Knowing & Understanding

To "know" is to "successfully predict".
To "understand" is to have "a rationale" to support the prediction.

E.g.

I "know" this switch operates the light.
I "understand" that the switch completes an electrical circuit.

I "know" that Henry VIII had six wives (I predict reading this in a history book).
I "understand" how Henry managed to usurp the Popes authority in order to "annul marriages".

All understanding is limited by assumption of at least one axiom (Godel Theorem).
All "knowledge" is subject to context.

Fresco

Is a multiple choice exam an accurate way to determine understanding? How did you decide which fact was knowledge and which was understanding? Please don't answer with Godel's Theorem I hardly know the woman.

Nope. It can be measured by an essay. An explaination of the answer and the reasoning behind why you came to the answer you did. The understanding of an answer, versus memorization of an answer. Math tests where you have to work the problem are ways to determine understanding because you must show that you know how you got to the answer.

coberst,

I agree with Bella Dea regarding "understanding", and I would say "facts" are publically agreed "knowledge".

The difference between knowledge and understanding is that the latter is a network of "knowledge" from which other "knowledge/predictions" can be infered.

The segmentation of such a network into discrete "facts" tends to be arbitrary and the network tends to resist "counter examples" by virtue of its interdependent weblike structure.. Thomas Kuhn outlined this resistance prior to a potential paradigm shift in "Structure of Scientific Revolutions". New paradigms such as Relativistic Physics tend to delimit earlier ones such as Newtonian Physics rather than dismiss them out of hand. Hence in the teaching and learning of a subject there are various levels of understanding according to the breadth of the paradigm adopted and the observations embraced. There is no ultimate paradigm (Godel :wink: ).

Bella

I s addition knowledge or understanding? Is calculus knowing or understanding?