Chaitin Articles

Gligoroski, Danilo and Dimovski, Aleksandar (2001) Chaitin Articles. In: Proceedings of the Second Conference on Informatics and Information Technology. Institute of Informatics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University in Skopje, Macedonia, Skopje, Macedonia, pp. 93-102. ISBN 9989-668-28-0


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In this paper, we'll discuss how to Godel's paradox "This statement is false / unprovable" which yields his famous result on the limits of axiomatic reasoning, Chaitin contrasts that with his theory, which is based on the paradox of "The first uninteresting positive whole number". This paradox leads to results on the limits of axiomatic reasoning, namely the most part of numbers are uninteresting or random, but we can never be sure, we can never prove it, in individual cases. And these ideas culminate in discovery that some mathematical facts are true for no reason, they are true by accident, or at random. In other words, God not only plays dice in physics, but even in pure mathematics, in logic, in the world of pure reason. Sometimes mathematical truth is completely random and has no structure or pattern that we will ever be able to understand.

Item Type: Book Section
Uncontrolled Keywords: Godel’s theory, Berry paradox, program-size complexity, Borel’s number, Turing’s halting problem, Turing’s number, redundant, Omega number, positive results
Subjects: International Conference on Informatics and Information Technologies > Computer Science
International Conference on Informatics and Information Technologies > Software Engineering
Depositing User: Vangel Ajanovski
Date Deposited: 28 Oct 2016 00:15
Last Modified: 28 Oct 2016 00:15

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