 Algebra is of philosophical interest for at least two reasons. From the perspective of foundations of mathematics, algebra is strikingly different from other branches of mathematics in both its domain independence and its close affinity to formal logic. Furthermore the dichotomy between elementary and abstract algebra reflects a certain duality in reasoning that Descartes, the inventor of Cartesian Dualism, would have appreciated, wherein the former deals with the reasoning process and the latter that which is reasoned about, as respectively the mind and body of mathematics.