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Single Idea 15924

[filed under theme 2. Reason / D. Definition / 8. Impredicative Definition ]

Full Idea

On Zermelo's view, predicative definitions are not only indispensable to mathematics, but they are unobjectionable since they do not create the objects they define, but merely distinguish them from other objects.

Gist of Idea

Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them?

Source

report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Shaughan Lavine - Understanding the Infinite V.1

Book Ref

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.107


A Reaction

This seems to have an underlying platonism, that there are hitherto undefined 'objects' lying around awaiting the honour of being defined. Hm.