About

Non-elementary is written by me, AJT.

Twenty years ago I wrote an undergraduate thesis on Gödel's incompleteness theorems. Since then, a master's in logic and formal grammar, a PhD in computational linguistics, a career in AI, and along the way most of the logic itself got set aside. This blog is where it's being rebuilt, evenings and weekends, alongside full-time work. It's a multi-year project rather than a course with an end date.

Why. Most of my work in AI rewards moving fast and staying on the surface, and I wanted something that rewards the opposite: understanding one thing properly, all the way down, rather than just well enough to use it. Logic is what I already know how to do that with. It takes doing the proofs, not reading about them, and it takes years rather than weekends.

The plan, roughly: set theory and first-order logic first, then model theory proper, then a specialisation and an attempt at something original. Alongside it, a couple of hours a week on the history and philosophy: the foundational crisis of the 1920s, Tarski, and the parts of philosophy of science and formal semantics that grew out of model theory.

What to expect. Notes from the actual work: proofs that took longer than expected, places where intuition failed, occasionally some history or philosophy when it changes how the mathematics reads. No fixed schedule, and no guarantee the plan survives contact with the material.

Elsewhere: X.