Since the discovery of the paradoxes of self-referentiality or self-reference respectively logicians and mathematicians tried to avoid self-reference when constructing formal systems. Yet "real" complex systems like the mind are characterized by self-reference and can accordingly only be modeled by formal systems that are also basically self-referential. In this article I show that and how self-referential computer programs, understood as algorithmic formal systems, are not only possible but

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... o since some time quite common in special branches of computer science. Examples for this argument are neural networks and so-called hybrid systems, i.e. combination of different sub systems. The hybrid system SOCAIN, a combination of a cellular automaton, a neural network and a genetic algorithm is an example for the fruitfulness of using self-reference in a systematic way. In particular, such systems consist of mutually dependent sub systems, i.e. form no static hierarchy. When more than a century ago Russell discovered his famous paradox of the set that consists of all sets, which do not contain themselves as elements; he draw attention to the problem of self-referentiality: A formal system must not be selfreferential in order to avoid the according paradoxes. Consequently formal systems like the Principia Mathematica of Russell and Whitehead (the theory of types) and the set theoretical axioms system of Zermelo and Fraenkel (ZFC) were constructed by banning self-referentiality. For example, in ZFC a set is of a higher order than its elements and hence a set cannot include itself as an ele-How to cite this paper