Paradoxes, Self-Referentiality, and Hybrid Systems: A Constructive Approach

Full-Text HTML XML Download Download as PDF (Size:395KB) PP. 48-63
DOI: 10.4236/ojpp.2017.71004    606 Downloads   750 Views  
Author(s)    Leave a comment


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 also 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.

Cite this paper

Klüver, J. (2017) Paradoxes, Self-Referentiality, and Hybrid Systems: A Constructive Approach. Open Journal of Philosophy, 7, 48-63. doi: 10.4236/ojpp.2017.71004.


[1] Czarnecki, K., & Eisenecker, U. W. (2000). Generative Programming. New York: Addison Wesley.
[2] Gödel, K. (1931). über formal unentscheidbare Sätze der PrincipiaMathematica und verwandter Systeme I. Monatsheftefür Mathematik und Physik, 38, 173-198.
[3] Goonatilake, S., & Khebbal, S. (1995). Intelligent Hybrid Systems. London: John Wiley Sons.
[4] Hofstadter, D. R. (1979). Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basics Books.
[5] Kauffman, S. (1993). The Origins of Order. Oxford: Oxford University Press.
[6] Klüver, C., & Klüver, J. (2013). Self-Organized Learning by Self-Enforcing Networks. In I. Rojas, G. Joya, & J. Cabestany (Eds.), Proceedings of the 12th International Work-Conference on Artificial Neural Networks (IWANN 2012), Part I. Lecture Notes in Computer Science, Vol. 7902, Springer, Berlin, Heidelberg, 518-529.
[7] Klüver, J., & Schmidt, J. (2007). Recent Results on Ordering Parameters in Boolean Networks. Complex Systems, 1729-1745.
[8] Klüver, J. (2000). The Dynamics and Evolution of Social Systems. New Foundations of a Mathematical Sociology. Dordrecht, NL: Kluwer Academic Publishers.
[9] Penrose, R. (1989). The Emperor’s New Mind. Concerning Computers, Minds, and the Laws of Physics. New York: Oxford University Press.
[10] Stoica, C., Klüver, J., & Schmidt, J. (2004). In the Looking Glass: The Self-Modeling of Social Systems. In Y. Bar-Yam, & A. A. Minai (Eds.), Unifying Themes in Complex Systems II. Proceedings of the Second Conference on Complex Systems. Boulder: Westview Press.
[11] Tarski, A. (1956). Logic, Semantics, Metamathematics. Oxford: Oxford University Press.
[12] Tipler, F. J. (1994). The Physics of Immortality. New York: Double Day.
[13] Turing, A. M. (1937). On Computable Numbers, with an Application to the Entscheidungsproblem. Proceedings of the London Mathematical Society Series 2, 42, 230-265.

comments powered by Disqus

Copyright © 2017 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.