more from Michael Hallett

### Single Idea 17834

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets]

Full Idea

The non-categoricity of the axioms which Zermelo demonstrates reveals an incompleteness of a sort, ....for this seems to show that there will always be a set (indeed, an unending sequence) that the basic axioms are incapable of revealing to be sets.

Gist of Idea

Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal

Source

Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1215)

Book Reference

'From Kant to Hilbert: sourcebook Vol. 2', ed/tr. Ewald,William [OUP 1996], p.1215

A Reaction

Hallett says the incompleteness concerning Zermelo was the (transfinitely) indefinite iterability of the power set operation (which is what drives the 'iterative conception' of sets).