Logical Seeing

This chapter serves as an interlude. Our goal in the following chapters is to show how tools of logic can used to uncover essential features of familiar number structures. We will be inspecting number structures with our logic glasses on, but we need to get used to wearing those glasses. In this chapter we will take a look at some easy to visualize structures—finite graphs—and we will examine them from the logical perspective. In other words, later, logic will help us to see structures; now, simple structures will help us to see logic. A concept of symmetry of a graph is introduced in Definition 2.1 followed by Theorem 2.1, which is crucial for many further developments. Both, the definition and the theorem, will be generalized later to arbitrary mathematical structures.