ROME – A core principle in logic is the law of non-contradiction, which states that a proposition and its opposite cannot both be true at the same time. In the notation of the discipline, this idea is expressed as “p and not-p” … ¬(p ∧ ¬p) is the proper formula.

For Vatican-watchers, the choice of the letter “p” has to seem especially apt, since we’ve just been served up a juicy, towering apparent contradiction between a pope and a high-profile prelate – an impasse which, naturally, turns on another pope.

In his inflight press conference returning from the South Sudanese capital of Juba on Sunday, Pope Francis took a question about tensions in the Catholic Church that seemed to open up after the Dec. 31 death of Pope Benedict XVI.

In his response, Francis accused some unnamed people of “instrumentalizing” Benedict’s death to score political points, and he insisted that Benedict was not “embittered” by the new directions Francis set.

“He was always at my side, supporting, and if he had a problem, he told me and we talked. There weren’t problems,” Francis said.

“Some stories that say Benedict was embittered for what the new Pope did, are stories from a ‘wireless phone’ [an expression meaning ‘gossip’],” Francis said. “On the contrary, I consulted Benedict for some decisions to be made, and he agreed. He agreed.”

“I wanted to say clearly who Pope Benedict was, and that he wasn’t embittered,” Francis insisted.

Taken at face value, those statements would appear to directly contradict the testimony of German Archbishop Georg Gänswein, the closest aide to Pope Benedict.

In media interviews and a set of memoirs after Benedict’s death, Gänswein described the late pope’s disappointment over a couple of decisions by Pope Francis, including the Latin Mass and an opening to communion for divorced and civilly remarried Catholics.

On the subject of Pope Francis’s 2021 decision to reverse Benedict’s liberalization of permission for the old Latin Mass, Gänswein said in an interview with Die Tagespost that “it hit him pretty hard … I believe it broke Pope Benedict’s heart.”

Hard to square an allegedly broken heart, isn’t it, with the claim that Benedict “wasn’t embittered”?

Gänswein expanded on Benedict’s reaction in his book.

“At a personal level, he encountered a decisive change of course and considered it a mistake, since it jeopardized the attempt at peace that had been made 14 years earlier,” he wrote.

“Benedict especially thought it was wrong to prohibit the celebration of Mass in the old rite in parish churches, since it’s always dangerous to paint a group of the faithful into a corner, making them feel persecuted and inspiring a feeling that they have to defend their identity against an enemy.”

Again, it’s a little tough to reconcile terms such as “mistake” and “wrong” with Francis’s repeated claim regarding Benedict that “he agreed … He agreed.”

In a Jan. 6 piece on these seemingly irreconcilable versions of events, veteran Italian Vatican writer Franca Giansoldati in the newspaper Il Messaggero put the situation this way: “The question inevitably arises of who’s lying, instrumentalizing the memory of the emeritus pontiff: His secretary, or even – a clamorous thing – Pope Francis.”

Anyone who’s ever taken a logic class, however, knows that before invoking the law of contradiction, you have to rule out the possibility of equivocation – that is, that the terms in the propositions aren’t being used the same way.

Here’s a classic example used when teaching syllogisms:

• “Nothing is better than God.”
• “A ham sandwich is better than nothing.”
• “Therefore, a ham sandwich is better than God.”

It’s a classic case of what’s known as the “semantic fallacy,” meaning that while there are apparently only three terms being used here – “nothing,” “God” and “ham sandwich” – in reality there are four, because “nothing” is being used in two different senses.

So, is it possible that Francis and Gänswein are actually saying different things? The obvious answer is, “Sure.”

It’s entirely possible that when Francis insisted “there weren’t problems,” that Benedict “agreed” and was not “embittered,” he meant something like, “for the most part” or “in the main” – in Italian, the phrase would be tutto sommato, akin to “all things considered.”

Putting it that way doesn’t exclude the possibility of differences on a couple of specific points, but implies those differences weren’t the main thing.

Similarly, Gänswein may have accented a few regrets from Pope Benedict, but he also took pains to emphasize Benedict’s loyalty to Francis, recalling that when Benedict addressed the cardinals on Feb. 28, 2013, the day his resignation took effect, he said his successor was among them and then added extemporaneously, “To whom I promise my unconditional reverence and obedience.”

Moreover, Gänswein notes, Benedict always referred to Francis, either in person or in writing, as “Holy Father,” and said Mass every day pledging his communion with the reigning pope during the Eucharistic prayer.

In other words, it’s not necessarily that anybody is lying. Francis may be claiming he and Benedict had a fundamentally warm rapport, and Gänswein, without denying that, may be saying that there were nevertheless a few differences. In all honesty, it would be fairly stunning were that not the case.

For sure, there’s tension between what one might call the “Francis” camp in Catholicism and the “Gänswein” constituency. Whether there’s an actual contradiction between Francis and Gänswein, however – well, that all depends on how logical you want to be.