Gödel’s Theorems

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The big book

An Introduction to Gödel’s Theorems  was first published in 2007 with the second edition appearing in 2013. A corrected version of the second edition is now available as a freely downloadable PDF. (The current version of this PDF is dated August 2020.)

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.) Note that since this reprint isn’t coming from a publisher with a marketing department, you will need to ask your university librarian to order a printed copy for the library.

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 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 (137 pp.) based on my notes for the lectures I used to give to undergraduate philosophers taking the Mathematical Logic paper in Cambridge. Earlier versions have been circulated and much downloaded for a decade (and I know have been used for lecture courses elsewhere). This new version has been tidied-up into a book format. You can think of it 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 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 book available from Amazon: US link; UK link. Find on your local Amazon by using the ISBN 1916906311 in their search field.

The paperback is Amazon-only. There is also a hardback intended for libraries and available to order from bookshops and library suppliers  as well as Amazon. Its ISBN is 1916906303. Please do ask your university librarian to order a printed copy for the library.

Added September 2022: I am currently working on a second edition of GWT, and have got to the point where there is now a third full draft. This too is now free to download (and hopefully not too error-ridden). Downloading is promising to let me know about any errors you find! Current version is dated Sept 25.

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.
  • GWT: For 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 short-lived earliest printed version of GWT, see here.


There is are exercises with solutions for early chapters in IGT2. Now that I see that they are being made use of, I plan to add further exercises:

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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