Single Idea 14128

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

Full Idea

It is claimed that ordinals are prior to cardinals, because they form the progression which is relevant to mathematics, but they both form progressions and have the same ordinal properties. There is nothing to choose in logical priority between them.

Gist of Idea

Some claim priority for the ordinals over cardinals, but there is no logical priority between them

Source

Bertrand Russell (The Principles of Mathematics [1903], §230)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.241


A Reaction

We have an intuitive notion of the size of a set without number, but you can't actually start counting without number, so the ordering seems to be the key to the business, which (I would have thought) points to ordinals as prior.

Related Idea

Idea 14129 Ordinals presuppose two relations, where cardinals only presuppose one [Russell]