1. Formal systems
Before introducing first order logic, I want to present a “toy example” of the issues we will face, and the results we are after.
In a formal system we present a set of rules about manipulation of finite strings of symbols, and attempt to study which strings can be obtained through these manipulations.
Informally, this corresponds to the syntactic part of logic, and the beginning of proof theory.
I will follow an example from Richard Kaye’s book The Mathematics of Logic.