Based on the Catholics I’ve talked to, it seems like most Catholics are heretics and don’t even realize it. Many Catholics are firm believers in God, but do not think that God’s existence can be proven with certainty. They merely have ‘faith’ that God exists. However, based on some of the statements which the Catholic Church identifies as infallible, such people are heretics.
According to the Catholic Catechism, “Our holy mother, the Church, holds and teaches that God, the first principle and last end of all things, can be known with certainty from the created world by the natural light of human reason.” This was declared infallibly by both the first and second Vatican Councils. While the Catholic Church does not claim that one single argument proves all of God’s attributes, it does claim that proofs for the existence of God allow people to use reason to attain certainty that God exists (Catholic Catechism).
According to the First Vatican Council, anyone who says that God cannot be known with certainty from the natural world is considered anathema. The word ‘anathema’ is often misunderstood, so I turn to a quote from Catholic apologist Jimmy Akin’s article which clears up a lot of Protestant misconceptions about anathema and explains what it really is:
Catholic scholars have long recognized that when an ecumenical council applies this phrase to a doctrinal matter, then the matter is settled infallibly. (If a council applied the phrase to a disciplinary matter, then the matter would not be settled infallibly, since only matters of doctrine, not discipline, are subject to doctrinal definition.)
Thus, when Trent and other ecumenical councils employed anathema sit in regard to doctrinal matters, not only was a judicial penalty prescribed but a doctrinal definition was also made. Today, the judicial penalty may be gone, but the doctrinal definition remains. Everything that was infallibly decided by these councils is still infallibly settled.
This has consequences under current canon law. Those things that are both divinely revealed by God and proposed as such by the Church cannot be obdurately denied or doubted without the offense of heresy (CIC  751). Heresy does carry a penalty of automatic (latae sententiae) excommunication (can. 1041, 2º), though this does not apply to those who have never been members of the Catholic Church (can. 11), and even then there is a significant list of exceptions (can. 1323).
So someone who denies that the existence of God can be known with certainty is considered a heretic and is automatically excommunicated (excommunication applies only to mentally capable adults who knowingly and without coercion deny that God’s existence can be known with certainty). Someone cannot deny the teaching that God’s existence can be proved with certainty from the natural world without being automatically excommunicated from the Catholic Church.
This poses a problem for many Catholics who merely have faith in God but do not think that the natural world definitively proves that God exists. This also poses a problem for Catholics who have seriously studied the arguments for and against God’s existence and who conclude that while the evidence leans towards God’s existence, it is not enough to establish his existence with certainty.
According to the Catechism, some people may not believe that the existence of God can be known with certainty due to not being willing to surrender oneself or due to “disordered appetites” that lead men to believe what they want to believe rather than what is true. However, this is not a good answer for those people who really want Catholicism to be true and are willing to humbly submit themselves.
If someone has studied all the arguments people have given for the existence of God and thinks they provide evidence for God’s existence but fall short of establishing it with certainty, is there any way to avoid being seen as a heretic who is automatically excommunicated? One escape route I can find is to say that it only says that God ‘can’ be known with certainty, not that he ‘is’ known. Perhaps it is true that God can be proved with certainty, it’s just that no one has figured out how to do it yet after thousands of years. Perhaps it is also true that pigs can fly, it’s just that no pig has yet decided to fly in the presence of humans. There is also the problem that this interpretation appears inconsistent with the Bible, which says that “since the creation of the world God's invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that men are without excuse” (Romans 1:20).
I guess another response would be to say that even if something is declared infallible, that declaration might not itself be infallible, and even if the declaration was declared infallible, the declaration that the declaration was infallible might not itself be infallible. I think this is true, but if someone rejects even the most firmly established Catholic doctrines, then the label ‘Catholic’ loses all meaning. Someone could believe absolutely anything (the pope is the anti-Christ, Jesus never existed, Oprah Winfrey is God) and consider themselves a Catholic. So this Catholic doctrine seems to be a serious problem for those who do not think that the existence of God can be proved with certainty.
It is also a problem for convincing an atheist that Catholicism is true. You would not only have to convince him or her that God probably exists, but that God’s existence can be established with certainty based on the evidence from the natural world. This would require a great deal more evidence than merely establishing that the likelihood of God existing is more than 50%.
I believe that this is a doctrine that more Catholics should be aware of (and if you agree, pass the word along to your Catholic friends). I know that if I was a Catholic who didn’t think that God could be proven with certainty and I heard about this doctrine, I would really want to investigate and find out how God can be proven. If my religion taught that the creator of all space and time had profoundly demonstrated his existence through the natural world, I wouldn’t just say “Whatever, I don’t really care”, I’d be taking advantage of the opportunity to witness God’s power and goodness through his creation, to connect the everyday world with the divine creator. If I found the proof I sought (proof that could withstand even the best atheist arguments), I would come away with greater admiration and respect for God’s majesty and would feel a deep sense of peace. And if I searched and searched and did not find any proof that God exists, I may realize that the religion I thought was true may not be true after all.