EXTENDING MECHANICS TO MINDS reunites the sciences of mind and body by reworking the mathematical axioms of modern rational mechanics to analyze thinking in terms of mental forces (motivations, desires, communications) that produce mental motions (reasoning, learning) of mental substances (minds, beliefs) exhibiting mental inertia (habits, memory) and requiring mental effort (attention, persistence). Mental forces prove to be real forces, not mere metaphor; mental inertia helps understand the limits to rational calculation; and different kinds of minds represent different types of mental materials. The book uses precise mental models developed in artificial intelligence to illustrate analyses that provide psychology and economics with new characterizations of bounded rationality; provide mechanics with new types of materials exhibiting the constitutive kinematic and dynamic properties characteristic of different kinds of minds; and provide philosophy with a rigorous theory of hybrid systems combining discrete and continuous mechanical quantities. The resulting mechanical reintegration of the physical sciences that characterize human bodies and the mental sciences that characterize human minds opens traditional philosophical and modern computational questions to new paths of technical analysis.