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Ideas for 'General Draft', 'On Formally Undecidable Propositions' and 'Dthat'

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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17835	Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M]
	Full Idea: Gödel's incompleteness results of 1931 show that all axiom systems precise enough to satisfy Hilbert's conception are necessarily incomplete.
	From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Michael Hallett - Introduction to Zermelo's 1930 paper p.1215
	A reaction: [Hallett italicises 'necessarily'] Hilbert axioms have to be recursive - that is, everything in the system must track back to them.