What is an Operational Definition? LO26984

From: AM de Lange (amdelange@gold.up.ac.za)
Date: 07/11/01

Replying to LO26959 --

Dear Organlearners,

Hanching Chung <demingtw@ms17.hinet.net> writes in the
Subject: What is THE problem? LO26959

>Perhaps now is 'sometime' in your context.
>Please kindly explain 'The truth sets you free' is
>an operational definition instead of a language

Greetings dear Hanching,

Your requirement "no language game" reminds me of a saying by Plato: "You
can discover more of a person in one hour of play than in a year of

First of all, let us study your requirement " no language game". Liveness
("becoming-being") is essential to both languages and games. In a language
the "becomings" are primarily reflected by verbs and the "beings" by
nouns. In a game all the "becomings" are focussed on a particular becoming
like "kicking the ball" in soccer. The "beings" of the game are its rules.
Consequently in neither languages nor games can we avoid liveness as an
essential pattern.

Or as Marshall McLuhan wrote:
. "The form of a game is of first importance.
. For it is the pattern[s] of a game that give[s]
. it relevance to our inner lives, and not who is
. playing nor the outcome of the game."
He could have written the same for the "patterns of a language", better
known as its grammer.

The distinction between an ontological definition and an operational
definition hinges on accepting liveness as essential to the distinction.
In an ontological definition a specific entity ("being") is described in
terms of other already known structures. In an operational definition a
specific entity ("being") is founded upon a already known processes.

For example, in chemistry a molecule is usually ontologically defined as a
consisting of a collection of atoms connected together. The best known
operational definition in physics is that of work. Work has to be
calculated by multplying the magnitude of a force with the component of
its displacement along the direction of its action.

But let me get closer to an example from your own writing. In your
reply "Tragedy of the Commons Issues LO26956" to Don Dwiggens
you wrote:
. "Perhaps with some similar reasons, the late
. H. A. Simon advised me that sciences should be
. based on 'topics' ( my terms, in the sense of
. Aristotle's ) instead of any particular persons
. ( i.e., what Aristotle said ).
This seems to me like an ontological definition of the sciences.

The operational definition of a science would be to apply the scientific
method (reflect, observe, speculate, falsify, reflect) on a particular
domain. Many domains have been recognised like inanimate matter (leading
to chemistry), earth materials (leading to geology) and living matter
(leading to biology).

Because of this very operational definition of science, the discipline
Operational Research was first ever recognised during WWII as a key to
victory. (See for example J Ziman, "The Force of Knowledge", pp 320-335) A
decade later on Operational Research began to take effect outside warfare
in the management of organisations.

Truth concerns the quality "true" of character. Other qualities of
character are for example "good" (ethics), "right" (morality) and "beauty"

As for truth itself, I find that all the Bible writers over a period of
almost two thousand years did not deal with truth as a topic which can be
studied independently from the other topics concerning character. In other
words, they dealt with truth in the wholeness of character. However, I
wish to avoid using the Bible to explain "the truth will set you free"
because it will most probably cause even more confusion. The history of
truth studies outside the Bible shows clearly that certain patterns like
wholeness and liveness, not exclusive to the religious realm, are
involved. So I will rather focus on these patterns outside the Biblical
context. This will make us aware of the confusion which we have to avoid
when studying truth from the religious realm, whether it be from the
Bible, Veda, Koran or any other religious codification.

This recognition of wholeness in studying truth had been the same among
early Greek thinkers like Archimedes. However, beginning with Aristotle,
most philosophers afterwards dealt with truth as a subject which could be
studied independently (i.e. on its own). From Aristotle we even get the
name logic for this study. He also gave logic its ontological flavour
which persisted for more than two thousand years. Logic became the
collection of true propositions, arranged into an ordered structure,
almost like a molecule in terms of atoms.

But in the 1800s the writing appeared on the wall for the ontological
status of logic with the operational work of Boole who tried to calculate
logic with algebra. This example gave many people the idea to introduce
other actions into logic than merely calculating as action. The turning
point came late in the 1800s with the work of Frege in his "Begriffslehr".
He not only succeeded in distinguishing between "true statements" (being)
and "infering truely" (becoming), but even to symbolise these two
complements. Following Goethe's idea of "Steigerung" (staggering), he
succeeded in creating many of the known theorems of tradional logic.

