 Anything else means we just can't tell.
                        > >
                        > Dave,
                        > With regard to number 1 above, 112-002 has r = 0.51917 and
                        > p<0.0001, but I see no need to posit any documentary relationship
                        > between the passages containing these categories. The observed positive
                        > correlation can be accounted for as the result of Luke having overlaid
                        > his style on all the material in his gospel. The same argument applies
                        > to 112-012 with r = 0.32063 and p<0.0001 .

                        I shouldn't have included the word 'documentary'. As you've just shown,
                        other kinds of relationships apply equally well.
                        >
                        > With regard to number 2 above, 202-112 has r = -0.29366 and p<0.0001. I
                        > see no reason, however, why the 202 passages (the double tradition) and
                        > the 112 passages (the triple tradition), should not have been "Q" and
                        > Mark in the Fleddermann Hypothesis in which Mark is a documentary
                        > descendant of Q. The observed negative correlation could well be the
                        > result of Luke having followed the 202 words of Q (along with Matthew)
                        > but having supplied words of his own choosing in the triple tradition in
                        > the 112 words, the styles therefore being observably different and
                        > producing a negative correlation. The negative correlation does not rule
                        > out a documentary relationship, therefore.

                        You are right. A negative correlation doesn't rule out a documentary
                        relationship. It is possible that 112 is the result of Luke editing part of
                        Q so heavily that the word frequency patterns in 202 and 112 are so
                        different as to produce a negative correlation. However, this is a bit like
                        a witness on a stand being forced to answer the question: "Yes, but is it
                        possible?", even when the chances of it having happened that way are so low
                        as to make it almost certain that it didn't happen.

                        That's the problem with ANY statistical method. It can't totally rule out
                        even highly improbable events, because there's no absolute proof of
                        anything. In this particular case, is it possible that Luke could have so
                        changed that words of Q that 112 looks so unlike Q? Yes, he could have done
                        it, and therefore we can't totally rule it out. However, such a change is
                        tantamount to saying that what Luke did is read passages in Q and then
                        completely re-write them. Again, it's possible. However, is it likely? Is
                        it probable? Do we have any evidence that Luke had a tendency to do this?
                        And even if Luke DID do this, can we say that this then produces a
                        'relationship' between 202 and 112?

                        > With regard to 3 above, I would simply omit the word "else", and say
                        > that we just can't tell any documentary particular documentary
                        > relationship from the correlations results observed. Of course the
                        > "General Documentary Hypothesis" is true, but no particular synoptic
                        > documentary hypothesis can be falsified or verified from the observed
                        > HHBC correlations. In this respect, the 2DH, FH, GH, 3SH, and so on, are
                        > safe.

                        We can't 'prove' anything from the correlations, and therefore no hypothesis
                        can be provably falsified or verified. However, this is no different from
                        any other evidence that has been brought to bear on the synoptic problem -
                        there's no absolute proof! All we have is possibilities and probabilities,
                        and what's likely and what's not. If you insist that this particular
                        evidence doesn't "tell any [] particular documentary relationship", then you
                        must allow that the same applies to all the other evidence, so why don't we
                        all just give up now?

                        Dave Inglis
                        david@...
                        3538 O'Connor Drive
                        Lafayette, CA, USA



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                      • Emmanuel Fritsch
                        I have some objections to the first mail of ... I absolutely disagree about this conclusion. Consider the following schema : pMk + pMt = Mt (with predominance
                        Message 11 of 26 , Jan 28, 2002
                          I have some objections to the first mail of
                          David Inglis that launched this thread :

                          > I'm trying to put together some solid arguments for various conclusions
                          > based on Dave Gentile's data. Because I go any further, please could I ask
                          > anyone who is interested to find holes in the following reasoning. Note:
                          > In the descriptions below Mt, Mk, and Lk represent the synoptists who
                          > created the Gospels of Matthew, Mark, and Luke respectively.
                          >
                          > Four categories contain words common to either two or all three of the
                          > Gospels. These are 222, 220, 202, and 022. Starting with 222, this
                          > contains triple tradition words that appear in Matthew, Mark, and Luke.
                          > Assuming that these common words were not all independently selected by Mt,
                          > Mk, and Lk, then these words all came from the same source (which I'm going
                          > to call T).

                          I absolutely disagree about this conclusion.

                          Consider the following schema :

                          pMk + pMt => Mt (with predominance of pMt)
                          pMk + Mt => Mk (with predominance of pMk)
                          Mk + Mt => Lk

                          You may find in 222 some words originally found
                          in pMt, and some others originally found in pMt.

                          I think synoptic problem would be so easy to solve if
                          each xyz category would have been written by a single
                          author, without interferences with the other.

                          For instance, Brian may answer you (and I disagree with
                          Brian, but this is another trouble) that in his own theory,
                          sondergut Lukan genealogy of Jesus comes from the original
                          document, and so should share some comon vocabulary with 222.

                          a+
                          manu

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                        • Brian E. Wilson
                          Dave Inglis wrote -- ... Dave, I think we can prove some things from the correlations. For instance, we can prove beyond reasonable doubt that each synoptist
                          Message 12 of 26 , Jan 29, 2002
                            Dave Inglis wrote --
                            >
                            >We can't 'prove' anything from the correlations, and therefore no
                            >hypothesis can be provably falsified or verified. However, this is no
                            >different from any other evidence that has been brought to bear on the
                            >synoptic problem - there's no absolute proof! All we have is
                            >possibilities and probabilities, and what's likely and what's not. If
                            >you insist that this particular evidence doesn't "tell any []
                            >particular documentary relationship", then you must allow that the same
                            >applies to all the other evidence, so why don't we all just give up
                            >now?
                            >
                            Dave,
                            I think we can prove some things from the correlations. For
                            instance, we can prove beyond reasonable doubt that each synoptist
                            redacted his source material (whatever that may have been) in is own
                            way. What we cannot do is use just the correlations to prove true any
                            particular documentary relationship between the synoptic gospels.

