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[XTalk] Re: Proof?

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  • Bob Schacht
    ... Dave, You do mean contradictions, don t you? The practice you refer to above is also known as selective use of evidence, usually meant negatively, with
    Message 1 of 104 , Sep 2, 2002
      At 11:13 AM 9/1/2002 -0400, David C. Hindley wrote:
      >..."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.

      Dave,
      You do mean "contradictions," don't you? The practice you refer to above is
      also known as "selective use of evidence," usually meant negatively, with
      the implication that evidence is chosen to fit a preconceived (not
      inductively derived) theory.

      >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.

      There is a difference between a normative rule and a categorical rule. "All
      1st century Galilean oil lamps were colored red" is a categorical rule.
      Delete the word "all" and you have a normative rule, which automatically
      allows for idiosyncratic exceptions. Archaeological typology seldom uses
      the word "all." In the realm of human behavior (including history),
      normative rules are the best that one can usually hope for. Categorical
      rules were favored by some who advocated the existence of "cultural
      universals," but I don't know of any that are not so vague as to be
      useless, such as "all people use language" or some such.

      Normative rules are quite useful. A rule of history or behavior that is
      true 95% of the time is quite worthwhile.


      >"Probable" means that a hypothesis can be confirmed by means of
      >statistical analysis.

      I don't like the word "confirmed" in this context. "Supported" is better.
      The usual statistical term is "not rejected".

      >In logical terms, this would be called a statistical syllogism.

      Please clarify. Like Mike, I'm not sure what you mean. Most purely
      statistical hypotheses are in the form of "Null Hypotheses" to the effect
      that the means are equal, and similar bland statements that we interpret in
      plain english.

      >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.

      I don't think this is a fair comparison because you are comparing a *very*
      general proposition (viz., "Historical
      hypotheses are generally not amenable to statistical analysis...") with a
      very specific proposition about defective part rates of widgets. I also
      have a problem with the way you envision of the process of random
      selection, especially with the part about a "known universe." There are
      many branches of experimental science where the "universe" is no more
      well-known than human behavior. Random does not mean you have to put
      everything visibly on a table in front of you before selecting. It mainly
      means that care has been taken to eliminate all sources of bias from the
      process of selection, and that the sample is sufficiently large to cover
      whatever 'sins' have been committed by slight biases in the selection
      process. Think of soil samples in geology, or plant samples in botany. Both
      are essentially exploratory in nature, and are not necessarily drawn form
      "a known universe" in the sense you mean.

      BTW, random samples are not necessarily the gold standard in most sciences
      that use sampling, because random sampling can sometimes produce odd
      results in controlled tests (especially when samples are too
      small). Instead, combination strategies are usually preferred, such as
      stratified random sampling, where the known universe is partitioned to
      ensure diversity of the samples randomly selected within each partition.


      >"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.

      True. However, this opens the door wide for subjectivity, because what,
      say, Barbara Thiering finds "plausible" may strike me as "incredible."

      >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.

      With exception noted, I pretty much agree with this paragraph. However, it
      is best in these situations to spell out the grounds of plausibility,
      rather than merely asserting them.


      > >>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)

      I'm not sure I like this differentiation. I am more inclined to Mike's(?)
      position that "probable" should mean more likely than not, and that
      plausible represents a broader spectrum of possibilities, including
      possibilities that are not probable. Plausibilities are a dime a dozen, and
      generally don't get us very far. On just about any subject, I can produce a
      number of plausible hypotheses at the drop of the hat, very few of which
      anyone would consider probable.


      >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>

      Hey, don't give up yet! <g>
      Bob


      >Respectfully,
      >
      >Dave Hindley
      >Cleveland, Ohio, USA
      >
      >
      >
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    • 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
        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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