Gödel’s Theorems

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The big book

An Introduction to Gödel’s Theorems  was first published by CUP in 2007 with the second edition appearing in 2013.

A corrected version of the second edition is now available as a freely downloadable PDF.

Many people, however, prefer if possible to work from a physical book. So you can also get a print-on-demand copy of this version as a very inexpensive large format book from Amazon. US link; UK link. Find on your local Amazon by using the ASIN identifier B08GB4BDPG in their search field.  (You don’t get the original pretty cover; but the quality of the printing and paper is very acceptable, especially given the low price.)

The book previously appeared in the series, ‘Cambridge Introductions to Philosophy’ from CUP.  But don’t let that mislead you! IGT is actually a fairly techie logic book, originally intended for advanced philosophy undergraduates and postgraduates. It is quite long (388 pp.) and is full of theorems — so many mathematics students should find it useful too. Still, it does aim to give a relatively relaxed and approachable exposition of the technicalities around and about the incompleteness theorems and related results, and it does also provide a modest amount of more philosophical commentary on the interpretation and significance of the theorems.

A shorter book

Gödel Without (Too Many) Tears is a much shorter book (146 pp.) based on my notes for the lectures I used to give to undergraduate philosophers taking the Mathematical Logic paper in Cambridge. You can think of this as a cut-down version of the longer book, aiming to give some of the key technical facts about the incompleteness theorems without too many digressions. It is still full of technical exposition and quite short on philosophical asides — the main aim is to put a reader in a position where they can begin to understand what’s going on in discussions of supposed philosophical implications of the incompleteness theorems.

This book is now in a second edition and is available as a freely downloadable PDF.

But again, many will find it easier to work from the decently produced but extremely inexpensive print-on-demand paperback, with the ISBN 1916906358.

The paperback is Amazon-only. There is also be a hardback intended for libraries and available to order from bookshops and library suppliers  as well as Amazon. Its ISBN is 1916906341. Please do ask your university librarian to order a printed copy for the library.

Corrections to current versions

  • IGT: For just a handful of minor known corrections for the current downloadable PDF/print-on-demand Amazon version, see here.

Corrections to older versions

  • If you are the proud owner of the 2007 first edition of An Introduction to Gödel’s Theorems,  IGT1, you are very warmly encouraged to upgrade to the much better second edition! For the many needed corrections to the various printings of IGT1, see here.
  • For relatively minor corrections to the 2013 CUP printed version of IGT2, see here.
  • For corrections to the very short-lived earliest printed version of GWT, see here.
  • For corrections for the main first edition of GWT, see here.


There are exercises with solutions for early chapters in IGT2. Now that I see that they are being made some use of, I plan to add further exercises one day, but this isn’t a top priority:

More on Gödel’s Theorems

  • Lectures on the First Incompleteness Theorem — just four introductory lectures given in Easter term 2011 as a supplement to Thomas Forster’s earlier Part III Maths course on Computable Function Theory. (The first three don’t require any background in the theory of computation over an above a grip on the idea of a primitive recursive function and the idea of coding: only the fourth appeals to results like the unsolvability of the halting problem.)
  • Back to Basics: Revisiting the Incompleteness Theorems. The notes for a three-lecture series given to mathematicians at a Cambridge weekend workshop for graduates in 2009. They complement the book by approaching things in a rather different order.
  • Expounding the First Theorem — extensive (though far from completed) notes on the expository tradition. Version 2: From 1931 to 1953.

Other relevant notes

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