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Single Idea 8661

[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers ]

Full Idea

The natural numbers are quite primitive, and are what we first learn about. The order of objects (the 'ordinals') is one level of abstraction up from the natural numbers: we impose an order on objects.

Gist of Idea

The natural numbers are primitive, and the ordinals are up one level of abstraction

Source

Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4)

Book Ref

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.12


A Reaction

Note the talk of 'levels of abstraction'. So is there a first level of abstraction? Dedekind disagrees with Friend (Idea 7524). I would say that natural numbers are abstracted from something, but I'm not sure what. See Structuralism in maths.

Related Idea

Idea 7524 Order, not quantity, is central to defining numbers [Dedekind, by Monk]