more from Richard Dedekind

Single Idea 13508

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers]

Full Idea

Dedekind's natural numbers: an object is in a set (0 is a number), a function sends the set one-one into itself (numbers have unique successors), the object isn't a value of the function (it isn't a successor), plus induction.

Gist of Idea

Dedekind gives a base number which isn't a successor, then adds successors and induction

Source

report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William D. Hart - The Evolution of Logic 5

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.124


A Reaction

Hart notes that since this refers to sets of individuals, it is a second-order account of numbers, what we now call 'Second-Order Peano Arithmetic'.