more from Keith Hossack

### Single Idea 23621

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory]

Full Idea

I propose that numbers are properties, not sets. Magnitudes are a kind of property, and numbers are magnitudes. …Natural numbers are properties of pluralities, positive reals of continua, and ordinals of series.

Gist of Idea

Numbers are properties, not sets (because numbers are magnitudes)

Source

Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro)

Book Reference

Hossack, Keith: 'Knowledge and the Philosophy of Number' [Routledge 2021], p.1

A Reaction

Interesting! Since time can have a magnitude (three weeks) just as liquids can (three litres), it is not clear that there is a single natural property we can label 'magnitude'. Anything we can manage to measure has a magnitude.