back to ideas for this text


Single Idea 13015

[from 'Investigations in the Foundations of Set Theory I' by Ernst Zermelo, in 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII ]

Full Idea

Zermelo used a weak form of the Axiom of Foundation to block Russell's paradox in 1906, but in 1908 felt that the form of his Separation Axiom was enough by itself, and left the earlier axiom off his published list.

Gist of Idea

Zermelo used Foundation to block paradox, but then decided that only Separation was needed

Source

report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.2

Book Reference

-: 'Journal of Symbolic Logic' [-], p.484


A Reaction

Foundation turns out to be fairly controversial. Barwise actually proposes Anti-Foundation as an axiom. Foundation seems to be the rock upon which the iterative view of sets is built. Foundation blocks infinite descending chains of sets, and circularity.