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

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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 1 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 2 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 3 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 4 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".
_

Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
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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 5 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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