International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 283-289

Fixed points and self-reference

Raymond M. Smullyan

Department of Philosophy, Indiana University, Bloomington 47405, Indiana, USA

Received 15 May 1982

Copyright © 1984 Raymond M. Smullyan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is shown how Gödel's famous diagonal argument and a generalization of the recursion theorem are derivable from a common construation. The abstract fixed point theorem of this article is independent of both metamathematics and recursion theory and is perfectly comprehensible to the non-specialist.