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Ideas for 'Topics', 'Russell's Mathematical Logic' and 'The Universe as We Find It'

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2 ideas

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

10039	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.

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique

18500	How could structures be mathematical truthmakers? Maths is just true, without truthmakers [Heil]
	Full Idea: I do not understand how structures could serve as truthmakers for mathematical truths, ...Mathematical truths are not true in virtue of any way the universe is. ...Mathematical truths hold, whatever ways the universe is.
	From: John Heil (The Universe as We Find It [2012], 08.08)
	A reaction: I like the idea of enquiring about truthmakers for mathematical truths (and my view is more empirical than Heil's), but I think it may be a misunderstanding to think that structures are intended as truthmakers. Mathematics just IS structures?