                            I think, too, that we can provably falsify some documentary hypotheses.
                            It is easy to put forward a synoptic documentary hypothesis that can be
                            shown beyond reasonable doubt to be false. Consider, for instance, the
                            hypothesis that Mark used Luke as his only source, and Matthew used Mark
                            as his only source. Beyond reasonable doubt this is false, since the
                            double tradition occurs in both Luke and Matthew in similar wording and
                            order. Therefore, on the hypothesis posited, we are driven to the
                            unreasonable conclusion that Matthew would have had coincidentally to
                            have produced out of his own head the double tradition found in Luke.
                            And so the hypothesis posited is false beyond reasonable doubt.

                            I do not think we are left with only what is possible or probable. We
                            have the certainty that some hypotheses are false beyond reasonable
                            doubt.

                            Moreover, I would suggest that the logical conclusion of your argument
                            above is not that we should all just give up now, but rather that anyone
                            who is trying to find absolute proof of a synoptic documentary
                            hypothesis should realize he is on the wrong track. Scientists do not
                            attempt to find absolute proof of their hypotheses. They have more sense
                            than to try and do the impossible. Why should we attempt the impossible
                            in the study of the synoptic problem?

                            Isn't what we need a method that does not aim at absolute proof, but at
                            the hypothesis that best fits the observed facts? I would suggest that
                            this might be (1) posit any synoptic documentary hypothesis, however
                            ridiculous it might seem, (2) test the hypothesis against the data
                            observed in the synoptic gospels. If it accounts for the data without
                            difficulty, accept it as a solution to the synoptic problem. Otherwise
                            go back to the beginning, (3) if more that one solution is found, use
                            Ockham's Razor to reject unnecessarily complex hypotheses, and if more
                            than one solution still remains, accept the most probable one, (4)
                            assume that the accepted solution is only provisional, and go back to
                            step (1) thus indefinitely continuing the loop.

                            Best wishes,
                            BRIAN WILSON

                            >HOMEPAGE http://www.twonh.demon.co.uk/

                            Rev B.E.Wilson,10 York Close,Godmanchester,Huntingdon,Cambs,PE29 2EB,UK
                            > "What can be said at all can be said clearly; and whereof one cannot
                            > speak thereof one must be silent." Ludwig Wittgenstein, "Tractatus".
                            _


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                          • Brian E. Wilson
                            Emmanuel Fritsch wrote -- ... Emmanuel, On my hypothesis, the 222 words are what Mt, Mk and Lk coincidentally agreed in retaining from the common source, as
                            Message 13 of 26 , Jan 29, 2002
                              Emmanuel Fritsch wrote --
                              >
                              >For instance, Brian may answer you (and I disagree with Brian, but this
                              >is another trouble) that in his own theory, sondergut Lukan genealogy
                              >of Jesus comes from the original document, and so should share some
                              >common vocabulary with 222.
                              >
                              Emmanuel,
                              On my hypothesis, the 222 words are what Mt, Mk and Lk
                              coincidentally agreed in retaining from the common source, as the
                              synoptists each independently selected, and edited, the same material.
                              Sondergut Luke was selected by only Luke, and is overlaid by his style
                              as he edited his source material. The style of 222 is therefore
                              artificially created by the coincidental agreement of all three
                              synoptists, whereas the style of sondergut Luke could well be largely
                              the style of writing of Luke himself. My hypothesis is therefore fully
                              consistent with the styles of 222 and sondergut Luke being very
                              different. The difference of style is not a problem for the LTH.

                              The same sort of difference apparently occurs within the triple
                              tradition passages. One of the advantages of the Hieke, Hoffmann and
                              Bauer "Synoptic Concordance" (HHBC) is that it identifies the 222 words
                              in common in the triple tradition, and distinguishes these from the more
                              frequent 112 words found only in Luke that are in the same triple
                              tradition passages. As we have seen above, the 222 words are in a style
                              artificially-created by the coincidental agreement of all three
                              synoptists in the triple tradition, and here, the 112 words, are where
                              Luke has overlaid the triple tradition with his own style. Notice that
                              the 112 words are more frequent in the triple tradition than the 222
                              words. Luke drastically imposes his own style on his source material in
                              the triple tradition. The negative correlation 222-112 in Dave Gentile's
                              correlations results, high-lights the difference between the
                              artificially-created style of 222 in the triple tradition, and the
                              overlaid style of Luke in the more numerous 112 words in the same
                              passages.

                              On this view, of course, the positive 112-002 correlation is fully
                              consistent with both 112 and 002 representing Luke's style. Luke's
                              overlaid style in triple tradition 112 passages correlates positively
                              with Luke's overlaid style in 002 sondergut passages.

                              The style of the common source is preserved almost wherever at least two
                              synoptists agree in wording in parallel passages. (A few exceptions
                              could have arisen if, by coincidence, two synoptists independently
                              supplied the same alteration to the wording of the common source, for
                              instance Mt and Lk agreeing in altering a paratactic KAI to DE within
                              the triple tradition passages, but Mk retaining KAI, and so on.) Thus,
                              in W. R. Farmer's SYNOPTICON, the words with backgrounds in blue,
                              yellow, green and red, are virtually all words from the common source,
                              amounting to just over 8,000 words all told. A possible exception is
                              that some of the words with red backgrounds within triple tradition
                              passages (that is, some of the 212 words, the positive minor agreements)
                              could have been the result of Mt and Lk coincidentally supplying the
                              same wording in their editing of the common source, where Mk retains the
                              original wording.

