Are there minding machines? In this paper, I consult historical, philosophical, and empirical sources in trying to answer this intriguing question. My historical and philosophical discussions focus on five famous Frenchmen (Michele de Montaigne, René Descartes, Salomon de Caus, Julien Offray de La Mettrie, and Jacques Vaucanson) and one famous American (William James). My review of empirical research focuses on five topics in contemporary comparative cognition: associative/causal learning, short-term memory, number discrimination, relational cognition, and metacognition. I conclude that natural minding machines do exist; they are humans and animals. Minding may be said to mediate the complex changes in behavior that humans and animals overtly exhibit. In that same sense, computers and other mechanical devices are often considered to be artificial minding machines. Nevertheless, many thinkers deem such artificial minding machines to be pale replicas of natural minding machines that are built from the “wrong stuff.” No matter how much progress in artificial intelligence advances the computing power of these devices, they may never attain the intricacy and flexibility of nature’s minding machines.