Offered through the University of Melbourne

PHIL30043: The Power and Limits of Logic is a University of Melbourne undergraduate subject. It covers the metatheory of classical first order predicate logic, beginning at the Soundness and Completeness Theorems (proved not once but twice, first for a tableaux proof system for predicate logic, then a Hilbert proof system), through the Deduction Theorem, Compactness, Cantor’s Theorem, the Downward Löwenheim–Skolem Theorem, Recursive Functions, Register Machines, Representability 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 Vimeo.


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





Undecidability and Incompleteness

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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.



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