Because of the resistance of many traditional philosophers (inclined to
ontology) to this operationalization of logic, symbolic logic slipped out
of philosophy into mathematics as a major field of the latter up to this

In the 1970s a profound paradigm shift happened in mathematics. Since
Euclid mathematicians tried representing mathematics ontological, i.e. in
terms of a small collection of structures. This epoch spanning some two
thousand years culminated in the "set theory foundation" of mathematics
after WWII. According to this foundation the concept "set" (collection of
elements) was the only trivial (non-mathematical) concept needed for all
mathematics. However, it was gradually realised that more than "set" was
needed to overcome the growing set of inconsistencies. Eventually it was
realised that both "set" (being) and "functor" (becoming) were needed as
undefined (primitive) concepts. Soon afterwards mathematics became
recasted in terms of Category Theory.

Category Theory freed mathematics from it structure-like conception.
Mathematics are now constructed by means of diagrams consisting of
"arrows" (becomings) and "objects" (beings). For the first time ever
mathematicians began to explore far beyond the boundaries set up by the
grammer of a natural language for its sentences consisting of "verbs"
(becomings) and nouns ("beings").

One such a diagram is a deceptively simple one looking like a square and
called a "pullback" diagram. It has four objects at its corners and four
arrows along its sides. Describing this diagram with sentences of a
natural languages is more than a nightmare. Yet its construction finds
many applications in mathematics.

But its application to logic had a profound impact. Not only the objects
(beings) "value-true" and "value-false" may be recognised in logic, but
also the arrows (becomings) "make-true" and "make-false". When both these
two arrows are applied to a truth, they result in the category [true,
false]. In other words, "make-true" protects the truth's value true
whereas "make-false" converts it into the value false. On the other hand,
when applied to a farce, "make-false" protects the farce's value false
whereas "make-true" converts it into the value true.

I do not want to stop at this highly abstract recollection. So allow me to
give an example of such "make-true" and "make-false" arrows. We all will
say that "blood is red" is a truth. How will we convert it into a false
statement? It is easy. Illuminate blood with a pure green light and its
colour will become black. Why? The haemoglobin of blood absorbs all
colours of light except red light which is reflected by it.

In other words, by illuminating blood with any colour of light which
contains the colour red, we have applied the arrow "make true" to the
truth "blood is red". But by illuminating blood with any colour of light
which does not contain the colour red, we have apllied the arrow "make

It took scientists more than a century to uncover most of the two main
physiological functions of blood, namely "feeding" and "cleaning". Parts
of the body which are not easily washed by blood (like the eye's retina
and bones) thus need more attention in case of a possible decrease in
blood supply or otherwise infections.

We may throw the light of hard-core science so much upon the physical
functions of blood that we may claim all spiritual functions of blood to
be false. But remember the example above that only that colour of an
object can be reflected which is contained in the colours of the light
shone upon the object. So when we use a different light than that of
science, will we still be able to claim that blood has no spiritual
functions, perhaps again feeding and cleaning as its main functions?

As a Christian I owe you some explanation, although you do not have to
accept it. I confess that the physical blood of Jesus (who refered to
himself as the truth) once sacrificed on the cross feeds and cleans my
spirit daily, thus freeing me of my sins. But I cannot ever claim that
others learners must have the same confession as I. Nor can anyone else
claim that I must use only the light of hard-core science to know the
truth for this restriction will never set me free.

As for thinking that I am playing language games, perhaps it may
appear to be the case. However, I discovered some thirty years ago
by observing closely my pupils what may be used as an operational
definition of learning:
. "To learn is to create".
Today I am more than ever convinced of this truth whatever the colour
of light shone upon it.

With care and best wishes


At de Lange <amdelange@gold.up.ac.za> Snailmail: A M de Lange Gold Fields Computer Centre Faculty of Science - University of Pretoria Pretoria 0001 - Rep of South Africa

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