Full Idea
The iterative conception does not provide a conception that unifies the axioms of set theory, ...and it has had very little impact on what theorems can be proved.
Gist of Idea
The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs
Source
Shaughan Lavine (Understanding the Infinite [1994], V.5)
Book Reference
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.149
A Reaction
He says he would like to reject the iterative conception, but it may turn out that Foundation enables new proofs in mathematics (though it hasn't so far).