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Kurt Gödel
Posted By : at 2007-04-28 09:50:35
(It is this theorem that is generally known as the Incompleteness Theorem.) If the system is consistent, then the consistency of the axioms cannot be proved within the system. These theorems ended a hundred years of attempts to establish a definitive set of axioms to put the whole of mathematics on an axiomatic basis such as in the Principia Mathematica and Hilbert's formalism. It also implies that a computer can never be programmed to answer all mathematical questions. In hindsight, the basic idea of the incompleteness theorem is rather simple. Gödel essentially constructed a formula that claims that it is unprovable in a given formal system. If it were provable it would be wrong, so one could prove wrong statements in this system. Otherwise there would be at least one true
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