                              Best wishes,
                              BRIAN WILSON

                              >HOMEPAGE http://www.twonh.demon.co.uk/

                              Rev B.E.Wilson,10 York Close,Godmanchester,Huntingdon,Cambs,PE29 2EB,UK
                              > "What can be said at all can be said clearly; and whereof one cannot
                              > speak thereof one must be silent." Ludwig Wittgenstein, "Tractatus".
                              _

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                            • David Inglis
                              ... . ... Mt, ... going ... As understand it, all you re saying is that T could be more than one document, which is fine by me. I wasn t trying to suggest
                              Message 14 of 26 , Jan 29, 2002
                                Emmanuel Fritsch wrote:

                                > I have some objections to the first mail of
                                > David Inglis that launched this thread :
                                .
                                > > Four categories contain words common to either two or all three of the
                                > > Gospels. These are 222, 220, 202, and 022. Starting with 222, this
                                > > contains triple tradition words that appear in Matthew, Mark, and Luke.
                                > > Assuming that these common words were not all independently selected by
                                Mt,
                                > > Mk, and Lk, then these words all came from the same source (which I'm
                                going
                                > > to call T).
                                >
                                > I absolutely disagree about this conclusion.
                                >
                                > Consider the following schema :
                                >
                                > pMk + pMt => Mt (with predominance of pMt)
                                > pMk + Mt => Mk (with predominance of pMk)
                                > Mk + Mt => Lk
                                >
                                > You may find in 222 some words originally found
                                > in pMt, and some others originally found in pMt.

                                As understand it, all you're saying is that 'T' could be more than one
                                document, which is fine by me. I wasn't trying to suggest that the "same
                                source" had to be just one document. Perhaps I should change it to read
                                "same source or sources".

                                Dave Inglis
                                david@...
                                3538 O'Connor Drive
                                Lafayette, CA, USA





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                              • Emmanuel Fritsch
                                ... But even that is not strictly good. Just looking to the answer of Brian to my mail, I find this words : As we have seen above, the 222 words are in a
                                Message 15 of 26 , Jan 29, 2002
                                  I wrote :
                                  > You may find in 222 some words originally found
                                  > in pMt, and some others originally found in pMt.

                                  David Inglis answered :
                                  > As understand it, all you're saying is that 'T' could be more than one
                                  > document, which is fine by me. I wasn't trying to suggest that the "same
                                  > source" had to be just one document. Perhaps I should change it to read
                                  > "same source or sources".

                                  But even that is not strictly good. Just looking to
                                  the answer of Brian to my mail, I find this words :

                                  "As we have seen above, the 222 words are in a style
                                  artificially-created by the coincidental agreement of
                                  all three synoptists in the triple tradition"

                                  So according Brian, 222 vocabulary may also come from coincidence,
                                  and not from an assumed document.

                                  And as I said before, even in the LTH, a so simple synoptic theory,
                                  you may think that sondergut wear some LT original vocabulary. And
                                  this may be said for all the XYZ category.

                                  I do not want to say Brian is right or false. I just want to
                                  point that consensus should be hard to find on your proof, just
                                  from the beginning.

                                  a+
                                  manu

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                                • David Inglis
                                  ... Like you, I believe that each synoptist redacted his source material (whatever that may have been) in [h]is own way . Indeed, I doubt that there s anyone
                                  Message 16 of 26 , Jan 29, 2002
                                    Brian Wilson wrote:
                                    > Dave,
                                    > I think we can prove some things from the correlations. For
                                    > instance, we can prove beyond reasonable doubt that each synoptist
                                    > redacted his source material (whatever that may have been) in is own
                                    > way.

                                    Like you, I believe that each synoptist "redacted his source material
                                    (whatever that may have been) in [h]is own way". Indeed, I doubt that
                                    there's anyone who disagrees with this statement. However, the correlations
                                    don't provided ANY proof of this, since the statement is self-evident, and
                                    requires no proof. In other words, this statement would work with ANY set
                                    of correlations, or ANY hypothesis, since what you are saying, in effect is:
                                    "each synoptist used whatever source materials he chose to use, copied
                                    whatever parts he wanted to copy, and changed whatever parts he wanted to
                                    change, in whatever way he wanted to change them".

                                    Dave Inglis
                                    david@...
                                    3538 O'Connor Drive
                                    Lafayette, CA, USA




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                                  • David Inglis
                                    ... same ... As I understand Brian, he is correct here. Whatever T (the source of 222) was the vocabulary of 222 can come from a coincidental agreement among
                                    Message 17 of 26 , Jan 29, 2002
                                      Emmanuel Fritsch wrote:

                                      > David Inglis answered :
                                      > > As understand it, all you're saying is that 'T' could be more than one
                                      > > document, which is fine by me. I wasn't trying to suggest that the
                                      "same
                                      > > source" had to be just one document. Perhaps I should change it to read
                                      > > "same source or sources".
                                      >
                                      > But even that is not strictly good. Just looking to
                                      > the answer of Brian to my mail, I find this words :
                                      >
                                      > "As we have seen above, the 222 words are in a style
                                      > artificially-created by the coincidental agreement of
                                      > all three synoptists in the triple tradition"
                                      >
                                      > So according Brian, 222 vocabulary may also come from coincidence,
                                      > and not from an assumed document.

                                      As I understand Brian, he is correct here. Whatever T (the source of 222)
                                      was the vocabulary of 222 can come from a coincidental agreement among the
                                      synoptists. For some (unknown) reasons they each decided to include all the
                                      222 words in their own gospels, and these reasons (which could be
                                      coincidental) determined the vocabulary in 222. Now it is just possible
                                      that each synoptist decided to include the same passage, and that each
                                      independently used some words in that passage that were exactly the same,
                                      even though they had no immediate common source for the passage. However,
                                      unless they each fabricated this passage, then I think you have to admit
                                      that ultimately there must have been a common source of some kind, even if
                                      it was only oral. It is also possible that by the time this story reached
                                      the synoptists some of the words were different, and that one or more
                                      synoptist coincidentally made changes that brought the words back into
                                      alignment. So, yes, it is just possible that some of the words in 222 did
                                      not come an immediate common source and are there by chance or coincidence,
                                      but I cannot believe that these words constitute more than a tiny fraction.

