BCSSS

International Encyclopedia of Systems and Cybernetics

2nd Edition, as published by Charles François 2004 Presented by the Bertalanffy Center for the Study of Systems Science Vienna for public access.

About

The International Encyclopedia of Systems and Cybernetics was first edited and published by the system scientist Charles François in 1997. The online version that is provided here was based on the 2nd edition in 2004. It was uploaded and gifted to the center by ASC president Michael Lissack in 2019; the BCSSS purchased the rights for the re-publication of this volume in 200?. In 2018, the original editor expressed his wish to pass on the stewardship over the maintenance and further development of the encyclopedia to the Bertalanffy Center. In the future, the BCSSS seeks to further develop the encyclopedia by open collaboration within the systems sciences. Until the center has found and been able to implement an adequate technical solution for this, the static website is made accessible for the benefit of public scholarship and education.

A B C D E F G H I J K L M N O P Q R S T U V W Y Z

HALTING PROBLEM 2)3)

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TURING demonstrated by his uncomputability theorem that there is no effective mechanical procedure for deciding whether an arbitrary program will ever finish its computation and halt.

G. CHAITIN thus parallels TURING 'S work with GÖDEL's incompleteness theorem: "Kurt GÖDEL, the Austrian logician and Alan TURING, the father of the computer, showed that it is impossible to obtain both a consistent and complete axiomatic theory of mathematics and a mechanical procedure for deciding whether an arbitrary mathematical assertion is true or false, or is provable or not" (1990, p.44).

CHAITIN himself connected both aspects of this intrinsic limit to logical systems validation through his concept of algorithmic incompressibility.

According to J. CASTI: "… since the two problems are logically equivalent, the fact that the Halting Problem has no solution implies that the Decision Problem is also unsolvable. So we run up against a brick wall in trying to get to the heart of things by following a set of rules" (1990, p.137).

Of course, more or less provisionally and satisfactory solutions of any practical decision problem still remain possible. But we should always be aware of their limits.

Categories

  • 1) General information
  • 2) Methodology or model
  • 3) Epistemology, ontology and semantics
  • 4) Human sciences
  • 5) Discipline oriented

Publisher

Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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