Logic has been described as “the subject in which nobody knows what one is talking about, nor whether what one is saying is true.” This means in logic we don’t analyse the content of statements, or even have a way of expressing that content, we’re just concerned with how those statements are connected.
It’s time to start making statements with actual content. We’ll do this in two settings, elementary arithmetic and set theory. We’ll start with elementary arithmetic because it’s more familiar, although formal proofs in elementary arithmetic may not be.