                                      > And as I said before, even in the LTH, a so simple synoptic theory,
                                      > you may think that sondergut wear some LT original vocabulary. And
                                      > this may be said for all the XYZ category.

                                      Yes, of course. Some of 002 could potentially have come from part of a
                                      common source that only Luke selected. However, as I pointed out, the
                                      styles of 222 and 002 are so different that if 002 does still contain words
                                      from this common source, then then also constitute only a tiny fraction.

                                      Dave Inglis
                                      david@...
                                      3538 O'Connor Drive
                                      Lafayette, CA, USA




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                                    • Brian E. Wilson
                                      Brian Wilson wrote -- ... Dave Inglis commented -- ... Dave, I am saying more than this. I am saying that no synoptist made it all up out of his own head. That
                                      Message 18 of 26 , Jan 30, 2002
                                        Brian Wilson wrote --
                                        >
                                        >each synoptist redacted his source material (whatever that may have
                                        >been) in is own way.
                                        >
                                        Dave Inglis commented --
                                        >
                                        >the statement is self-evident, and requires no proof. In other words,
                                        >this statement would work with ANY set of correlations, or ANY
                                        >hypothesis, since what you are saying, in effect is: "each synoptist
                                        >used whatever source materials he chose to use, copied whatever parts
                                        >he wanted to copy, and changed whatever parts he wanted to change, in
                                        >whatever way he wanted to change them.
                                        >
                                        Dave,
                                        I am saying more than this. I am saying that no synoptist made it
                                        all up out of his own head. That is not self-evident. In theory a
                                        synoptist could have fabricated all the material in his gospel. I am
                                        also saying that no synoptist merely copied the wording of his source
                                        material. That is not self-evident. In theory, any synoptist could have
                                        produced his gospel entirely by copying only the wording of the source
                                        materials he used. There is no necessity that any writer impressed his
                                        own style on his source material. I am also saying that, accepting the
                                        "General Documentary Hypothesis" that each synoptic gospel is in some
                                        way documentarily linked to the others, it is unnecessary to use any
                                        particular documentary hypothesis to account for the observed
                                        correlations. That is not self-evident. Otherwise you would not be
                                        considering the possibility of proving that 222 was not written by Luke.
                                        I am saying that the idea that each synoptist did redact his source
                                        material in his own way is crucial for understanding the observed
                                        correlations. This is not self-evident either.

                                        In mathematics, it is self-evident that any even number greater than 6
                                        can be expressed as the sum of two different prime numbers, (8 = 5 + 3,
                                        10 = 7 + 3, 12 = 7 + 5, 14 = 11 + 3, ... 200 = 37 + 163, ... and so on),
                                        but mathematicians are still waiting for some genius to prove this self-
                                        evidently true statement. They would love to have such a proof, since it
                                        might well be useful for proving dozens of other self-evidently true,
                                        but as yet unproved, statements in number theory. Being self-evident
                                        does not prove a statement true, or place it beyond being proved true.

                                        In a nut-shell, I would suggest that the statement that each synoptist
                                        redacted his source material in his own way is not self-evident, and
                                        that even if it were, that would not place it beyond being proved true
                                        beyond reasonable doubt.

                                        With regard to your own question whether it can be proved from the
                                        observed correlations that 222 was not written by Luke -- I think this
                                        is not possible, since you are trying to prove that Luke was the
                                        documentary descendant of "222", and that "222" was not the documentary
                                        descendant of Luke. I would suggest that the observed correlations
                                        provide no directional indicators of the kind that would be needed to
                                        prove this conclusion. A correlation between any two categories would be
                                        equally consistent with documentary dependence in either direction.

                                        If, for example, on the Two Document Hypothesis, Luke could have
                                        overlaid his style on the 222 passages he took from Mark (resulting in
                                        many 112 words within these passages in Luke), then equally, on the
                                        Griesbach Hypothesis, Mark could have overlaid his style on the 222
                                        passages he took from Luke (resulting in many 121 words within these
                                        passages in Mark). The correlations are consistent with both
                                        possibilities. They give no indication of the *direction* of any
                                        supposed documentary dependence.

                                        Best wishes
                                        BRIAN WILSON

                                        >HOMEPAGE http://www.twonh.demon.co.uk/

                                        Rev B.E.Wilson,10 York Close,Godmanchester,Huntingdon,Cambs,PE29 2EB,UK
                                        > "What can be said at all can be said clearly; and whereof one cannot
                                        > speak thereof one must be silent." Ludwig Wittgenstein, "Tractatus".
                                        _

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                                      • Maluflen@aol.com
                                        In a message dated 1/30/2002 5:28:46 AM Eastern Standard Time, brian@TwoNH.demon.co.uk writes:
                                        Message 19 of 26 , Jan 30, 2002
                                          In a message dated 1/30/2002 5:28:46 AM Eastern Standard Time,
                                          brian@... writes:

                                          << In mathematics, it is self-evident that any even number greater than 6
                                          can be expressed as the sum of two different prime numbers, (8 = 5 + 3,
                                          10 = 7 + 3, 12 = 7 + 5, 14 = 11 + 3, ... 200 = 37 + 163, ... and so on),
                                          but mathematicians are still waiting for some genius to prove this self-
                                          evidently true statement. They would love to have such a proof, since it
                                          might well be useful for proving dozens of other self-evidently true,
                                          but as yet unproved, statements in number theory. Being self-evident
                                          does not prove a statement true, or place it beyond being proved true.>>

                                          Brian, are you using the term "self-evident" properly here? It is certainly
                                          not self-evident to me that "any even number greater than 6 can be expressed
                                          as the sum of two different prime numbers". At the very least, you would have
                                          to introduce here the scholastic distinctions between that which is "per se
                                          nota quoad se" and that which is "per se nota quoad nos", if not even the
                                          further distinction between what is "per se nota quoad nos" and what is
                                          self-evident in an even more narrow sense: "per se nota quoad nos sapientes".
                                          An example of the last mentioned category would be, for instance, the
                                          statement that "immaterial beings are not in a place". I would suggest that
                                          your statement is at best in that last category (dico insipiens ego!).

