The Flaw in Gödel's proof of his Incompleteness theorem

You might be expecting to find here a brief summary of the flaw in Gödel's proof. However, it is impossible to give a proper explanation of the flaw in the proof in a few short sentences. This should not be surprising; if it was that simple to explain the flaw, one would have expected that the flaw in the proof would be relatively simple to discover.

A brief summary inevitably means making shortcuts and simplifications. Because of that, there would necessarily be deficiencies in the explanation - if that was not the case, then a brief summary would contain all of the information of the full article! Experience shows that, regardless of whatever warnings one makes about such deficiencies that a brief summary might contain, they are ignored by a multitude of irrational individuals. These persons take delight in spreading misinformation, quoting material from the brief summary as though it was material from the full explanation. Because of that, no attempt will be made here to give a brief summary.

A Simplified explanation of Gödel's proof and the flaw in the proof

If you are not familiar with the details of Gödel's proof, I suggest that you either read the simplified explanation of Gödel's proof on this website, or read the novel The Shackles of Conviction . Both include an explanation of the theorem and the flaw in Gödel's proof of it in a simplified way that makes it accessible to the general reader.

A Detailed explanation of the flaw in Gödel's proof

On the other hand, if you are very familiar with the details of Gödel's theorem, you will probably also want to see the details of the flaw in Gödel's proof as covered in the paper:

The Fundamental Flaw in Gödel's proof of his Incompleteness Theorem (PDF)

The paper gives a comprehensive demonstration of the flaw in Gödel's proof of his Incompleteness Theorem. The link above is a link to the latest version. Please note that the central argument of the paper remains unchanged thorughout the revisions. The revisions have been to make the principles easier to understand. If you want to see the previous versions please see the sitemap.

Responses to the demonstration of the flaw in Gödel's proof

If you would like to see some of the responses that I have received regarding the demonstration of the flaw in Gödel's proof, please see here.