I’ve noticed that some of my posts that have gotten the most hits are my introductions to mathematical logic. Overall, I’m pretty happy with that series of posts, though I think since then I’ve come up with clearer and more precise ways of talking about the primary distinctions: syntax, semantics, and proof systems.

A little while ago, I gave a talk on the subject of “true but unprovable” statements. The goal of the talk was just to explore this notion and explain what exactly it means to a logician. In the course of developing the talk, I ended up re-summarizing the basics of mathematical logic. I think this summary makes a good “companion piece” to my earlier introductory series, as well as being more standard in its presentation. The most important slide is this one:

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