I crafted the prompt and Claude drafted the dialog using a passage about memory from Augustine’s Confessions as the catalyst for the imaginary conversation. I asked for some changes, Claude made some suggestions, and I executed them.
Note this passage toward the end:
Gödel said, “Disordered love?”
“Yes. To love a lower thing as though it were higher. To love one’s own power more than truth. To love the image more than the living being. To love the tower more than the city.”
The reply is by Augustine and it amounts to a definition of idolatry. The tower, presumably, is the Tower of Babel.
ChatGPT created the image. I uploaded the full dialog and asked from an image based on the passage from Augustine’s Confessions. That began an iterative process resulting in the image immediately below. The dialog follows.
I want you to create an imaginary conversation between St. Augustine, Kurt Gödel, and Pope Leo XIV. It should take place in Gödel’s office at the Institute for Advanced Study. After the men introduce themselves – assume Augustine can understand and speak English, and perhaps wonder a bit how they became gathered together, Pope Leo leads off, saying that, while working on his recent encyclical, Magnifica Humanitas, one of his colleagues pointed out a passage in Augustine’s Confessions (to follow) that resonated with Gödel’s proof of incompleteness. Given the role that arithmetic plays in Gödel’s proof we should note that Augustine wouldn’t have known about arithmetic. Nor, for that matter, would he have known about computers. He is likely to have known about sophisticated mechanical devices like the Antikythera Mechanism and the Sphere of Archimedes, but never have seen one. But he would have seen complex water clocks (clepsydrae).
Here’s the passage from the Confessions (Book Ten, Chapter VIII). Perhaps Leo reads it aloud.
Great is this power of memory, exceedingly great, O my God–a large and boundless inner hall! Who has plumbed the depths of it? Yet it is a power of my mind, and it belongs to my nature. But I do not myself grasp all that I am. Thus the mind is far too narrow to contain itself. But where can that part of it be which it does not contain? Is it outside and not in itself? How can it be, then, that the mind cannot grasp itself?
A great marvel rises in me; astonishment seizes me. Men go forth to marvel at the heights of mountains and the huge waves of the sea, the broad flow of the rivers, the vastness of the ocean, the orbits of the stars, and yet they neglect to marvel at themselves. Nor do they wonder how it is that, when I spoke of all these things, I was not looking at them with my eyes–and yet I could not have spoken about them had it not been that I was actually seeing within, in my memory, those mountains and waves and rivers and stars which I have seen, and that ocean which I believe in–and with the same vast spaces between them as when I saw them outside me. But when I saw them outside me, I did not take them into me by seeing them; and the things themselves are not inside me, but only their images. And yet I knew through which physical sense each experience had made an impression on me.
Perhaps sometime late in the conversation Albert Einstein might drop in to see what they were talking about.
Here is a first pass. I’ve kept it staged, conversational, and conceptually explicit, with Einstein entering late as a useful destabilizer.
The Mind Too Narrow to Contain Itself A conversation in Kurt Gödel’s office at the Institute for Advanced Study
Gödel’s office was narrow, orderly, and dim. Books stood in ranks along the wall, interrupted by folders, loose papers, and a blackboard covered with marks whose austerity made them seem less written than engraved. Outside the window the trees of Princeton trembled slightly in the wind. The afternoon light had the washed patience of late autumn.
Kurt Gödel stood beside his desk, thin and formal, dressed in a dark suit. He had the air of a man who had been expecting visitors and yet was not at all reassured by their arrival.
The first visitor was an African bishop in ancient dress, compact and alert, his face alive with inquiry. He looked about the room with frank astonishment, then settled his gaze on the blackboard.
The second was an elderly man in white, gentle but grave, wearing a small pectoral cross. His eyes moved from Augustine to Gödel and then to the papers on the desk.
“I believe,” the man in white said, “that introductions are in order.”
Gödel inclined his head. “Kurt Gödel. Institute for Advanced Study.”
The bishop smiled faintly. “A place for contemplation?”
“For research,” said Gödel.
“Then it may be the same thing, if rightly ordered. I am Augustine, bishop of Hippo.”
Gödel blinked once. “Yes. I had inferred as much.”
The man in white bowed slightly. “And I am Leo, servant of the servants of God.”
Augustine turned to him. “Bishop of Rome?”
“Yes.”
Augustine’s face softened. “Then I greet you as a brother, though I confess I do not understand how we have been gathered. This room is strange to me. These lamps burn without flame. These marks”—he gestured toward Gödel’s symbols—“are neither Greek nor Latin, though I suspect they are meant to compel the mind.”
“They are logical formulae,” Gödel said.
“Ah,” said Augustine. “Then they are meant not merely to persuade, but to bind.”
Leo smiled. “That is well put.”
Gödel gestured toward the chairs. “Please.”
They sat. Augustine examined the chair before trusting his weight to it. Leo remained composed, as though papal audiences in the offices of dead mathematicians were not wholly outside the bounds of pastoral duty.
Leo opened a folder.
“Professor Gödel, Saint Augustine, I will explain why I wished for this conversation, though the means by which it has been granted are beyond my competence. While I was working on my recent encyclical, Magnifica Humanitas, one of my colleagues pointed out a passage from Augustine’s Confessions. It seemed to him to resonate with your incompleteness theorem.”
Gödel looked sharply interested.
Augustine looked from one to the other. “Incompleteness?”
“A result in mathematical logic,” said Gödel. “Roughly speaking, in any sufficiently strong formal system capable of expressing arithmetic, there will be true statements that cannot be proven within that system, assuming the system is consistent.”
Augustine was silent for a moment.
“You say: a structure of reasoning may contain truths that it cannot reach by its own lawful motions?”
Gödel’s expression altered, almost imperceptibly. “That is not an inaccurate first formulation.”
“But I must be careful,” Augustine continued. “You speak of arithmetic. I know number, of course. I know that three is not five, and that if two men enter a room where two already sit, there are four. I know arithmetic as number, measure, and reckoning. But you seem to speak of arithmetic as though it were also a mirror in which reasoning may behold its own form. That I do not know.”
Gödel nodded. “Exactly. The novelty is not number alone, but the coding of statements, proofs, and rules as numbers. Nor would you know the modern notion of a formal system: axioms, rules of inference, recursive procedures, symbolic codings of syntax.”
“I know rules,” said Augustine. “And I know the temptation to mistake the rule for the truth it serves.”