                                          Leonard Maluf

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                                        • Brian E. Wilson
                                          Brian Wilson wrote -- ... Leonard Maluf asks -- ... Leonard, Yes, as far as mathematicians are concerned. They have no doubt at all that the statement is true.
                                          Message 20 of 26 , Jan 31, 2002
                                            Brian Wilson wrote --
                                            >
                                            >In mathematics, it is self-evident that any even number greater than 6
                                            > can be expressed as the sum of two different prime numbers, (8 = 5 +
                                            >3, 10 = 7 + 3, 12 = 7 + 5, 14 = 11 + 3, ... 200 = 37 + 163, ... and so
                                            >on), but mathematicians are still waiting for some genius to prove this
                                            >self-evidently true statement. They would love to have such a proof,
                                            >since it might well be useful for proving dozens of other self-
                                            >evidently true, but as yet unproved, statements in number theory. Being
                                            >self-evident does not prove a statement true, or place it beyond being
                                            >proved true.
                                            >
                                            Leonard Maluf asks --
                                            >
                                            >Brian, are you using the term "self-evident" properly here?
                                            >
                                            Leonard,
                                            Yes, as far as mathematicians are concerned. They have no doubt
                                            at all that the statement is true. It has been checked by computer for
                                            millions of even numbers. Generally, the larger the even number the
                                            more instances can be found of two different prime numbers into which it
                                            can be split. Thus, 20 splits into 3 + 17 and 7 + 13, giving only two
                                            instances. In the case of 200, however, this splits into 3 + 197, 7 +
                                            193, 19 + 181, 37 + 163, 43 + 157, 61 + 139, 67 + 133, 73 + 127, and 97
                                            + 103, giving nine instances. The number of instances for 2000 is larger
                                            still, and so on. Number theory is littered with "statements" that are
                                            self-evidently true, have not yet been proved true, and for which very
                                            sensible people are in fact looking for a proof.

                                            I wrote the above as part of a reply to the argument that since it is
                                            self-evident that each synoptist redacted his source material in his own
                                            way, it follows that it would be ridiculous for me to think in terms of
                                            trying to prove this true. I disagree with the premise of the argument.
                                            I think it is by no means self-evident that any synoptist redacted his
                                            source material in his own way. Moreover, I would suggest that, in any
                                            case, the argument is not valid, since, in number theory in mathematics,
                                            there are many self-evidently true statements that have not yet been
                                            proved true and for which many very sane people have been trying to find
                                            proof. So it is not ridiculous for anyone to try and find proof of a
                                            statement that is self-evidently true.

                                            Best wishes,
                                            BRIAN WILSON

                                            >HOMEPAGE http://www.twonh.demon.co.uk/

                                            Rev B.E.Wilson,10 York Close,Godmanchester,Huntingdon,Cambs,PE29 2EB,UK
                                            > "What can be said at all can be said clearly; and whereof one cannot
                                            > speak thereof one must be silent." Ludwig Wittgenstein, "Tractatus".
                                            _

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                                          • Maluflen@aol.com
                                            In a message dated 1/31/2002 12:32:20 PM Eastern Standard Time, brian@TwoNH.demon.co.uk writes:
                                            Message 21 of 26 , Jan 31, 2002
                                              In a message dated 1/31/2002 12:32:20 PM Eastern Standard Time,
                                              brian@... writes:

                                              << Leonard Maluf asks --
                                              >
                                              >Brian, are you using the term "self-evident" properly here?
                                              >
                                              Leonard,
                                              Yes, as far as mathematicians are concerned.>>

                                              Which at best would give the original statement a "per se nota quoad
                                              sapientes" qualification.

                                              << They have no doubt at all that the statement is true. It has been checked
                                              by computer for millions of even numbers. Generally, the larger the even
                                              number the
                                              more instances can be found... >>

                                              Brian: I don't wish to sound like I'm nit-picking, but none of this makes
                                              "any even number greater than 6 can be expressed as the sum of two different
                                              prime numbers" a self-evident proposition. In Logic, a self-evident
                                              proposition is one in which, once the terms of the subject and predicate are
                                              understood, the proposition is immediately seen to be true, as in the
                                              statement "a whole is greater than one of its parts". I don't see how your
                                              original proposition can in any way fit that criterion -- for anyone. The
                                              terms of your proposition can be fully understood without the slightest
                                              approach to an immediate grasp of its truth. If the proposition were
                                              self-evident to Mathematicians, they would not waste a moment of time
                                              checking out thousands of even numbers by use of a computer, as you describe,
                                              to determine whether the statement holds in individual cases. This would be
                                              as silly as cutting up and checking out a million pies in an effort to
                                              determine whether it is really true, in all cases, that a whole is greater
                                              than any of its parts. I doubt that even the British are that empirical! In
                                              light of your careless use of the term "self-evident", I am surprised that
                                              you question the self-evident character of the proposition that "any
                                              synoptist redacted his source material in his own way". You are correct that
                                              it is not a self-evident proposition, but I'm not sure how you arrive at that
                                              conclusion on your own sloppy understanding of what a self-evident
                                              proposition is.

