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Single Idea 17459

[from 'Cardinality, Counting and Equinumerosity' by Richard G. Heck, in 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic ]

Full Idea

The interest of Frege's Theorem is that it offers us an explanation of the fact that the numbers satisfy the Dedekind-Peano axioms.

Clarification

Frege's Theorem says arithmetic rests on one-one correspondence

Gist of Idea

Frege's Theorem explains why the numbers satisfy the Peano axioms

Source

Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6)

Book Reference

-: 'Notre Dame Journal of Formal Logic' [-], p.204


A Reaction

He says 'explaining' does not make it more fundamental, since all proofs explain why their conclusions hold.