more from Oliver,A/Smiley,T

Single Idea 14247

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Mathematics as Set Theory / a. Mathematics is set theory]

Full Idea

Identifying numbers with sets may mean one of three quite different things: 1) the sets represent the numbers, or ii) they are the numbers, or iii) they replace the numbers.

Gist of Idea

Sets might either represent the numbers, or be the numbers, or replace the numbers

Source

Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.2)

Book Reference

'Metaphysics (Philosophical Perspectives 20)', ed/tr. Hawthorne,John [Blackwell 2006], p.147


A Reaction

Option one sounds the most plausible to me. I will take numbers to be patterns embedded in nature, and sets are one way of presenting them in shorthand form, in order to bring out what is repeated.