I have been asked, on a number of occasions, to write a response to the controversy surrounding Bishop Barron's sympathy for Hans Urs von Balthasar's contention that we can reasonably hope that all people will be saved. I have avoided this only because Bishop Barron has been very clear about his position on the reality of hell, rooted in the very notion that God loves each one of us so much that He will allow us to reject Him for all eternity, if we so choose - and the possibility of such a choice is real. What he has said is entirely consistent with the mind of the Church. And I cannot do much more than remind people that von Balthasar is one of the greatest theologians of the 20th century, not to mention that Bishop Robert Barron is unlikely to assert anything that hasn't been carefully thought through - and much less assert anything that can be credibly challenged by a few YouTubers with massively inflated egos.
To offer some defense of the claim that we can reasonably hope that all people will be saved, however, I can at least draw on an analogy from an old paradox familiar to anyone who has studied probabilities, especially the epistemological implications of certain probabilistic claims. I am referring in particular to the lottery paradox. This might help shed some light on the reasonableness of the von Balthasar's contention.
The lottery paradox arises from a probabilistic consideration of a typical lottery. To make matters simple, consider that we have purchased a ticket out of a 1000 ticket lottery. Moreover, there is only one winning ticket. That my ticket is the winning ticket is highly unlikely; there is only a 0.001 chance that I am holding it. So too, person #2 has no more than a 0.001 chance of holding the winning ticket, that is, it is unlikely that he holds the winning ticket, not to mention person #3, #4, and so on. In light of those odds, it seems reasonable for me to look at my ticket and say: "This is not the winning ticket". Now consider each claim conjunctively {p#1& p#2& p#3…p#1000}. What we have reasonably said for each ticket is that "It is not the winning ticket". Hence, it is reasonable to conclude that not one of the 1000 tickets purchased is the winning ticket. This of course is paradoxical - not to mention absurd - , because we know on another level that there is a single winning ticket.
What does this have to do with the problem of whether we can reasonably hope that everyone is saved? According to Bishop Barron, von Balthasar avoids adopting a full scale Apocatastasis of the kind we find in Origin or Barth - that everyone will be saved in the end. The contention, however, is that we may reasonably hope that all people will be saved. And indeed, the more a person comes to an interior awareness of the inexhaustible and absolutely unexpected mercy of God, its boundless and incomprehensible nature, it is hard for such a person to believe that anyone can be in hell - so many mystics have experienced as much. At the same time, the more we come face to face with the reality of human evil - and very few of us do, especially those in the Church - , it is hard to doubt that some people are in hell. This is a paradox that the mystic lives with, and he sees no need to resolve it, unlike the mathematician in the face of the lottery paradox. However, let's try a thought experiment. We will assume that when the world ends, 200 billion people will have lived on the earth. You are in a room seated on a chair, and each person of that 200 billion will enter the room, stand before you for about 10 seconds, and then leave. In light of what you know, through faith, of the mercy of God, in light of the Incarnation of the Second Person of the Trinity, his death upon the cross, his resurrection, etc., are you able to say with absolute certainty that this person will not be saved? No, on the contrary, no matter how evil a life this person has led, I cannot say that I know this person will not be saved, that he did not repent at the final split second of his life and plead for God's mercy. On the contrary, in light of the passion, death, and resurrection of Christ, I can hope that this single person is in heaven, that this person is saved by the infinite and inexhaustible and ever-unexpected mercy of God, that despite whatever evil he might have done in this life, God will have given him some opportunity for final repentance, whether that was within that split second duration of time it took for him to receive the bullet in the head from an enemy soldier and definitively and irreversibly die, or whatever the case may be. You or I have no idea what the final outcome was, but we can and do hope that he turned to God in a final plea for mercy.
And so, each person stands before you, one at a time, which will take 10 seconds x 200,000,000,000. After each person has come through the room and has stood before you - just as you considered each lottery ticket that was purchased - , you can now say, considering the conjunction of each and every instance, that there is a reasonable hope that not one of them is damned, that each one of the 200 billion is in heaven.
As on one level we know that there is a winning ticket, similarly, on one level we know that hell exists; for Jesus did say: "And they will go away to eternal punishment, and the upright to eternal life" (Mt 25, 46). The Apocatastasis position does not resolve the paradox, but denies it. But von Balthasar does not adopt the Restitutionism of Origin/Barth - that all will be saved in the end, and Bishop Barron is congenial to von Balthasar's contention because he has tasted the reality of that theological paradox. The lottery paradox is a probability problem that is resolved mathematically, but the theological paradox of having a reasonable hope that everyone is saved against the backdrop of the biblical assertions about hell is not resolved mathematically. Rather, it is a paradox that remains; for it is a lived paradox, and a hopeful one. It is a paradox that leaves us suspended, as it should, for it is within that epistemic suspension that we are able to pray that each and every person we encounter will in the end be saved by Christ.