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unders[w84,jmc]		understanding and other mental terms

	For AI purposes, we need characterizations, as precise
as the terms admit and we can discover, of a wide collection
of mental terms.

	We begin with understanding.  The word is used in a
variety of way, e.g. "He understands me", "He understands
chemistry".  However, will concentrate on the notion of understanding
a sentence.

	We agree that a person can hear or read a sentence and even
memorize it and still not understand it.  He can also misunderstand
it.  Consider the epsilon-delta definition of continuity.  A function
f: R → R is continuous at the real number  a  iff for every  ε > 0,
there is a real number  delta > 0  such that whenever  |x - a| < delta,
we have  |f(x) - f(a)| < ε.  We use this example, because some of
you readers won't understand it and those that do will remember when
they didn't or at least their interaction with people who don't.

	Suppose we ask a student to prove that the function  f(x) = x
is continuous at  x = 0, and he says "Take delta = ε".  I think we
would agree that he understood the definition even if he could not
apply it to more complicated examples.

	This suggests taking understanding to mean or at least
involve being able to draw sufficiently obvious conclusions.
from the definition.  Actually we might be satisfied with a
more passive understanding.  For example, he should be satisfied
with taking  delta = ε  in the above example and reject taking
delta to be some fixed number or ε/2.  It would not suffice if
he could only draw or accept purely propositional consequences
of the sentence, e.g. its disjunction with some other sentence.

	Understanding is often sharply perceivable subjectively,
i.e. a person usually knows whether he understands or not.
This presumably involves integrating what is expressed in the
sentence with the knowledge the person already has.  From
the point of view of formalization, this suggests taking
understands(<person>,<sentence>) as a primitive concept to be
connected with others by axioms.  The doctrine is the following.
If we believe that we have more to learn about a concept that
may not amount to learning about other concepts, then it is best
to take that concept as primitive rather than trying to define
it in terms of others.