John Henry Newman, the Victorian convert, theologian and cardinal recently sainted by Francis, once suggested that there had been a “temporary suspense” of the church’s magisterium, its teaching authority, during eras in which the papacy failed to teach definitively or exercise discipline on controversial subjects. And the church’s saints from such periods include bishops who stood alone in defense of orthodoxy, sometimes against misguided papal pressure.

But you can also see in my conversation with the cardinal how hard it is to sustain a Catholicism that is orthodox against the pope. For instance, Burke himself brought up a hypothetical scenario where Francis endorses a document that includes what the cardinal considers heresy. “People say if you don’t accept that, you’ll be in schism,” Burke said, when “my point would be the document is schismatic. I’m not.”

But this implies that, in effect, the pope could lead a schism, even though schism by definition involves breaking with the pope. This is an idea that several conservative Catholic theologians have brought up recently; it does not become more persuasive with elaboration. And Burke himself acknowledges as much: It would be a “total contradiction” with no precedent or explanation in church law.