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Single Idea 10233

[from 'Philosophy of Mathematics' by Stewart Shapiro, in 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism ]

Full Idea

A traditional Platonist has to face the possibility that all of the Peano Axioms are false.

Gist of Idea

Platonism must accept that the Peano Axioms could all be false

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 4.7)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.131


A Reaction

This would be because the objects exist independently, and so the Axioms are a mere human attempt at pinning them down. For the Formalist the axioms create the numbers, and so couldn't be false. This makes me, alas, warm to platonism!