Tagged: Incompleteness Theorem

Incompleteness Theorem

The Incompleteness Theorem is Gödel’s main contribution to 20th century thought. Gödel showed that within a logical system such as Russell and Whitehead had developed for arithmetic, propositions can be formulated that are undecidable or undemonstrable within the axioms of the system. That is, within the system, there exist certain clear-cut statements that can neither be proved or disproved. Hence one cannot, using the usual methods, be certain that the axioms of arithmetic will not lead to contradictions. It appears to destroy the hope of mathematical certitude through the use of the obvious methods. It also deconstructs an ideal of science, that we...