A syllogism is a logical argument and is thereby exactly what Aristotle is using to describe and organize his system of categories. Just as a syllogism is an equation of truths, the categories are simply equations for understanding and quantifying composition or structure.


The terms topology and geometry explored by Barr on pages 2 and 3 describe the permanence associated with topology versus the contingencies associated with topology. Furthermore, the strict parameters of geometry are identified as characteristically opposed to the understanding of topology.


Social and emotional affects and effects of architecture are not always direct results of physical geometry. Although light, air, orientation, acoustics and other environmental influences are often quantified using computational software, the attitudes and persuasions of a designer are difficult to describe or predict in pure geometry.