PHIL30043: The Power and Limits of Logic

March 2021

at the University of Melbourne

PHIL30043: The Power and Limits of Logic (or, as I like to call it, Kurt Gödel’s Greatest Hits) is a University of Melbourne undergraduate subject. It covers the metatheory of classical first order predicate logic, beginning at the Soundness and Completeness Theorems, Compactness, Cantor’s Theorem, the Downward Löwenheim–Skolem Theorem, Recursive Functions, Register Machines, Representability, the Indefinability of Truth and the Undecidability of Predicate Logic, and ending up at Gödel’s Incompleteness Theorems and Löb’s Theorem.

Kurt Godel, seated
Kurt Gödel, seated

The subject is taught to University of Melbourne undergraduate students (for Arts students as a part of the Philosophy major, for non-Arts students, as a breadth subject). Details for enrolment are here. I make use of video lectures I have made freely available on YouTube.


The course is divided into four major sections, taught over 12 weeks. Here is a list of all of the videos, in case you’d like to follow along with the content.

Soundness and Completeness

Countability and Compactness


Undecidability and Incompleteness


I’m Greg Restall, and this is my personal website. I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the Director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology I like thinking about – and helping other people think about – logic and philosophy and the many different ways they can inform each other.


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