godel tagged posts

Summary of Godel’s Incompleteness Theorem

Kurt Godel presented a theory of mathematics that demonstrates that anything that can be measured, or contained, cannot be dependent upon itself for explanation or existence. The excerpts below from various sources give a summary of the implications of his theorem; for greater detail, the articles and book listed at the end are strongly recommended. (These statements were pulled from several sources; they are not my own material, other than the section on “Implications”)

“Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.”

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