This volume is motivated in part by the observation that opposites permeate
everything around us, in some form or another. Its study has attracted the
attention of countless minds for at least 2500 years. However, due to the lack
of an accepted mathematical formalism for opposition it has not been explicitly
studied to any great length in fields outside of philosophy and logic. Despite
the fact that we observe opposition everywhere in nature, our minds seem to
divide the world into entities and opposite entities; indeed we use opposition
everyday. We have become so accustomed to opposition that its existence is
accepted, not usually questioned and its