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

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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 1 of 26 , Feb 5, 2002
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      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 2 of 26 , Feb 5, 2002
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        > >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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