So for me it's based on the Siri Theory. I agree in principle with the formal/material distinction (makes perfect sense) ... but just believe that Siri was the rightfully-elected Pope, and that he was forced to step down under duress, which would make his resignation invalid, and thus legitimate election to the office (the material aspect) would have been impeded by Siri's rightful posession of it, until his death in 1989. By that time, there were no legitimate electors left form the Pius XII era, or if there was 1 or 2 (I doubt it due to the age limit started I think by Montini ... perhaps for this reason?), who knows who they voted for.
Others believe that Bergoglio's election was (materially) invalid due to the collusion (St. Gallen mafia) or alternatively because of his non-resignation (munus vs. ministerium).
Interestingly, just the other day on Taylor Marshall's show / video, someone chatted in (the SuperChat where you pay to get your question answered) about whether any popes in recent memory had been elected but turned down the election. Marshall casually mentioned that Siri turned it down in 1958. Oh, really, Taylor? So, how do you know this? Siri never said one way or the other, since he said he was bound by the oath. Consequently, that was clearly an attempt by Marshall to contradict (falsely, with no information) the Siri Theory.
The material election of the pope is merely saying that
a) the duly appointed Cardinals
b) held a valid election (per election rules in place)
c) and a new pope was elected, accepted and rules the vatican govt.
Whether or not every Cardinal is a raging heretic, who has been spiritually nullified by canon law, or by Divine Law, is irrelevant. God gave to St Peter the power to 'bind and loose'. Part of the papacy is material/human and part is spiritual.
The Siri thesis proves the point that a material pope is possible. Thus, even if every cardinal was a formal heretic (and I don't think ALL of them are), you can still have the valid election of a material/governing pope. He would simply have 0 spiritual authority and be under imposition of a vast array of canon law excommunications (same as the Cardinals).
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