Wednesday September 12, 2007

Vector Logic

Geometry for Jews
(March 2003)
discussed the
following figure:

The 4x4 square

Some properties of
this figure were also
discussed last March
in my note
The Geometry of Logic.

I learned yesterday from Jonathan Westphal, a professor of philosophy at Idaho State University, that he and a colleague, Jim Hardy, have devised another geometric approach to logic: a system of arrow diagrams that illustrate classical propositional logic. The diagrams resemble those used to illustrate Euclidean vector spaces, and Westphal and Hardy call their approach “a vector system,” although it does not involve what a mathematician would regard as a vector space.