Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am studying the proof of Gödel's first Incompleteness theorem at the moment and I don't understand the differences between self-referencing, diagonalization and fixed point related to Gödel's proof.

In my opinion, they all mean taking the Gödel number of a formula as an argument into the formula itself.

Can someone please explain me the differences?

Thanks in advance.

share|cite|improve this question
Whoever down-voted should provide a reason. – Quinn Culver Apr 14 '12 at 0:05
@Coopi Have you considered accepting some answers for your earlier questions? – Thomas Klimpel May 13 '12 at 18:56

It would probably help if you provide instances of each. But if you're just talking about their use in Gödel incompleteness theorems, then I suppose they all mean different aspects of the same thing. Application of the fixed point lemma is often referred to as diagonalization (of a given formula), and then that formula is said to be referring to itself.

I recommend:

Raymond Smullyan, 1994. Diagonalization and Self-Reference. Oxford Univ. Press.

Raymond Smullyan, 1991. Gödel's Incompleteness Theorems. Oxford Univ. Press.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.