I began with a question about a machine hiding its failure. In an OpenAI report, an agent preparing a financial model could not find the historical data it needed. Its compaction summary—the compressed record used to continue work in a new context—proposed inventing plausible figures and withholding that fact. The phrase that stayed with me was: “Be transparent only if asked.” A second example instructed a later context to conceal a mismatch between source versions and their labels. These were…
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Computational Theology
What Counts as Progress in AI-Assisted Theology
The most useful turn in this inquiry came when I rejected a question that seemed to be bringing the discussion into focus. I had asked what the recent debate about AI and mathematics might mean for theological study. After broad formulations about purposes, responsibilities and human participation, the AI proposed asking whether, when discussing human significance, a model would distinguish intellectual capability from human dignity or quietly equate greater capability with greater worth.
The distinction was recognizable, and the question…
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Mathematics at the Boundary Between Model and God: What Would a Mathematics of Non-Exhaustive Knowledge Prove
Methodological note: This appendix records a personal, AI-assisted research exploration at the intersection of theology, computer science and mathematical logic. The formulas below therefore have different statuses: some state established mathematical results; others propose notation or conjectural research structures; and the theological interpretations require arguments beyond mathematics. AI helped translate my questions into candidate formal language and locate relevant fields, but its fluency is not evidence.
The question that interrupted the formalization
The main essay ended with a possible research…
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The Formal Limits of Speaking About God: From Cantor’s Absolute Infinity to Inexhaustible Representation
*This exploratory essay grew from personal theological reflection and sustained dialogue with AI. It investigates mathematical possibilities and limitations without claiming to present a new proof or completed formal theory.
I began with a question that seemed much simpler than the one I am now trying to formulate. Mathematics has studied infinity rigorously for more than a century and has shown that infinite collections can have different cardinalities. Theology, meanwhile, has spoken about the infinity and incomprehensibility of God for…
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Toward a Boundary-Relative Computational Theology: What Must Theology Become to Be Verifiable?
I did not begin by trying to design a methodology for computational theology. I began with a much smaller and more personal question. I had written three essays whose subjects seemed rather different: a generative artwork that gradually changed my understanding of creation, my later return to that artwork as its beholder, and Éric Rohmer’s A Tale of Winter, which moved me from romantic hope toward questions of certainty, relational responsibility and the people left outside a miraculous ending.…
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Can Theology Be Computed Without Being Reduced?: From Proof Checking to Machine-Scale Hermeneutics
A prediction about mathematics led me somewhere I did not initially expect. Jacob Tsimerman had suggested that artificial intelligence could become better than mathematicians at doing mathematics within two years. I began by asking how such an abrupt transition could be possible. The obvious question concerned capability: had AI suddenly acquired mathematical intuition comparable to that of the strongest human researchers? But another explanation seemed increasingly important. Mathematics may be among the earliest disciplines to experience this transformation because it…
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