more from Paul Benacerraf

Single Idea 13415

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

Full Idea

No account of an individual number is adequate unless it relates that number to the series of which it is a member.

Gist of Idea

An adequate account of a number must relate it to its series

Source

Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.169)


A Reaction

Thus it is not totally implausible to say that 2 is several different numbers or concepts, depending on whether you see it as a natural number, an integer, a rational, or a real. This idea is the beginning of modern structuralism.