Single Idea 17880

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics]

Full Idea

The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind.

Gist of Idea

Integers and induction are clear as foundations, but set-theory axioms certainly aren't


Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299)

Book Reference

'From Frege to Gödel 1879-1931', ed/tr. Heijenoort,Jean van [Harvard 1967], p.299

A Reaction

This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers.