This document introduces an object logic system for representing syllogisms pictorially using colored objects in boxes. It summarizes the history of symbolic logic from Aristotle to modern algebraizations. It then uses a box algebra system based on Kauffman's work to prove the "syllogistic unity" - that all valid syllogisms are equivalent through substitutions and transformations of the boxes and objects. This proof is conducted in 4 steps, reducing all 24 valid syllogism forms to a single representation. The document concludes by noting this proved an earlier claim of Christine Ladd-Franklin's about the derivability of syllogisms from a single formula.