2+2=5?

2+2=5?

“The difficulty of explaining ‘why I am a Catholic’ is that there are ten thousand reasons all amounting to one reason: that Catholicism is true.”

— G.K. Chesterton; Why I am a Catholic


As I wrote in a previous post, many Catholics who dissent from Amoris Laetitia because they say they are “thinking with their own heads” are usually thinking identically. They all seem to use the same arguments and the same slogans to get their points across.

One of those slogans is the “2+2=5” catchphrase. They posit that Pope Francis is clearly contradicting previous popes and councils, so trying to harmonize all of these teachings doesn’t make sense on the face of it. In doing so, they reject any such attempt to harmonize Francis’s teachings with Tradition as “violence against the intellect,” or as impossible as trying to prove that 2+2=5.

The trouble with this is that it assumes that “2+2=5” is an apt descriptor of pro-Francis apologetics. Once you assume that, you may dismiss any pro-Francis apologetics as inherently illogical. This means you will never be able to change your mind, even if you’re wrong. People should be very cautious before accepting such a non-falsifiable statement as true, lest they become entrapped in it. To insist that pro-Francis apologists are trying to assert 2+2=5 without trying to understand their point of view can lead to grave error.

Let me show you how this logic can backfire:

  1. Saying that faith is compatible with reason is like trying to prove that 2+2=5
  2. Saying that God is simultaneously One and Triune is like trying to prove that 2+2=5
  3. Saying that Jesus Christ is fully human and fully divine at the same time is like trying to prove that 2+2=5
  4. Saying that the Body of Christ is present in the Eucharist while the accidents of bread remain is like trying to prove that 2+2=5

In all of these instances, we see how “2+2=5” is used as an excuse for intellectual laziness. It enables you to refuse to admit that reality is harder to grasp than what you are prepared to accept. If reality confuses you, then you must (they believe) make reality conform to what you understand. This mentality, in which reality must conform to our thoughts and not the other way around, is actually pretty close to that relativism that is decried in Catholic circles. It is also dangerous from a religious point of view; for, as St. Augustine says, “Si comprehendis, non est Deus” (“If you understand, then it is not God”).


Still, is it really true that trying to square Amoris Laetitia with orthodoxy (namely with Pope St. John Paul II’s Veritatis Splendor and Familiaris Consortio) is really an attempt to prove that “2+2=5”?

According to my experience, it is not. In fact, those apparently contradictory documents are speaking on different levels. For example, where Familiaris Consortio and Amoris Laetitia conflict is on a matter of discipline, not doctrine. As far as doctrine is concerned, all the documents agree, because they are talking about different things. Veritatis Splendor talks about objective evil while Amoris Laetitia talks about subjective culpability. All of these points are doctrinally sound, but they arrived at different conclusions relating to praxis, because they valued different aspects of reality.

Of course, if you try to force Amoris Laetitia’s praxis into the level of Veritatis Splendor, then you are indeed trying to say that “2+2=5”. Because then you are allowing Communion to people that commit an intrinsically evil sin, that can never be justified.

However, as Amoris Laetitia makes clear, the pope is not talking about the objectivity of the sin of adultery. He is not saying that adultery is not evil. He is saying, in accordance with the Catechism #1857, that a sin’s gravity is not sufficient to establish whether a person is in a state of mortal sin or not. AL #301 makes this perfectly clear. So, if the sinner is not in mortal sin, he may take Communion.

This is perfectly orthodox. It doesn’t contradict any doctrinal teaching I know of. And yet, Catholics that dissent from the Pope will ignore this even if someone explains this to them. They will then go on talking about “adultery is mortal sin” and how the “Pope is saying that adultery is not adultery”, ignoring that that’s not what this is all about. No one is saying that divorced and remarried people living more uxorio are not committing adultery. No one is saying that adultery is not a mortal sin, provided all 3 conditions for mortal sin are met. No one is saying that marriage is not indissoluble.

But if you try to explain to them we’re not saying that adultery is not a sin, or even a potentially mortal sin, they will retort that we’re twisting ourselves into pretzels, trying to prove something like “2+2=5.”

I would venture to say that some of these folks believe this because they are very bad at math. Yes, they are sufficiently good at math to know that “2+2=4,” but they will often take that in very unusual directions.

