{"id":166,"date":"2006-04-28T02:28:00","date_gmt":"2006-04-28T10:28:00","guid":{"rendered":"https:\/\/pierrejoris.com\/blog\/?p=166"},"modified":"2006-04-28T02:28:00","modified_gmt":"2006-04-28T10:28:00","slug":"kurt-godel","status":"publish","type":"post","link":"https:\/\/pierrejoris.com\/blog\/kurt-godel\/","title":{"rendered":"Kurt G\u00f6del"},"content":{"rendered":"

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G\u00f6del with Einstein at Princeton, 1950<\/p>\n

Happy 100th birthday, Kurt G\u00f6del!<\/p>\n

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G\u00f6del was born on 28 April 1906 in the city of Br\u00fcnn, part of the Austro-Hungarian empire (now Brno in the Czech republic). After WWI, which did away with the Austro-Hungarian empire, he grew up as a citizen of the newly created country of Czechoslovakia, becoming an Austrian citizen in 1929, and an American citizen in 1948. From 1938 until his death in 1978, G\u00f6del was at the Institute for Advanced Study in Princeton.<\/span><\/div>\n

G\u00f6del proved a series of fundamental results in logic, starting with the completeness theorem for predicate logic, which he proved in his doctoral dissertation in 1929. <\/span>The incompletene<\/span>ss theorems<\/span> (1931) are what he is famous for, but his work in set theory and constructivism has also been of great importance. <\/span>In the incompleteness theorems G\u00f6del<\/b> proved fundamental results about axiomatic systems showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system.<\/span><\/p>\n

This theorem has been used over and over again in all kinds of fields \u2014 especially in the human sciences. Even if over-deployed, it is a useful way of thinking about other than mathemetical systems. I especially like what R\u00e9gis Debray did with G\u00f6del’s Incompleness theorem in his (badly translated, heavily abridged and unhappily much maligned) Critique of Political Reason. Here’s one quote from that book:<\/span><\/p>\n

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