WEQATAL vs. QATAL statistics (non-circularity)

Henry Churchyard churchh at usa.net
Sun Aug 27 16:34:58 EDT 2000


> From: Rolf Furuli <furuli at online.no
>> Henry Churchyard wrote:
>>> From: Rolf Furuli <furuli at online.no
>>>> Henry Churchyard wrote:

>>>> It is this hypothesis (of the posited identical relative semantic
>>>> frequency distributions of QATAL and WEQATAL, or the formal
>>>> statistical "independence" of a QATAL vs. WEQATAL variable with
>>>> respect to a semantic meaning variable) that I have shown above
>>>> to be rejected five hundred times more conclusively than is
>>>> usually considered necessary statistically.

>>> To get your two-dimensional table, you assume that QATAL and
>>> WEQATAL *are* two different morphological categories.  as far as
>>> *semantics* is concerned, this assumption makes the situation
>>> completely circular, because what shall be proved is assumed.  in
>>> a language where tense is not grammaticalized we cannot ascribe a
>>> different *semantic* meaning to verbs with past, present, perfect,
>>> and future reference.  True, the function or use of the verbs is
>>> different, and this is described by your analysis.  But this is
>>> pragmatics and not semantics.  In tenseless languages, particular
>>> forms are often used with a certain time reference (due to
>>> linguistic convention), but these forms do not represent tense
>>> because they can also be used for other time referenses.  Thus
>>> their time reference is pragmatic and not semantic.

>> When you're trying to explore whether two things share the same
>> properties or each have different properties, then you must treat
>> the two separately, as a provisional research assumption, or you
>> can't even begin to get to grips with the question.  If a social
>> scientist were to try to examine whether or not Protestants and
>> Catholics have different incomes, he would have to collect income
>> data separately for the two groups.  So there's nothing logically
>> circular about my little two-dimensional tables; their existence
>> arises from the very basic fact that it's impossible to test
>> whether or not two entities are different by assuming beforehand
>> that they're the same.

> For a scientist to compare income data of the two Catholics and
> Protestants, he first *must decide* which persons are Catholics and
> which are Protestants in order to be sure that he deals with two
> different groups.  Similarly with QATAL and WEQATAL.  If there
> should be any meaning in a comparison of the temporal reference of
> QATAL and WEQATAL, we first must decide (assume) that they ARE two
> different groups (Catholics and Protestants). But then we have
> assumed what we should prove, namely, that QATAL and WEQATAL *are*
> two different groups.

I'm sorry, but there is simply no logical circularity whatever in the
procedure here.  First we make the unquantified intuitive observation
(i.e. working hypothesis) that it seems like there is very likely is
some "non-compositionality" in the denotation of the morphologically
complex form _w at +qatal_ (i.e. that the denotation of this form does
not seem to be a simple combination of the denotation of _qatal_ alone
and the usual denotation of the conjunction _w at -_, when attached to a
non-verb, say).  Here it really doesn't make any difference whether we
call the domain of this non-compositionality "meaning" (as a typical
morphologist certainly ordinarily would), or whether we call the
domain of this non-compositionality "differences in patterns of
predominant temporal reference usage" (as you do, seemingly reserving
the use of the sacred words "meaning" and "semantics" exclusively for
a deep abstract theoretical semantics-beyond-semantics).  What we
choose to call it is really a question of terminological definitions
and higher-level metatheoretical debates, and frankly just doesn't
have very much relevance to the concrete hands-on work of
data-gathering and hypothesis testing in this case.  Even if only mere
"predominant patterns of temporal reference usage" are involved here,
the hypothesis to be tested is still that the reference of _w at +qatal_
does not equal a simple combination of the reference of _qatal_ and
the reference of _w at -_, and I fail to see how attaching different
terminological labels invalidates the analysis (any valid
methodological criticisms should be substantive, and not merely
terminological).

