On logic and fuzziness

Artur Karp hart at POLBOX.COM
Sat Nov 7 22:47:25 UTC 1998

At 08:44 7.11.98 -0500, you wrote:
>H.M.Hubey wrote:
>> One of my teachers played this "joke" on us a long time ago.
>>         I have four bottles labeled A, B, C and X.
>>         I mix A & X and drink and get drunk.
>>         I mix A & Y and drink and get drunk.
>>         I mix A & Z and drink and get drunk.
>> What can you say?
>> Most people would say that X has alcohol.
>I mixed up my variables obviously. It should be X in all cases
>not X,Y, Z.
>Best Regards,


Sorry, but the logic of your teacher's "joke" kind of keeps escaping me -
even with the new set of two variables - A and X.

Which brings me to the question of logic as opposed to the way of thinking
that you seem to believe is prevalent in some "fuzzy" disciplines (like
historical linguistics).

But first - a bit of personal reminiscing.

During 1968/69 I had the opportunity to work as a documentalist at the
neolithic site (VI-II M BC) in Bylany (Czech Republic). I still remember
with what great caution syntheses were formulated, even if the specialists
working there had at that time over 250 000 carefully documented (and
statistically processed) objects at their disposal. The main problem - if I
remember well - had to do with the difficulty in evaluating the possible
impact of some important variables, like the natural horizontal and
vertical movement of the archaeological strata.

Scantier or more doubtful material would have allowed only weak, tentative
hypotheses. With "fuzzy" stratigraphy (in historical linguistics - "fuzzy"
etymology and "fuzzy" diachronical fonology/morphonology), the use of
sophisticated statistical instruments isn't necessarily conducive to
producing better quality theories. [Question: why cannot the Painted Grey
Ware be dated more precisely?] But it certainly gives work to statisticians
and probability theory specialists.

What kind of result can one expect if one wants to analyze statistically  a
very limited set of words? Like the one posted by S. Kalyanaraman on Nov. 5
(where he says: <<Since there are lots of theoretical possibilities, let us
also look at some transportation lexemes and IE synonyms, from Carl Darling
Buck to formulate some statistically testable hypotheses>>).

What is the minimum size of statistical series, below which there can be no
talk of statistically meaningful results (since probabilities would just
tend to dissolve in the thin air)? What happens if such a set contains
material of uncertain quality (mistakes, borrowings, calques; S.
Kalyanaraman's set has all these characteristics)?

I do not think the reluctance with which historical linguists reach for
mathematics-derived methods has anything to do with the "fuzziness" of
their discipline, or lack in logic, or the unwilingness to let themselves
tested against the presence of some <<"Aryan Racist Philosophy" of the 20th
century>> virus. It's rather - it seems - a question of the very basic
demands - testable quality and a proper size of series of objects (words)
being the most important of them.

Employing probability theory as neutral referee (<<It is math, and its
branch of probability theory is younger but is available for all those not
too pompous.>>) may be only warranted by the kind of material one has at
hand. Certainly, it is available - but not always helpful. (Although -
ultimately, it might help someone suddenly discover their ability to speak
in prose...)

There are times when one is clearly better off by sticking to good old
s(t)olid procedures.

Such procedures, however, since they are the product of pre-post-modernist
modes of thought, do not permit everything to be connected with everything.


Artur Karp, M.A.

University of Warsaw

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