  Consider next the iterative conception of set. As in the case of arithmetic, this conception (arguably) intrinsically justifies instances of Replacement and Comprehension for certain extensions of the language of set theory. But there are richer principles that are (arguably) intrinsically justified on the basis of this conception, namely, the set-theoretic reflection principles. These principles assert (roughly) that any property that holds of V holds of some initial segment Vα. These principles yield inaccessible and Mahlo cardinals (and more) and quite likely underlie Gödel's claims in the above passage. Some have argued that such reflection principles are intrinsically justified on the basis of the iterative conception of set and, moreover, that they exhaust the principles that can be intrinsically justified on that conception (see, for example, Tait (2001), reprinted in (2005b), pp. 283–284). 