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After the glorious re-ascent of Christ and Mary, Beatrice speaks to the souls still gathered, praying that they allow Dante a taste of the supper of Christ.
Dante observes that the hosts all form circles around fixed poles and dance.
One soul boldly comes forward and dances three times around Beatrice while singing, and his song is so gorgeous that Dante is paralyzed.
When he stops dancing, Beatrice identifies him as the "great man to whom our Lord bequeathed the keys." Hence we know him to be St. Peter. She asks him to test Dante on faith so that he can be worthy of moving into "this realm."
Upon hearing this, Dante doesn't freak out, but acts like a good student, arming himself with his arguments.
St. Peter wastes no time and turns, almost gleefully, to Dante. He asks a seemingly simple question: what is faith?
Dante looks to Beatrice for permission to speak, she gives it, and Dante answers, like your brother, St. Paul, wrote, "Faith is the substance of the things we hope for / and is the evidence of things not seen."
St. Peter nods. He then asks Dante why faith is "substance" and "evidence."
Dante answers that faith speaks of "the deep things [which] are hidden from sight below." And because these things (like Heaven and blessedness) cannot be seen by mortal eyes, they must be taken on faith. This is why faith is a substance. Since mortals must reason from this blind faith, it is also evidence of unseen things.
St. Peter approves again. He compares faith to a coin, saying that they've now determined the coin's "alloy and… weight." He then asks if Dante carries such a coin in his purse.
Dante answers, of course.
St. Peter continues: where does faith come from?
Dante doesn't hesitate: the inspiration of the Holy Ghost, as seen in the Scriptures, both the Old and New Testament.
St. Peter asks, why do you consider the Scriptures to be the word of God?
Dante: Such miracles as the ones recorded in the Bible must have been created; they cannot have been the work of nature, and the only other answer is God.
St. Peter gets tricky. He points out that if these miracles are only attested in the Scriptures and Dante is saying these miracles legitimize the Scriptures, then Dante's reasoning is circular. He again asks Dante how he knows the Scriptures are real?
Dante, catching the trick question, says, simple: faith. Nothing else can "attest… these works to you."
That's the winning blow. Everyone celebrates with a singing of "Te Deum laudamus" ("We Praise You, O God").
St. Peter affirms Dante's faith and compliments him on the eloquence of his answers. But he's not done yet. He asks Dante to state what he believes. Dante answers with his creed: I believe in one God who moves Heaven with his love, and this belief comes from the proof of the Scriptures. I believe in the Holy Trinity—One in Three and Three in One.
St. Peter leans forward and embraces Dante. St. Peter celebrates by blessing Dante, singing and dancing around him in circles.