Second, when it comes to the substantive details of the analysis, the
characteristic that was used to distinguish between WEQATAL and QATAL
status was one of external morphological/phonological form.  If we had
used "meaning" or "temporal reference" or whatever-you-want-to-call-it
as the criterion for deciding whether a form was a WEQATAL or a QATAL,
then there would indeed have been circularity.  (In the example above,
this would be as if we had decided whether to count a person as
Catholic or Protestant based on their income, and then tried to
calculate a correlation between income and the pseudo-"religion"
so-determined -- the results would have been hopelessly confused and
utterly meaningless as far as answering the original question.)
However the criterion for distinguishing between WEQATAL and QATAL was
strictly one of external phonological form (presence of prefixed w at -),
so that there is no circularity of this type.  Here you decided not to
try to distinguish "non-compositional reference" WEQATAL forms from
"compositional reference" WEQATAL forms, and this was a very
reasonable simplifying assumption for data-gathering (that I have no
objection to), since presumed "non-compositional reference" WEQATAL
only takes on a distinct morphological/phonological shape in a
minority of forms (i.e. stress-shifted 2nd.sg.masc. and 1st.sg.
forms), while presumed "compositional reference" WEQATAL never really
takes on a distinctive morphological/phonological shape (since
2nd.sg.masc. and 1st.sg. "non-compositional reference" WEQATAL forms
can fail to show stress-shift for a number of reasons).  Because of
these difficulties, and because of the unquantified intuitive
observation that "non-compositional reference" WEQATAL occurs much
more frequently in the text than "compositional reference" WEQATAL,
and because of the fact that failing to distinguish "non-compositional
reference" WEQATAL from "compositional reference" WEQATAL can never
create a spurious apparent correlation between
phonological/morphological form and reference in the data (but can
only weaken the apparent strength of a true correlation) -- therefore,
deciding to lump "non-compositional reference" WEQATAL and
"compositional reference" WEQATAL together is an unobjectionable
research strategy (I did much the same thing in a particular context
in Chapter 3 of my own dissertation).  However, because you've made
the decision ahead of time to amalgamate "non-compositional reference"
WEQATAL and "compositional reference" WEQATAL in your data, this means
that you can't use these numbers to argue that in fact no distinction
exists between "non-compositional reference" WEQATAL and
"compositional reference" WEQATAL.

Finally, the third stage in the procedure is evaluating the results of
of the statistical analysis.  As can be seen in the table below, there
are proportionally 9.72 times more WEQATAL forms than QATAL forms with
future reference, 7.97 times more WEQATAL forms than QATAL forms with
"OTHER" (modal) reference, 9.13 times more QATAL forms than WEQATAL
forms with past reference, 20.79 times more QATAL forms than WEQATAL
forms with perfect reference, and 5.71 times more QATAL forms than
WEQATAL forms with present reference.  In other words, since the
smallest of these numbers is 5.71, there is a strong distinction
between the frequencies of occurrence of QATAL and WEQATAL across all
five reference categories (as I've said before, many social scientists
would kill to get results which are as distinctive as these across the
columns of a table).  [As with the previous tables, the following must
be viewed with a fixed-width font:]

  Statistics for Table of SEMANT by CONJUG
                                                  Ratio of Column
    Frequency|  QATAL | WEQATAL|  Total             Percentages:
    ---------+--------+--------+                    ------------
    FUTURE   |    965 |   4100 |   5065
             |  6.93% | 67.36% |   25.31%        67.36/6.93=  9.72
    ---------+--------+--------+
    OTHER    |    397 |   1383 |   1780
             |  2.85% | 22.72% |   8.90%         22.72/2.85=  7.97
    ---------+--------+--------+
    PAST     |   7450 |    357 |   7807
             | 53.51% |  5.86% |  39.02%         53.51/5.86=  9.13
    ---------+--------+--------+
    PERFECT  |   2605 |     55 |   2660
             | 18.71% |  0.90% |  13.29%         18.71/0.90= 20.79
    ---------+--------+--------+
    PRESENT  |   2505 |    192 |   2697
             | 17.99% |  3.15% |  13.48%         17.99/3.15=  5.71
    ---------+--------+--------+
    Total       13922     6087    20009
                 100%     100%     100%

   Statistic    DF       Value     Prob
   ------------------------------------
   Chi-Square    4  12154.8415   <.0001
   Cramer's V           0.7794

Given these consistently high column-percentage ratio numbers, it's
not surprising that the hypothesis of non-interaction between
morphology and temporal/modal reference is rejected at the .0001
"confidence level" (i.e. five hundred times more decisively than would
be the case with the .05 confidence level which is usually considered
to be adequate), nor that the "Cramer's V" nominal-variable measure of
interaction "effect size" is at 78% of its maximum possible value (and
Cramer's V is symmetrical between row and column variables -- so that
a properly asymmetrically-calculated effect-size measure might have an
even higher value).

All this means that our initial, intuition-derived working hypothesis
that there is a systematic difference in temporal/modal reference
denotation between QATAL and WEQATAL is now decisively validated by the
results of the statistical test.  You may choose to call this
difference merely one of "predominant patterns of temporal reference
usage" (while morphologists would generally not hesitate to call this a
"meaning" difference) -- but this is only a high-level metatheoretical
quibble about terminology, which has no impact on the fact that
_w at +qatal_ has now been decisively proven to be non-compositional in
reference.  (This referential non-compositionality is evidence for
morphologically treating _w at +qatal_ as a distinctive morphological
entity -- at least in the majority of cases -- and not as a mere
accidental syntactic concatenation of clitic _w at -_ with independent
_qatal_.)

Whether or not the systematic reference difference between QATAL and
WEQATAL is also a "semantic" difference according to your particular
use of the word "semantic" is an entirely separate question (a
question which was not asked or assumed by the statistical analysis,
and which does not invalidate the statistical analysis).


