  It can be plausibly argued that the bizarre behaviour of the \(T\) function (and it is at its most bizarre in connection with the big sets) is just the paradoxes bubbling up again. Assertions to the effect that \(T\) is well-behaved have strong consistency strength (Orey [1955], [1956]) and play in NF studies the kind of rôle that large cardinal axioms play in ZF-like systems. Indeed there are some exact equivalents. The \(T\)-assertions may look odd, but their oddness is only skin-deep. They are actually expressing the same mathematics that happens in ZF, but through an unfamiliar formalisation.