Proof theory

Okay kiddo, proof theory is like a game where we try to figure out if something is true or false. Think about it like playing a puzzle game with rules. In this game, we have to follow certain steps in order to prove whether a statement is true or false.

For example, let's say we have the statement "All dogs have tails." We already know this is true, but how do we prove it? Well, we have to follow certain steps, like showing that every dog we can think of has a tail. If we can do that, then we can say that the statement "All dogs have tails" is true.

Proof theory is like that, but for more complicated statements. We use logic and symbols to help us figure out if something is true or false. This helps us in many different fields, like math, computer science, and philosophy.

So, when someone is talking about proof theory, they are talking about a special kind of reasoning that helps us figure out if something is true or false. It's like a puzzle game, but for grown-ups!