Levels of Learning LO4764

JOHNWFIELD@aol.com
Wed, 10 Jan 1996 11:52:29 -0500

Replying to LO4697 --

I wonder how many of those interested in Principia Mathematica and its
relevance to LO are aware that this work is founded in the Theory of
Relations enunciated by Augustus DeMorgan in 1847---and if you are, how
many are aware that the young Norbert Weiner (age 18 or so, as I
recall)--published a key paper in which he pointed out a significant
interpretational void in Principia Mathematica, having to do with the
meaning of "relation" in mathematical terms.

In my work, based on all of that stuff, I try to remember to make a sharp
distinction between "relation" and "relationship". I have yet to find any
other author that does this. However it is a key to effective
communication about complexity.

As far as LO is concerned, one of the four indexes of complexity that I
have defined is the DeMorgan Index. This index involves a count of the
number of distinct relationships among a set of problems involved in an
issue. That number is the same as the number of binary relations
contained in the binary matrix that defines the relation and by
association the relationship.

Those who are not familiar with these distinctions will have a hard time
proving that any learning is going on in an LO; because there is virtually
nothing in learning that does not involve relationships. Moreover those
who think that they can construct relationships without understanding
"relation" in the Wiener-Whitehead-Russell-DeMorgan sense are going to
have a very hard time when confronted with the precise definitions
mentioned here.

--
John N. Warfield
Johnwfield@aol.com