It is shown that, according to NF, many of the assertions of ordinal arithmetic involving the T-function which is peculiar to NF turn out to be equivalent to the truth-in-certain-permutation-models of assertions which have perfectly sensible ZF-style meanings, such as: the existence of wellfounded sets of great size or rank, or the nonexistence of small counterexamples to the wellfoundedness of ∈. Everything here holds also for NFU if the permutations are taken to fix all urelemente.
"Permutations and wellfoundedness: the true meaning of the bizarre arithmetic of Quine’s NF." J. Symbolic Logic 71 (1) 227 - 240, March 2006. https://doi.org/10.2178/jsl/1140641171