"Theoppositeofacorrectstatementisafalsestatement.Buttheopposite of a profound truth may well be another profound truth." - Niels Bohr 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 studiedtoanygreatlengthin?eldsoutsideofphilosophyandlogic.This, despite the fact that we observe opposition everywhere in nature, our minds seem to divide...