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RE: [XTalk] Re: Proof

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  • David C. Hindley
    ... the same way, namely: possible = probability 0 (hence of no interest) probable / likely = probability 50% (of great interest)
    Message 1 of 104 , Sep 1, 2002
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      Mike Grondin comments:

      >>I wonder if, in terms of probability, everyone understands these words in
      the same way, namely:

      'possible' = probability > 0 (hence of no interest)
      'probable'/'likely' = probability > 50% (of great interest)
      'plausible'/'credible' = probability "significant", but < 50%

      No mathematical value can be assigned to the latter category, tho
      intuitively it would seem to have to be at least 10-33%. It may in fact be
      only a measure of how closely a suggestion accords with
      one's intuitions.<<

      Hmmm. I would not understand these terms that way.

      "Possible" means that a hypothesis' premises are not contradicted. This is
      an open ended statement, though, and hypotheses with any degree of
      complexity can be proposed (Barbara Theiring's very complex hypotheses
      regarding Essenes and the sect(s) that created the DSS and Jewish
      pseudepigraphic literature might be a good example). Since hypotheses
      inferred from evidence usually means that the critic has consciously
      selected a subset of the total available data when formulating the
      hypotheses, it is possible that contractions can be found. Yet this is still
      a problem because the nature of historical evidence means it is not randomly
      selected and the limits of the universe populations are not known, meaning
      that a "contradiction" may not be provable in cases where probability is
      concerned. There would be a difference between saying "all 1st century
      Galilean oil lamps were colored red," based upon archeological results to
      date (and I am not saying they were all red), and finding a black one, which
      would contradict the hypothesis, and saying "most ..." or even "some ...,"
      which would be incapable of proof in statistical terms when it comes to
      historical data. Even if all preserved 1st century CE Galilean oil lamps
      were red, the accidents of preservation may have destroyed a large number of
      black or blue ones. We can never know.

      "Probable" means that a hypothesis can be confirmed by means of statistical
      analysis. In logical terms, this would be called a statistical syllogism.
      However, statistical syllogisms have some serious limitations. Historical
      hypotheses are generally not amenable to statistical analysis on the grounds
      that the universe population is not known nor can it be reliably estimated.
      A business that knows it must manufacture an order for a million widgets
      with less than 1% defective parts can calculate with reasonable accuracy how
      many random samples must be drawn to reliably estimate whether the targeted
      allowable range of defective parts will be met. Historical evidence is not
      drawn from a known universe, and the evidence is not randomly selected.

      "Plausible" and "credible" are terms that describe our subjective
      evaluations of hypotheses that cannot be confirmed statistically within a
      reasonable degree of doubt. This will be based on our knowledge of
      contemporary literature and archeology, which knowledge is bound by nature
      with our interpretations of these statements or evidence. These kinds of
      terms are likely the best to use with historical hypotheses. It is easy to
      call "incredible" a hypothesis that assumes that ancient Akkadians flew
      aircraft made of aluminum and were powered by Briggs & Stratton reciprocal
      engines. We can be pretty sure that manned flight, smelting of aluminum and
      knowledge of internal combustion engines was not available to ancient
      Akkadians, as no traces of the required technologies are known in the region
      or period from archeology or ancient literature/records. But if we
      hypothesize that 2nd century Romans had developed a mechanical plane
      astrolabe for use in calculating planetary positions, the question of
      plausibility is much more certain. Although no physical examples are known
      so far, we know they had the technology to produce them, and statements in
      the works of Claudius Ptolemy can be interpreted to allow such a
      possibility. But there us no way to confirm this possibility, unless an
      archeologist someday finds a plane astrolabe that can be dated to the 2nd
      century or earlier. Thus, for the time being, it is plausible.

      >>It's always POSSIBLE (> 0%) that further evidence will radically alter the
      picture, since the evidence available from the real world is never
      scientifically selected, but that's what makes "the world of probabilities"
      what it is.<<

      The simple fact that "evidence available from the real world is never
      scientifically selected" is exactly what makes historical hypotheses
      "possible" rather than "probable." Our fixing of the possible into our
      knowledge of the period and place is what makes it "plausible." It seems to
      me that we should really consider possibility and plausibility as related,
      and differentiate this set of constructs from probability.

      POSSIBLE
      PROBABLE (in cases where statistical proofs can be calculated)
      PLAUSIBLE (in all other cases, including historical)

      Someday, if I can ever find the time, I hope to look into this matter mush
      more seriously. The "if" part is the killer ... <g>

      Respectfully,

      Dave Hindley
      Cleveland, Ohio, USA
    • Thomas G. Barnes
      I know this is off topic, however, during the past few days I noticed the discussion going on about the use of copyrighhted material. Anyway, my question is
      Message 104 of 104 , Nov 13, 2002
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        I know this is off topic, however, during the past few days I noticed the
        discussion going on about the use of copyrighhted material. Anyway, my
        question is this, how do I properly cite a web page I used information from
        in an academic paper. I am a student and an interested historical Jesus
        individual. I realize this is off topic so please send reply to me off the
        list.

        Thomas G. Barnes
        Philadelphia, PA
        Temple University
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