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2 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers

18842	Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt]
	Full Idea: Menzel proposes that an ordinal is something isomorphic well-ordered sets have in common, so while an ordinal can be represented as a set, it is not itself a set, but a 'property' of well-ordered sets.
	From: Ian Rumfitt (The Boundary Stones of Thought [2015], 9.2)
	A reaction: [C.Menzel 1986] This is one of many manoeuvres available if you want to distance mathematics from set theory.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals

18834	Infinitesimals do not stand in a determinate order relation to zero [Rumfitt]
	Full Idea: Infinitesimals do not stand in a determinate order relation to zero: we cannot say an infinitesimal is either less than zero, identical to zero, or greater than zero. ….Infinitesimals are so close to zero as to be theoretically indiscriminable from it.
	From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.4)