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Single Idea 10067

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic ]

Full Idea

Gentzen proved the consistency of arithmetic from assumptions which transcend arithmetic.

Gist of Idea

Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic

Source

report of Gerhard Gentzen (works [1938]) by Alan Musgrave - Logicism Revisited §5

Book Ref

-: 'British Soc for the Philosophy of Science' [-], p.126

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A Reaction

This does not contradict Gödel's famous result, but reinforces it. The interesting question is what assumptions Gentzen felt he had to make.