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

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• 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
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• 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
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• ... 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@...
• ... 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

> 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@...
• ... 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@...
• 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@...
• 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@...
• ... 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@...
• ... 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

Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
List Owner: Synoptic-L-Owner@...
• ... 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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• 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).

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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• 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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• 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
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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• ... . ... 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).
>
>
> 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

Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
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• ... 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.

> 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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• ... 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

Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
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• ... 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:

> > 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 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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• 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 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.
>
>
>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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• 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:

>
>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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• 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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• ... 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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• 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 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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• ... 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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