                                              Leonard Maluf

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                                            • Brian E. Wilson
                                              Leonard Maluf wrote -- ... Leonard, It is clear you are not a mathematician. When I was teaching mathematics in a state comprehensive school three miles from
                                              Message 22 of 26 , Feb 1, 2002
                                                Leonard Maluf wrote --
                                                >
                                                >In Logic, a self-evident proposition is one in which, once the terms of
                                                >the subject and predicate are understood, the proposition is
                                                >immediately seen to be true, as in the statement "a whole is greater
                                                >than one of its parts".
                                                >
                                                Leonard,
                                                It is clear you are not a mathematician. When I was teaching
                                                mathematics in a state "comprehensive" school three miles from here, a
                                                thirteen-year old boy (Peter "D", from the town of Godmanchester where I
                                                live), pointed out that it is simply not true that "a whole is greater
                                                than one of its parts". In class, we were exploring the idea of negative
                                                numbers using a "number-line" showing positive whole numbers going in
                                                one direction ( +1, +2, +3, +4 ...->>), and negative whole numbers in
                                                the opposite direction (<<-...-4, -3, -2, -1), from a central zero. We
                                                were discussing the key idea that a negative number (however far away
                                                from zero) is smaller than any positive number, this being indicated
                                                under the number-line by an arrow labelled "smaller" pointing in the
                                                direction from positive to negative. Above the number-line, another
                                                arrow labelled "greater", pointed in the opposite direction. Peter
                                                correctly observed that since -3 = -1 + -2, and, since -3 is the
                                                smallest number of these, that therefore the whole (-3) is ***smaller***
                                                than one of its parts (-1).
                                                >
                                                >I don't see how your original proposition can in any way fit that
                                                >criterion -- for anyone.
                                                >
                                                I am not surprised, since your criterion does not even fit the example
                                                you give, does it?
                                                >
                                                >The terms of your proposition can be fully understood without the
                                                >slightest approach to an immediate grasp of its truth. If the
                                                >proposition were self-evident to Mathematicians, they would not waste a
                                                >moment of time checking out thousands of even numbers by use of a
                                                >computer, as you describe, to determine whether the statement holds in
                                                >individual cases. This would be as silly as cutting up and checking out
                                                >a million pies in an effort to determine whether it is really true, in
                                                >all cases, that a whole is greater than any of its parts. I doubt that
                                                >even the British are that empirical!
                                                >
                                                I think your understanding of self-evident is flawed, as indicated by
                                                the failure of your example to fit the criterion you state. In order to
                                                realize that a statement is self-evident it is essential to recognize
                                                first what paradigm of thought is being used. Mathematicians running a
                                                computer check for thousands of even numbers are not necessarily trying
                                                to determine that the statement given above is true. Using their nous,
                                                they would at the same time have out-putted the pairs of prime numbers
                                                concerned, and the number of these for each even number being
                                                considered, and noticed the progression that, generally, bigger even
                                                numbers have more instances of being the sum of a pair of prime numbers.
                                                Such empirical explorations enable the mathematician to be clearer in
                                                what paradigm of thought the investigation is being carried out. They
                                                are far from being silly. The insight that the statement is self-evident
                                                follows after the paradigm of thought has been identified.

                                                Perhaps an example would help. In traditional Euclidian Geometry, an
                                                axiom is defined as a self-evident statement. One of the Euclidian
                                                axioms is that the shortest distance between two points is a straight
                                                line joining them. However, to take your "Logic" definition of "self-
                                                evident", even if the subject ("the shortest distance between two
                                                points") and the predicate ("is a straight line joining them") is
                                                understood, the proposition is *not* immediately seen to be true. It is
                                                self-evident, but only after considerable reflection and appeal to
                                                experience. To "see" that the axiom is self-evident, we may have to re-
                                                call having to walk round obstacles preventing us following a straight
                                                line path, and realizing that this detour entailed taking a greater
                                                number of paces. We would perhaps have to think for a while what we mean
                                                by a "straight" line. No straight line between two points would be
                                                visible, for instance, because it has no thickness. The whole process is
                                                difficult, in fact. This is because it is not necessarily true at all.
                                                In modern geometries using curved space (rather than Euclidean space),
                                                the shortest distance between two points is not a straight line but a
                                                curved geodesic joining them. (In this country, people playing bowls on
                                                a "crown green", which is a hump with an approximately constant
                                                hyperbolic cross-section, come to learn through experience that the
                                                shortest distance between two points on the surface of the green is not
                                                a straight line joining them, but a curved geodesic path.) What is
                                                "self-evident" depends on the paradigm of thinking we are using. To
                                                recognise that a statement is self-evident we need consciously to
                                                identify our paradigm of assumptions. A self-evidently true statement in
                                                one paradigm (Euclidean space) may be false in another (an alternative
                                                curved-space geometry). It is sloppy thinking to assume that there is
                                                only one paradigm in which it may be determined whether any statement is
                                                self-evidently true.
                                                >
                                                >In the light of your careless use of the term "self-evident", I am
                                                >surprised that you question the self-evident character of the
                                                >proposition that "any synoptist redacted his source material in his own
                                                >way".
                                                >
                                                In the light of the above, I am not surprised that you are surprised,
                                                Leonard.
                                                >
                                                >You are correct that it is not a self-evident proposition
                                                >
                                                I am delighted that we do agree on this. I think it is worth stressing
                                                that it is in no way self-evident that any synoptist redacted his source
                                                material in his own way. In fact this was the chief point I was trying
                                                to make in reply to an argument to the contrary from someone else who
                                                was the one who introduced the idea of "self-evident" redaction into the
                                                discussion.
                                                >
                                                >but I'm not sure how you arrive at that conclusion on your own sloppy
                                                >understanding of what a self-evident proposition is.
                                                >
                                                I arrived at the conclusion on the assumption that seeing whether a
                                                statement is self-evident or not may have to follow considerable
                                                reflection and recognition of the paradigm of thought in which it is
                                                being considered, and that being self-evidently true neither proves that
                                                it is true nor places it beyond being proved true.

