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Parsimony

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  • Gentile, David
    Chuck Jones writes: Thanks for articulating something that bothers me much better than I ever have been able to. Lost sources are not a hypothesis (this also
    Message 1 of 1 , Jun 28, 2006
      Chuck Jones writes:

      Thanks for articulating something that bothers me much better than I
      ever have
      been able to. Lost sources are not a hypothesis (this also bothers me),
      as, too
      repeat myself, Luke refers to "many accounts." They add nothing onerous
      to
      Occam's Razor, and in fact ignoring Lk's reference as an ingredietn
      while
      working toward solutions is bad methodology.

      Your diplomatic phrase "authorial creativity" is often, it seems to me,
      a
      euphamism for chinese-acrobat-contortion explanations of unaddressed
      data. They
      describe not what Lk did in other places, not what his usual tendencies
      were,
      not what he said about how he wrote his book, not what one would expect
      an
      author to do, but rather what he *had to have done* in order for theory
      X to
      work out.

      I like Einstein's quote that an explanation should be as simple as
      possible,
      but no simpler. To me, a hypothesis that credibly addresses 95% of the
      synoptic
      passages is more effective than one that addresses 70%. I'll take
      "effective"
      over "simpler" any day.

      =========



      Chuck,



      Let me expand a little on what Bob wrote. The idea that "simple is
      better", let's call it the "parsimony principle" is not limited to
      Occam's razor. I'll try to give an example in a moment. But first,
      regarding lost sources, Luke tells us that there were "many accounts".
      Besides taking him on his word here, we have other indications from
      other authors of lost Christian documents. All in all, it seems quite
      probable other documents existed. However, when looking for synoptic
      problem "solutions", we are talking about *specific* possible lost
      documents. It's not a question of whether various accounts existed, it
      is a question involving the existence of a specific document, and
      whether or not Luke used it as a source.



      (For the record, I favor a theory that involves a saying source, but
      with some differences when compared to general scholarship on the
      subject).



      Now, for "simpler is better" -



      Suppose we have the following data points.

      X=1 y=2

      X=2 y=3

      X=3 y=4

      X=4 y=5

      *X=5 y=5*

      X=6 y=7

      X=7 y=8



      Let's only consider two hypotheses, along with the possibility that both
      are false.



      Hypothesis A) Y=X+1

      Hypothesis B) Y=X+1 except when X is divisible by 5, then Y=X



      We will judge one hypothesis or the other "better" if it has a higher
      probability of predicting future results. Or rather than "future" which
      does not apply to our synoptic problem, we could say that "the better
      hypothesis has a higher probability of correctly describing what we
      presently can *not* know directly, based on what we do know directly"



      In our above example, we can note that hypothesis B does more accurately
      describe our existing dataset. It is right 7 out of 7 times. Hypothesis
      A is wrong once. It only gets 6/7. Hypothesis A is simpler. But
      hypothesis B is better at describing the existing data. "B" can not be
      eliminated by Occam's razor. Never-the-less, the "parsimony principle"
      here, does indeed lead to the conclusion that hypothesis A is better.



      Consider - when x = 10, what would you bet that y was, if you had to
      bet, 10, or 11? I would bet 11. Hypothesis A is more likely to correctly
      describe what we can not now directly observe (what happens when x=10).



      If I make a calculation here using Bayesian statistical ideas, and some
      simplifying assumptions, I get that hypothesis A has about a 71% chance
      of being correct, that when x=10, y will = 11.



      So, in this example, the more complex hypothesis, even though it is not
      strictly susceptible to Occam's razor, is probably a less useful
      predictor (or a less correct description of objective reality, if I make
      a philosophical leap), than the simpler hypothesis.



      Obviously if future observations tended to confirm hypothesis B, it
      would become the better hypothesis, in spite of its added complexity.
      But as it stands, A is better.



      Dave Gentile

      Riverside, IL

















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