I prefer a mathematical definition. I need to set up two categories
with objects and associative morphisms that map one into or onto
another. A functor carries the objects, and the morphisms from one
category to the other. Then, a statement, which is a morphism in the
category of minds, is understood or not depending on the direction in
which a certain properly constructed arrow points. I will work this
out in detail, but the point is that understanding *anything* is like
understanding a true statement. It is an easy generalization. I have
put a lot of work into diagramming true statements in functorial
notation lately - following Tarski and Russell, somewhat.
The main idea is that, if the reader of the statement understood it, the
image in his mind would be the same as if his mind's eye were in the
mind of the writer of the statement so that his mental image of the
content of the statement were the same as that of the writer of the statement - as in the morphism "If I were you, ... ", assuming the writer
of the statement understood what he wrote and it were true. The arrow
I have in mind points to a true picture of an impression of reality
conveyed by the statement.
Regards / Tom Wayburn
P.S. I wish I could send this fancy diagram I made. It really helps.
But, when I get a chance, I'll "tell" the diagram.