Are you ready to be confused? Then read on.
Most Catholics by now are aware of the heresy called "sedevacantism". In short, it teaches that there is no pope on earth, and that Pope Pius XII was the last valid pope. All those since then are popes in name only. The term sedevacantism comes from the Latin sedes vacans, meaning "empty chair" - in other words, the chair of the Saint Peter is empty. So the sedevacantist teaches that John Paul II was an impostor and the same for Benedict XVI. The incredibly strange and non-Catholic Society of Saint Pius V (not the Society of Saint Pius X) is officially sedevacantist. Click here to learn about the Society of Saint Pius V.
Okay, so that's sedevacantism. I think it's sheer lunacy, but at least I can understand it. Here's another position that is even more odd: sedeprivationism. Sedeprivationism follows the thought of the quasi-schismatic French theologian Michel Louis Guérard des Lauriers. The term means that there is a privation in the occupant of the chair of Saint Peter, i.e. something lacking.
According to sedeprivationism, Popes John XXIII, Paul VI, John Paul I, John Paul II and Benedict XVI were and are defective popes because they espoused the heresies of "Modernism".
Here is where sedeprivationism becomes difficult to understand. According to sedeprivationists, the consent of these five men (J23 through B16) to become pope was faulty or defective on account of their so-called heretical views. As a result, they each became potentially pope, but did not attain to fullness of the papacy. In other words, they became pope materialiter sed non formaliter or "materially but not formally".
Apparently, Mel Gibson is sedeprivationist and not a sedevacantist. I had a conversation with someone who recently met with Gibson to discuss this issue and Gibson seemed to grant that Benedict XVI is the pope but also that he is a faulty or defective pope. This would make him a sedeprivationist of sorts.
Thus, the sedeprivationist (like Gibson) does not believe that the papal chair is empty, only that the material popes who have occupied it are formally defective.
Does that makes sense?
Theologically, it doesn't make sense to me.