                                                Of course, if we posit the Griesbach Hypothesis, life becomes easier. It
                                                is then transparently clear that both Luke and Mark redacted their
                                                source material in their own way. I imagine we would agree on that also.
                                                Maybe the most important task is to posit and justify a synoptic
                                                documentary hypothesis. I would suggest that, in the last resort, how we
                                                understand the redaction procedures of any synoptist, and how we
                                                understand any synoptic gospel, depends to some extent on what synoptic
                                                documentary hypothesis we hold.

                                                Best wishes,
                                                BRIAN WILSON

                                                >HOMEPAGE http://www.twonh.demon.co.uk/

                                                Rev B.E.Wilson,10 York Close,Godmanchester,Huntingdon,Cambs,PE29 2EB,UK
                                                > "What can be said at all can be said clearly; and whereof one cannot
                                                > speak thereof one must be silent." Ludwig Wittgenstein, "Tractatus".
                                                _

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                                              • Horace Jeffery Hodges
                                                ... When I was teaching mathematics in ... class, we were exploring the idea of negative numbers using a number-line .... We were discussing the key idea
                                                Message 23 of 26 , Feb 2, 2002
                                                  Brian wrote:

                                                  -------------------------------------------------------
                                                  When I was teaching mathematics in ... class, we were
                                                  exploring the idea of negative numbers using a
                                                  "number-line" .... We were discussing the key idea
                                                  that a negative number (however far away from zero) is
                                                  smaller than any positive number, this being indicated
                                                  under the number-line by an arrow labelled "smaller"
                                                  pointing in the direction from positive to negative.
                                                  Above the number-line, another arrow labelled
                                                  "greater", pointed in the opposite direction. Peter
                                                  correctly observed that since -3 = -1 + -2, and, since
                                                  -3 is the smallest number of these, that therefore the
                                                  whole (-3) is ***smaller*** than one of its parts
                                                  (-1).
                                                  -------------------------------------------------------

                                                  The boy was very clever, but there's a sense in which
                                                  the number -3 is greater than either of the parts -2
                                                  or -1. If -3 signifies the amount of my debt, then my
                                                  whole debt is larger than either of the parts -2 or
                                                  -1.

                                                  Strange things happen with negative numbers, I guess.
                                                  The number -3 also has the "parts" -4 and +1. Here,
                                                  one part (-4) is -- on your student's reasoning --
                                                  smaller and the other (+1) larger.

                                                  Perhaps the strangeness can be explained as an
                                                  artifact of thinking of abstractions as having parts.
                                                  I'm not sure.

                                                  If you're interested, I can raise the issue on a
                                                  philosophers' listserve that I belong to. The issue
                                                  probably has more relevance there.

                                                  Jeffery Hodges

                                                  =====
                                                  Assistant Professor Horace Jeffery Hodges
                                                  Hanshin University (Korean Theological University)
                                                  447-791 Kyunggido Osan-City
                                                  Yangsandong 411
                                                  South Korea

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                                                • Maluflen@aol.com
                                                  In a message dated 2/1/2002 11:51:54 AM Eastern Standard Time, brian@TwoNH.demon.co.uk writes:
                                                  Message 24 of 26 , Feb 2, 2002
                                                    In a message dated 2/1/2002 11:51:54 AM Eastern Standard Time,
                                                    brian@... writes:

                                                    << Leonard Maluf wrote --
                                                    >
                                                    >In Logic, a self-evident proposition is one in which, once the terms of
                                                    >the subject and predicate are understood, the proposition is
                                                    >immediately seen to be true, as in the statement "a whole is greater
                                                    >than one of its parts".
                                                    >
                                                    Leonard,
                                                    It is clear you are not a mathematician. When I was teaching
                                                    mathematics in a state "comprehensive" school three miles from here, a
                                                    thirteen-year old boy (Peter "D", from the town of Godmanchester where I
                                                    live), pointed out that it is simply not true that "a whole is greater
                                                    than one of its parts".>>

                                                    I do hope you set him straight!

                                                    << In class, we were exploring the idea of negative
                                                    numbers using a "number-line" showing positive whole numbers going in
                                                    one direction ( +1, +2, +3, +4 ...->>), and negative whole numbers in
                                                    the opposite direction (<<-...-4, -3, -2, -1), from a central zero. We
                                                    were discussing the key idea that a negative number (however far away
                                                    from zero) is smaller than any positive number, this being indicated
                                                    under the number-line by an arrow labelled "smaller" pointing in the
                                                    direction from positive to negative. Above the number-line, another
                                                    arrow labelled "greater", pointed in the opposite direction. Peter
                                                    correctly observed that since -3 = -1 + -2, and, since -3 is the
                                                    smallest number of these, that therefore the whole (-3) is ***smaller***
                                                    than one of its parts (-1). >>

                                                    You ought to have commended him for being clever, but pointed out that he is
                                                    nonetheless, of course, quite wrong. Wrong, logically speaking, because
                                                    guilty of a fundamental fallacy, that of a surreptitious four-term syllogism
                                                    (an absolute no-no for correct logical thinking, in any domain), resulting
                                                    from a term ("whole") used equivocally in his implicit argument. When I said
                                                    before that the subject and predicate have to be clearly understood as a
                                                    prerequisite for seeing the truth of a self-evident proposition, I meant,
                                                    among other things, the removal of all such equivocities, and hence too,
                                                    clarity regarding the question of "what paradigm of thought is being used",
                                                    as you describe it. Peter would then have received a proper lesson in the
                                                    difference between being merely clever and being wise.

                                                    Since I take it you do, after all, have a logical mind, I am confident that
                                                    you will see the pertinence of the above to the remainder of your post as
                                                    well.

