Single Idea 18113

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic]

Full Idea

Peano Arithmetic is about any system of entities that satisfies the Peano axioms.

Gist of Idea

PA concerns any entities which satisfy the axioms

Source

report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 6.3) by David Bostock - Philosophy of Mathematics 6.3

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.183


A Reaction

This doesn't sound like numbers in the fullest sense, since those should facilitate counting objects. '3' should mean that number of rose petals, and not just a position in a well-ordered series.

Related Idea

Idea 14424 Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell]