1) The syllogism is a manner in which common attributes of categories and sub-categories are parsed to form logical relationships in human language through the use of the transitive property for the purpose of discerning a greater fundamental understanding of an objects function, use or nature.

2) Just as Aristotle used the syllogism to create broader and broader categories within a membership by reducing its description to as few common characteristics and discarding unlike elements, topology seeks to find a more fundamental insight to the spatial relations between elements by reducing their description and relinquishing both measurable quantity and orientation that are so crucial to the representation of Euclidean geometry within Cartesian space. For example, on page 4 of the reading on topology, Barr states that a "line does not have to remain straight" in topology. In a strict geometric interpretation, where a line is defined by three points within a straight relationship, once this alignment is broken, the element would now have to be called a curve or suffer division into two independent 'straight' lines. In the topological sense, the definition of a line is reduced to "the quality of being continuously connected along itself."

3) The aesthetic appreciation of the visceral experience of architecture is not done by algorithm. Nor the budget.