Full Idea
The idea of 'generating' sets is only a metaphor - the existence of the hierarchy is established without appealing to such dubious notions.
Gist of Idea
The set hierarchy doesn't rely on the dubious notion of 'generating' them
Source
John Mayberry (What Required for Foundation for Maths? [1994], p.414-2)
Book Reference
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.414
A Reaction
Presumably there can be a 'dependence' or 'determination' relation which does not involve actual generation.