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Ideas for 'fragments/reports', 'On the Foundations of Logic and Arithmetic' and 'Russell's Mathematical Logic'

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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
     Full Idea: It has turned out that the solution of certain arithmetical problems requires the use of assumptions essentially transcending arithmetic.
     From: Kurt Gödel (Russell's Mathematical Logic [1944], p.449)
     A reaction: A nice statement of the famous result, from the great man himself, in the plainest possible English.