Although mathematical ability and opinions about mathematics vary widely, even among educated people, there is certainly widespread agreement that mathematics is logical. Indeed, properly conceived, this may be one of the most important defining properties of mathematics.

Logical thought and logical arguments are not easy to come by, nor is it always clear whether a given argument is logical (that is, logically correct). Logic itself deserves study; the right tools and concepts can make logical argument easier to discover and to discern. In fact, logic is a major and active area of mathematics; for our purposes, a brief introduction will give us the means to investigate more traditional mathematics with confidence.