If you tell them that “1+3=4,” the more rigid among them will cry that it’s a lie! They see the different numbers, with which they are not as familiar, and then proceed to dismiss them as irrational.

Let us illustrate what’s going on here, shall we?

  • Doctrine of intrinsic evils + Indissolubility of marriage doctrine = Orthodoxy

But, it is also true that

  • Mortal sin doctrine + Subjective culpability doctrine = Orthodoxy

In other words, both “2+2=4” and “1+3=4”.

However, papal critics will claim that, because “2+2=4”, then it must mean that “1+3” cannot equal 4. Trying to assert that “1+3=4”, is as irrational to them, as trying to prove that “2+2=5”. Which is just bad math.


Math, however, is more complicated than that. That’s the beauty of it. If you say you like math, but restrict yourself to always solving the same equation (while dismissing all other equations as irrational undertakings), then you’re not much of a mathematician.

There is something even more important to point out. As intellectually stimulating as these complicated math problems are, the nobler purpose of math is to help us deal with real problems that we face on everyday life.

So, if you have a person that tries to get 4 apples, and then picks 2 from a tree and another 2 from another tree, then that person has effectively used math to solve a real problem. But let us assume that the person is trying to get 4 apples, and there are 3 apples in one tree and just 1 apple in another.

What would you say of a person that refuses to get 4 apples on this arrangement? What would you say to a person that would start to cry: “I can’t get 4 apples like this! I can only get 4 apples if there are 2 on one side and 2 on the other! It is not possible to solve this dilemma! What are you saying? I don’t care if you are an accredited mathematician and disagree! I’ve always learned it that way, so I must be right!”

You’d think that such person has an unsound mind, correct? That person is, indeed, inflicting violence on his intellect by refusing to learn, even from someone with authority.

Reality will not always be presented to you in simple terms that you can understand and with which you’re comfortable with. Sometimes you will have to solve equations more difficult or unfamiliar than “2+2=4.” Someone won’t get very far by just learning “2+2=4” and expecting that to be sufficient for his everyday life.

The math of God is much more complex than that, much more complex than mere arithmetic.  Any physicist can assure you of that. Let your pope assure you of that as well, and help you grow in wisdom towards God’s math.

[Photo credit: Anonymous, “God the geometerCodex Vindobonensis, c. 1220; Source: Wikimedia Commons]

Pedro Gabriel

Pedro Gabriel, MD, is a Catholic layman and physician, born and residing in Portugal. He is a medical oncologist, currently employed in a Portuguese public hospital. A published writer of Catholic novels with a Tolkienite flavor, he is also a parish reader and a former catechist. He seeks to better understand the relationship of God and Man by putting the lens on the frailty of the human condition, be it physical and spiritual. He also wishes to provide a fresh perspective of current Church and World affairs from the point of view of a small western European country, highly secularized but also highly Catholic by tradition.

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4 thoughts on “2+2=5?

  1. Another possible response would be that this type of ‘arithmetical’ thinking doesn’t apply to many Christian things.

    Marriage certainly doesn’t follow the laws of arithmetic. There, 1 + 1 certainly does not equal 2. In man-woman marriage, 1 person + 1 person often equals 3 persons, or 4. Or in my family’s case, it equals 7.

    Mercy is another item that obviously defies “mathematical thinking” since it does the opposite of what “the math” would dictate.

    The point is, if you insist on these simplistic mathematical analogies, you’ll fail to grasp the nature of some very important aspects of doctrine.

    1. An analogy is meant as way to communicate an idea more easily… not to be squeezed out until you get a counter example. Any analogy is inadequate in a sense. Did you get what he was trying to say? Then the role of the analogy ended there.

      1. Well, shucks. I must have written that poorly if it sounded like I was offering a counterexample to Pedro’s argument. I was trying to agree with him and contribute another “response” that could be used to answer Francis’ critics who try to deploy the analogy he is discussing.

  2. Maybe it’s because I have a scientific background that I liked this article. I felt that Mr Gabriel had captured well the essence of how the Francis critics tended to follow a common faulty logic in their repeated complaints.

    I am so grateful for this website. The poisonous narrative against Pope Francis is spreading like a disease in Catholic circles and reasoned responses are badly needed.

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