Dear Organlearners,
John Dicus <jdicus@ourfuture.com> writes:
> So she simply said, explain to me the difference between assumptions and
> mental models in common words. After I failed to convince either of us, I
> gave up too. Now I am convinced that the opposite of collective
> intelligence is a discrete possibility.
John, I can sympathise with you. Since English is not my mother tongue, I
have to make sure of the meaning of words either through a dictionary or a
specialised text book. People often use a word in such a way that I begin
to doubt those meanings of the word which I remember. Then I have to go
back to the books - often to find that the books seem not to apply any
more.
I will explain how I use assumption and mental model.
To understand an assumption, we have to begin with a proposition. A
proposition is a sentence describing anything either correctly (true) or
incorrectly (false). In other words, a proposition has one of two possible
truth values: "true" and "false". But what is important of a proposition
is that we do not know in advance which one of the two values it is.
We can also get another class of sentences of which the particular truth
value is known or accepted in advance. They may be called the "assuming"
sentences. The particular truth value they assume is usually "true". They
are of various kinds like axioms, postulates, lemmas, hypotheses,
theorems, facts, beliefs and even assumptions, depending on how they were
obtained and will be used.
An axiom, for example, is a sentence of which the truthvalue is obtained
by self-evidence. Axioms are used in valid inferences to arrive at
theorems. The truth value of the axiom is thus hereditary. An assumption,
on the other hand, is almost the opposite of an axiom. It is almost as if
the truthvalue of an assumption is accepted by arrogance, as if there is
no care whether the truthvalue is the correct one or not. We will soon see
that this arrocance can also become hereditary.
People often speak of an sentence as an assumption when they should have
spoken of it as an axiom, postulate, etc. The reason is very subtle. The
sentence usually begin with: "Assume that ......". That is why I called
them the "assuming" sentences. The fact that the sentence begin with
"Assume that ....." does not make them assumptions. What makes them
assumptions is the fact that their actual truthvalue is of no importance.
(If the actual truthvalue of your assumptions are important to you, then
you should not call them assumptions. Try to find a better descriptive
name like axioms, postulates, ....
A mental model is made up of interrelated sentences excluding
propositions. In other words, there is not a single sentence in a model of
which we do not know in advance its truth value. Thus all the sentences of
a model is of the "assuming" kind. This is why it is so easy to confuse a
mental model with assumptions. However, there is a marked difference
between a mental model and assumptions. The sentences of a model are
interrelated while assumptions need not to be interrelated.
A mental model often contain a number of assumptions as part of it.
Unfortunatly, these models are arrogant because of the heredity effect of
the arrogance contained in its assumptions. We can also make external
assumptions about a model. Obviously, they are not the same as any
possible assumptions within the model. They are usually the beginnings of
a new mental model.
Should we also include propositions into a mental model, then it becomes a
theory. A theory is thus logically incomplete and open when compared to a
model. Models are frequently used to test a theory, although not all
models are good testers. However, we cannot test a model by a theory
because there is nothing to argue about the truthvalues of the sentences
of a model.
John, I hope I did not confuse you even more.
Best wishes
--At de Lange Gold Fields Computer Centre for Education University of Pretoria Pretoria, South Africa email: amdelange@gold.up.ac.za
Learning-org -- An Internet Dialog on Learning Organizations For info: <rkarash@karash.com> -or- <http://world.std.com/~lo/>