On 14 Mrz., 23:36, fom <fomJ...@nyms.net> wrote: > On 3/14/2013 5:15 PM, WM wrote: > > > > > distinguishable, that means definable by finite words > > How does a definition "distinguish"?
A definition is a name. For instance one of many definitions of pi. That can be used to distinguish it from three.
Extensionality says that sets with same elements are identical. Therefore it must be possible, in ZF, to fix whether elements are same or not. Therefore it must be possible to compare and to recognize elements. For that sake you need names, unless the elements are material objects. That's part of ZF.