more from Stewart Shapiro

Single Idea 10274

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

Full Idea

According to structuralism, someone who uses small natural numbers in everyday life presupposes an infinite structure. It seems absurd that a child who learns to count his toes applies an infinite structure to reality, and thus presupposes the structure.

Gist of Idea

Does someone using small numbers really need to know the infinite structure of arithmetic?

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 8.2)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.254


A Reaction

Shapiro says we can meet this objection by thinking of smaller structures embedded in larger ones, with the child knowing the smaller ones.