Gödel's Theorem: A Very Short Introduction

When Kurt Godel published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing but the truth concerning arithmetic, it had a profound impact on mathematical ideas and philosophical thought. Adrian Moore places the theorem in its intellectual and historical context, explaining the key concepts and misunderstandings.

A.W. Moore is Professor of Philosophy at the University of Oxford and Tutorial Fellow in Philosophy at St Hugh's College, Oxford. He has held teaching and research positions at University College, Oxford, and King's College, Cambridge. He is joint editor, with Lucy O'Brien, of the journal Mind. In 2016 he wrote and presented the series A History of the Infinite on BBC Radio 4.

- 1: What is Gödels theorem?
- 2: The appeal and demands of axiomatization
- 3: Historical background
- 4: The key concepts involved in Gödel's theorem
- 5: The diagonal proof of Gödel's theorem
- 6: A second proof of Gödel's theorem, and a proof of Gödel's second theorem
- 7: Hilbert's programme, the human mind, and computers
- 8: Making sense in and of mathematics