What does Godel, Turing and Chaitin Teach Us About Faith?
7th January 2006
The work of Kurt Godel, Alan Turing and Gregory Chaitin made important contributions to the study of mathematics, computer science and philosophy. Godel’s Undecidability Theorem and Incompleteness Theorem threw out the notions, previously held, that we can increasingly measure and know everything in the universe. In fact, Godel’s theorems proves that even in formal systems, in which everything are supposed to cohere together logically, there will be contradictory statements.
Alan Turing went one step further and showed that some numbers and functions can’t be computed by any logical machine. More recently, Gregory Chaitin showed that the the results of Godel’s and Turing’s works underscored that there are fundamental limits in mathematics:
You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to come up with new rules and axioms, but by doing so you’ll only create a larger system with its own unprovable statements. The implication is that all logical systems of any complexity are, by definition, incomplete.
But what does this all mean?
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