> You are correct when you say that lumping Protestants and Catholics
> together it is impopssible to do the income test.  And similarly,
> without ASSUMING that QATAL and WEQATAL are two groups with
> different meaning, it is impossible to use my data to show that they
> are two different groups

No, this analogy does not hold.  When we say that Catholics and
Protestants have an identifying characteristic by which they can be
distinguished, we are not thereby assuming that they have different
incomes.  Similarly, when we classify QATAL-type forms as to whether
they have a prefixed _w at -_ or not, we're not making any semantic
assumptions whatsoever in doing so.  Whatever loose terminology we may
have happened to throw around when formulating our initial informal
intuitive working hypothesis, the formal test of this hypothesis (with
QATAL distinguished from WEQATAL purely by criteria of superficial
external phonological form, and with raw temporal/modal reference
categories as the values of the column variable) does not involve any
logical circularity, and makes no assumptions ahead of time as to
whether a difference which is "semantic" -- in your particular sense
of this term -- exists between morphological WEQATAL and morphological
QATAL.

So everything's hunky-dory from the point of view of methodology.


>> Anyway, the claim that correlations between morphology and the
>> categories of "Past", "Present", "Future", "Perfect", and "Modal"
>> must be absolute and exceptionless to be considered part of "real"
>> semantics, doesn't necessarily strike me as being a very helpful
>> theory -- since most of the time this theory seems to require you
>> to just throw up your hands and sweep whatever can't be fully
>> explained within a few very basic and simple parameters under the
>> carpet into the ill-defined catch-all region of "pragmatics".

> To have semantic meaning in the sense that I use the expression, a
> form should signal just one particular tense or one particular mood
> or one particular aspect.  There is no problem if a form both codes
> for a tense *and* a mood, or a tense *and* an aspect, as is the case
> in NT Greek.  But on the tense-plane, the mood-plane, and the aspect
> plane, the form should just code for one member.  The 100.00 % you
> mention in no way should be pressed.  In his classic book "Tense",
> Comrie shows there can be exceptions and special cases.  However,
> exceptions should be of the kind that they can be explained.  Of the
> five Hebrew groups, the different uses of four of them definitely
> excludes them as candidates for being a particular tense, aspect or
> mood.  The only group that *could* code for a tense, the past one,
> is WAYYIQTOL, because a past reference is seen in more than 90 % of
> the occurrences of this form.

Well, looking at things from the other point of view, as I did in the
table above, the column-percentage ratio numbers 9.72, 7.97, 9.13,
20.79, and 5.71 mean that proportionally 90.7% of all so-called
"suffix-conjugation" forms with future reference are WEQATAL, 88.9% of
all "suffix-conjugation" forms with OTHER/modal reference are WEQATAL,
90.1% of all "suffix-conjugation" forms with past reference are plain
QATAL, 95.4% of all "suffix-conjugation" forms with perfect reference
are plain QATAL, and lastly 85.1% of all "suffix-conjugation" forms
with present reference are plain QATAL.  If your theory can't take
into account such extremely strong regularities, then I think it's so
much the worse for your theory...

(These percentage numbers are not calculated in any mysterious way;
for example there are 55 WEQATALs with perfect reference and 2,605
plain QATALs with perfect reference, so that 2605/(2605+55) or 97.9%
of all raw "suffix-conjugation" occurrences with perfect reference are
plain QATAL.  However, these raw percentage numbers will always be
skewed in favor of plain QATALs by the fact that twice as many plain
QATALs occur overall as do WEQATALs; therefore to compensate for this
discrepancy -- which is irrelevant and confounding to the question of
relative temporal/modal reference distributions -- the calculation can
be redone in a corrected way as 2605/(2605+(13922/6087)*55), deriving
the same percentage 95.4% as in the previous paragraph.)


> A little less than one thousand WAYYIQTOLs with non-past reference
> is quite a great number if they are classified as exceptions.

Yes, but you count perfects as having "non-past reference" in this
sense, so I'm not sure that this is the most useful way of viewing
things...


>> It's true that semantic considerations can enter into establishing
>> the existence of morphological entities, but basically only to the
>> same degree that semantics enters into distinguishing allophones
>> and phonemes -- that is, only overall sameness or difference of
>> meaning is really relevant (and not the exact nature of the
>> specific meanings themselves); and a difference in the predominant
>> patterns of "temporal reference usage" would generally be
>> considered quite sufficient to establish a morphological contrast.
>> Once the morphological entities are established, you can debate at
>> length whether these differences in the predominant patterns of
>> temporal reference usage are properly "semantic" or "pragmatic" in
>> your particular theory, but it would be reversing the normal
>> procedure (and proposing a theoretical innovation which should be
>> explicitly recognized as a departure from the usual practice), to
>> say that ultra-subtle refinements of abstract "deep" semantic
>> theory can come back around and rewrite the basic morphology-based
>> definition of what is and what is not a morphological conjugation.

--
Henry Churchyard   churchh at usa.net   http://www.crossmyt.com/hc/



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