Combining Philosophers

Ideas for Hermarchus, W.H. Newton-Smith and Gerhard Gentzen

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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

10067	Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]
	Full Idea: Gentzen proved the consistency of arithmetic from assumptions which transcend arithmetic.
	From: report of Gerhard Gentzen (works [1938]) by Alan Musgrave - Logicism Revisited §5
	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.