### Single Idea 10674

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order]

Full Idea

A language with plurals is better for arithmetic. Instead of a first-order fragment expressible by an induction schema, we have the complete truth with a plural induction axiom, beginning 'If there are some numbers...'.

Gist of Idea

A plural language gives a single comprehensive induction axiom for arithmetic

Source

Keith Hossack (Plurals and Complexes [2000], 4)

Book Reference

-: 'British Soc for the Philosophy of Science' [-], p.420