Archive for July 4th, 2011

July 4, 2011

Geometry and logic (3)

by Neil Rickert

In my previous post in this series I talked about the idea of partition, or dividing up the world.

Let’s suppose that we start with the world, and then divide it into two parts.  Call those parts A and B.  Perhaps it is the division into night and day, something that newborn infants have problems with but begin to get after a while.  Next we divide those parts, based on some other characteristics.  So A is further partitioned into parts A1 and A2, while B is further partitioned into parts B1 and B2.

If we continue partitioning in this way, we will have a way of organizing the world into the partitions.  And that organization will look a bit like a tree, something similar to a family tree.  If our partition was into two parts at each stage, we will finish up with a particular type of tree diagram that is known as a binary tree.

There is a natural way of finding items on a binary tree.  And that is to use logic.  At each branch point you encounter, you make the decision “if what I am seeking has characteristic 1, then go down branch 1; otherwise go down branch 2.”

My suggestion here is that the reason we find logic to be useful, is that as part of our cognition and perception of the world, we have been applying what I have called “geometric method” to organize our world into a nested series of partitions.  We use this geometric or partitioning method as a way of identifying objects, and the usefulness of logic is a consequence of our basing object recognition on such a partitioning scheme.