Single Idea 17906

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers]

Full Idea

I would disagree with Quine. The explanation of cardinality - i.e. of the use of numbers for 'transitive counting', as I have called it - is part and parcel of the explication of number.

Clarification

'Transitive counting' is counting objects

Gist of Idea

To explain numbers you must also explain cardinality, the counting of things

Source

Paul Benacerraf (What Numbers Could Not Be [1965], I n2)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.275


A Reaction

Quine says numbers are just a progression, with transitive counting as a bonus. Interesting that Benacerraf identifies cardinality with transitive counting. I would have thought it was the possession of numerical quantity, not ascertaining it.

Related Idea

Idea 17905 Any progression will do nicely for numbers; they can all then be used to measure multiplicity [Quine]