Single Idea 8760

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism]

Full Idea

The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers.

Gist of Idea

Numbers do not exist independently; the essence of a number is its relations to other numbers

Source

Stewart Shapiro (Thinking About Mathematics [2000], 10.1)

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.258


A Reaction

This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate.