more from Ernst Zermelo

Single Idea 13017

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II]

Full Idea

Zermelo's Pairing Axiom superseded (in 1930) his original 1908 Axiom of Elementary Sets. Like Union, its only justification seems to rest on 'limitations of size' and on the 'iterative conception'.

Gist of Idea

Zermelo introduced Pairing in 1930, and it seems fairly obvious

Source

report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.3

Book Reference

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


A Reaction

Maddy says of this and Union, that they seem fairly obvious, but that their justification is of prime importance, if we are to understand what the axioms should be.