                                                    Leonard Maluf


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                                                  • Brian E. Wilson
                                                    Brian Wilson wrote -- ... Jeffery Hodges commented -- ... Jeffery, Yes, but this is not in a mathematical sense. It is true mathematically that -3
                                                    Message 25 of 26 , Feb 5, 2002
                                                      Brian Wilson wrote --
                                                      >
                                                      >When I was teaching mathematics in ... class, we were exploring the
                                                      >idea of negative numbers using a "number-line" .... We were discussing
                                                      >the key idea that a negative number (however far away from zero) is
                                                      >smaller than any positive number, this being indicated under the
                                                      >number-line by an arrow labelled "smaller" pointing in the direction
                                                      >from positive to negative. Above the number-line, another arrow
                                                      >labelled "greater", pointed in the opposite direction. Peter correctly
                                                      >observed that since -3 = -1 + -2, and, since -3 is the smallest number
                                                      >of these, that therefore the whole (-3) is ***smaller*** than one of
                                                      >its parts (-1).
                                                      >
                                                      Jeffery Hodges commented --
                                                      >
                                                      >The boy was very clever, but there's a sense in which the number -3 is
                                                      >greater than either of the parts -2 or -1. If -3 signifies the amount
                                                      >of my debt, then my whole debt is larger than either of the parts -2 or
                                                      >-1.
                                                      >
                                                      Jeffery,
                                                      Yes, but this is not in a mathematical sense. It is true
                                                      mathematically that -3 < -1 , but it is false that -3 > -1 , otherwise
                                                      mathematics grinds to a halt.
                                                      >
                                                      >Strange things happen with negative numbers, I guess. The number -3
                                                      >also has the "parts" -4 and +1. Here, one part (-4) is -- on your
                                                      >student's reasoning -- smaller and the other (+1) larger.
                                                      >
                                                      Not merely on the student's reasoning, but on the definition of smaller
                                                      and greater laid down by the system of maths being used. The statement
                                                      -4 < -3 is true. It is true also that +1 > -3. Any number "to the left"
                                                      of another number on the number-line is smaller, by definition. And any
                                                      number "to the right" of another number on the number-line is greater,
                                                      by definition. This is not strange. It is normal. It does indeed follow
                                                      that, since -3 = -4 + 1, that the whole (-3) is greater than one of its
                                                      parts (-4) and smaller than another of its parts (+1), but that actually
                                                      confirms my point that the statement that the whole is greater than any
                                                      one of its parts is not even true, let alone self-evidently true.

                                                      To come back to the subject of this thread, Leonard Maluf and I seem to
                                                      be agreed that it is not self-evident that any synoptist redacted his
                                                      source material in his own way. I would suggest that the earlier
                                                      introduction by someone else of the idea of "self-evident" redaction by
                                                      each synoptist has been shown to be very much an irrelevance. I have
                                                      enjoyed the excursus into mathematics, but maybe it would not be
                                                      appropriate to continue with this on Synoptic-L?

                                                      Best wishes,
                                                      BRIAN WILSON

                                                      >HOMEPAGE http://www.twonh.demon.co.uk/

                                                      Rev B.E.Wilson,10 York Close,Godmanchester,Huntingdon,Cambs,PE29 2EB,UK
                                                      > "What can be said at all can be said clearly; and whereof one cannot
                                                      > speak thereof one must be silent." Ludwig Wittgenstein, "Tractatus".
                                                      _

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                                                    • Emmanuel Fritsch
                                                      ... Just because you apply a bad definition of is a part of as pointed out by Leonard just before. I do not know exactly if Leonard is or not a
                                                      Message 26 of 26 , Feb 5, 2002
                                                        > >Strange things happen with negative numbers, I guess. The number -3
                                                        > >also has the "parts" -4 and +1. Here, one part (-4) is -- on your
                                                        > >student's reasoning -- smaller and the other (+1) larger.
                                                        > >
                                                        > Not merely on the student's reasoning, but on the definition of smaller
                                                        > and greater laid down by the system of maths being used. The statement
                                                        > -4 < -3 is true. It is true also that +1 > -3. Any number "to the left"
                                                        > of another number on the number-line is smaller, by definition. And any
                                                        > number "to the right" of another number on the number-line is greater,
                                                        > by definition. This is not strange. It is normal. It does indeed follow
                                                        > that, since -3 = -4 + 1, that the whole (-3) is greater than one of its
                                                        > parts (-4) and smaller than another of its parts (+1), but that actually
                                                        > confirms my point that the statement that the whole is greater than any
                                                        > one of its parts is not even true, let alone self-evidently true.

                                                        Just because you apply a bad definition of "is a part of" as
                                                        pointed out by Leonard just before. I do not know exactly if
                                                        Leonard is or not a mathematician, but I feel quite confident
                                                        with his logic, first with the Goldbach conjecture, and now
                                                        with the example of negative numbers.

                                                        Leonard wrote :
                                                        > When I said before that the subject and predicate have to be
                                                        > clearly understood as a prerequisite for seeing the truth of a
                                                        > self-evident proposition, I meant, among other things, the removal
                                                        > of all such equivocities, and hence too, clarity regarding the question
                                                        > of "what paradigm of thought is being used", as you describe it.

                                                        The main equivocity is the use of set vocabulary in arithmetic.
                                                        When you consider sets, for instance {1,2,a,b}, you may say it
                                                        is greater than all its parts, for instance {1,b}.

                                                        This property does not make sense when applied to arithmetic
                                                        (or you should define the way to go from sets to arithmetic)

                                                        a+
                                                        manu

                                                        PS : I know this is not the regular list to post this, and more over
                                                        Leonard answered before almost all what would have been to said about.
                                                        But I add one precision : the name of the property about even numbers
                                                        expressed as sum of two prime numbers is called "Goldbach conjecture",
                                                        and is known for more than three century, without having been demonstrated.
                                                        Not really self evident.

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