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Re: Improbable Probability Statements

At 8:33 PM +0000 5/22/97, Clayton Bartholomew wrote:

>I have dinner twice a month with an old friend who is a professional
>mathematician. I've talked to him several times about validity in
>probability arguments.

At the risk of being pedantic, I think it is important to note
that validity can only be a property of deductive arguments.
The arguments with which you are concerned are inductive.  An
argument is valid just in case its conclusion must be true given
that its premises are true.  An argument can be valid with false
premises.  A valid argument is sound iff it has true premises.

>Here is a concrete example:
>
>Bruce Metzger in his textual commentary on the GNT 3rd ed. (page
>320-21) has a full discussion of the variants for Acts 4:24. His
>concluding remark is all we are concerned with. He says that energeia
>is used nowhere else in Luke, and in the NT it is only used by Paul.
>Metzger considers this evidence against the reading of D for this
>variant.
>
>I am not the least bit interested in which variant is original in Acts
>4:24. What interests me is that a world class scholar (understatement)
>would consider this an argument.
>
>Luke has a large vocabulary. Luke has a number of NT hapax. Luke uses
>a number of words only once. So how do we concluded that it is
>*improbable* that Luke would use energeia only once? It does not
>follow.

The pertinent question is, What counts as evidence for the
conclusion, and how is the probability to be measured?  There are
many kinds of evidence.  In this case, one of which is that this
would mean that Luke would only use energeia once; to be weighed
against that fact that Luke's writings contain several hapax
legomena.  So, it would be difficult to assign a significant
advantage to either of these stacks.

It may well be that when these two aspects of the problem are
viewed in this way that they cancel each other out, but that
each may be a coherent part of a larger body of evidence, in
which they play an integral role (I don't know!)  One should
gather all the cards - and evidence for or against a reading
comes from a diversity of sources - and lay them on the table
before making a decision.  It may well be that even then it is
not possible to be reasonably dogmatic.

>Here is another kind of Argument:
>
>The relative pronoun normally follows it's antecedent therefore . . .
>
>The premise is true. But what comes in the second half of the
>statement is often not a valid inference from the premise. This is a
>type of probability statement. It may fall apart because it does not
>take indeterminacy seriously. Improbabilities taken as a class are
>frequent occurrences in any ancient text, the NT included. What I am
>saying is indeterminacy is part of the nature of phenomena in general.
>Language is no exception. Ancient texts are no exception.

But of course it is not a valid inference.  If it was a valid
(immediate) inference, it would not be open to question (granted
the truth of the protasis) as more evidence comes to light!  The
fact that one exception to the rule (= inductive generalization)
genuinely occurs does not make the rule less useful, it just means
that no conclusion is necessarily true on its basis.  Language is
deeper than speech!!!  Surface irregularities do not negate the
existence of a perfectly orderly, rational, deep structure.  It
just makes it more difficult to understand.  In a flowing stream,
a surface irregularity is an indication of the presence of a rock
in the depth.  If one looks intently past the surface irregularity,
one can see the outlines of the rock.

>Probability statements don't become useless simply because
>indeterminacy happens. Language is not chaos. But the kind of
>probability argumentation used by 19th century science is going to
>draw some smiles of disbelief at this stage of the game.
>
>Any sharp observer will see that these two examples are not identical
>nor do they make the same point. The second example is fuzzy and open
>ended. The second example does not prove anything. It only raises a
>question.

Carl, if you happen to read this, can the quote for today be:
"Indeterminacy happens"?  If we have votes, then this gets my
vote! :-)

In Christ,
Jim Beale
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