TItis book is the joint project of a philosopher, Lehrer, and a mathematician, Wagner. The book is, therefore, divided into a first part written by Lehrer, which is primarily philosophical, and a second part written by Wagner that is primarily formal. The authors were, however, influenced by each other throughout. Our book articulates a theory of rational consensus in science and society. The theory is applied to politics, ethics, science, and language. We begin our exposition with an elementary mathematical model of consensus developed by Lehrer in a series of articles [1976a, 1976b, 1977, 1978]. Chapter 3 contains material from [1978]. Lehrer formulated the elementary model