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Single Idea 17608

[from 'Investigations in the Foundations of Set Theory I' by Ernst Zermelo, in 4. Formal Logic / F. Set Theory ST / 1. Set Theory ]

Full Idea

Starting from set theory as it is historically given ...we must, on the one hand, restrict these principles sufficiently to exclude as contradiction and, on the other, take them sufficiently wide to retain all that is valuable in this theory.

Gist of Idea

We take set theory as given, and retain everything valuable, while avoiding contradictions

Source

Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro)

Book Reference

'From Frege to Gödel 1879-1931', ed/tr. Heijenoort,Jean van [Harvard 1967], p.200


A Reaction

Maddy calls this the one-step-back-from-disaster rule of thumb. Zermelo explicitly mentions the 'Russell antinomy' that blocked Frege's approach to sets.