Logical Seeing

Abstract

This chapter serves as an interlude. Our goal in the following chapters is to present a formalized approach to numbers, and then we will look at the number systems again to see how tools of logic are used to uncover their essential features. We will be inspecting the structure of the number systems 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 simple finite structures—finite graphs—and we will examine them from the logical perspective. In other words, later, logic will help us to see structures; now, some simple structures will help us to see logic. An important concept of symmetry of a graph is introduced in Definition 2.1 followed by equally important Theorem 2.1. Both, the definition and the theorem, will be generalized later to arbitrary mathematical structures.