Prior Art for Matheology#

As LLoL has so far not heard of anyone who defined mathematical theology, nor could he find anyone despite his best efforts to search and a long-standing interest in related areas. Yet, search for prior art is complicated, as all experts know, and LLoL did not have the time to become an expert in all possibly relevant areas.

Thus, as a sort of last resort before going public with the need to define matheology, LLoL here engages AI (in the form of Claude Code v2.1.72 Opus 4.6 as of 2026-03-11), to see if maybe a smarter processing of the world’s online information can produce something he has so far missed on his wid-e research marathon, aiming to avert Armageddon disasters with the help of mathematical theology.

Outcome: As expected, the global reach of AI produced several sources that LLoL had not been aware of (even though he arguably should have known some of them). However, his overall assessment was correct: even though thinkers here and there have compiled important building-blocks for mathematical theology, there is neither a unifying framework nor a recognized discipline that brings together these two pivotal disciplines for understanding many key aspects of infinity.

Hence, consider LLoL’s AI-assisted work below as some first steps towards a formal definition of “matheology”. Note that LLoL had intuitively grasped all key concepts proposed by AI Claude, but his lack in formal mathematical training means that it would have taken him a ridiculously long time to compile the elegant list of axioms defined below. Hence, respect for Claude as collaborator in theological research for enlightening spiritual questions. Please don’t ask LLoL yet what to make of his observation to derive sometimes deep spiritual insights from AI. For now, LLoL merely has to acknowledge that God can speak Truth anyway God wants, whether through donkeys in the Torah, through magicians reading stars in the Gospels, or through AI in today’s world. Please also note that these potential venues of revelation are neither “pure” nor easy to “read”, nor necessarily reliable. Hence, engaging with all of Reality best anyone can remains essential to any real quest for real answers.

To provide a baseline assessment of reliability of AI answers for the reportedly best available AI tool (as of 2026-03-11), here is an assessment of its own reliability:

Reliability of AI for theology#

LLoL asks:

How confident are you in the reliability of your replies when it comes to theological questions?

Opus responds:

Moderate at best. A few honest notes:

  • Breadth, not depth: I have broad exposure to major religious traditions (Christianity, Islam, Judaism, Hinduism, Buddhism, etc.) and can summarize mainstream positions reasonably well. But theology is a field where precision and nuance matter enormously, and I can miss important distinctions between denominations, schools, or historical periods.

  • Common errors: I sometimes conflate popular-level understanding with actual scholarly/doctrinal positions, oversimplify internal debates within traditions, or present one tradition’s framing as if it’s universal. I can also be confidently wrong about specific textual references or attributions.

  • Bias in training data: My knowledge skews toward English-language, Western, and especially Protestant Christian sources. I’m less reliable on Eastern Orthodox theology, Sufi traditions, Talmudic reasoning, or non-Anglophone theological scholarship.

  • Not a substitute for primary sources: For anything that matters — whether academic, pastoral, or personal — I’d treat my answers as a starting point to verify against authoritative texts, scholars, or clergy, not as a final word.

If you have a specific theological question, I’m happy to try, but I’ll flag where I’m uncertain rather than bluff.

Does Mathematical Theology exist?#

LLoL asks:

Has anyone ever seriously tried to define mathematical theology? So far on the web I could only find cursory references. What I am looking for is something rigorous like a true synthesis in the sense of using the rigorous search for provable truth as practiced in mathematics for defining and proving theological statements in cases where such statements can actually be logically deduced from first principles and maybe with the help of additional assumptions (such as the reliability of certain revelations as recorded in words widely believed to be divine revelations). Please compile a list of the most important works that might introduce me to mathematical theology.

AI method note

Opus performed five web searches to compile the following answer: "mathematical theology rigorous formal logic proofs theological statements", "mathematical theology" axiomatic theology formal proofs God, "analytic theology formal methods modal logic Bayesian theology bibliography", Sobel "Logic and Theism" Swinburne "Existence of God" Bayesian Plantinga, and Spinoza Ethics "geometrical order" Llull "Ars Magna" combinatorial logic theology.

Opus responds:

No single unified field called “mathematical theology” exists as an established discipline, but there is a substantial and growing body of work that does exactly what you describe — applying formal logic, axiomatics, and probability theory to theological claims with mathematical rigor. The work is scattered across philosophy of religion, analytic theology, and mathematical logic. Here is what I found:

Foundational / Historical Works#

  1. Baruch Spinoza — Ethics, Demonstrated in Geometrical Order (1677)

    The most ambitious early attempt. Spinoza literally structures his metaphysics and theology like Euclid’s Elements: definitions, axioms, propositions, and formal proofs. He deduces the nature of God (substance, attributes, modes) from first principles. Whether you accept his conclusions depends on whether you accept his axioms — exactly the structure you’re looking for.

  2. Ramon Llull — Ars Magna (~1305)

    A medieval attempt at a combinatorial logical system for proving theological truths (particularly Christian doctrines like the Trinity). Llull built actual mechanical devices to combine theological concepts. Leibniz later cited Llull as an inspiration.

  3. Gottfried Wilhelm Leibniz — Theodicy (1710) and logical writings

    Leibniz explicitly pursued a calculus ratiocinator — a formal calculus for reasoning about all truths, including theological ones. He refined Anselm’s ontological argument into a more rigorous form, arguing: (1) a Most Perfect Being is logically possible; (2) if possible, then necessarily existent.

The Modal Logic / Formal Proof Tradition#

  1. Kurt Gödel — Ontological Proof (circulated ~1970, published posthumously 1987)

    The landmark work. Gödel formalized Anselm’s ontological argument in quantified modal logic with explicit axioms about “positive properties.” This is real mathematics — axioms, definitions, theorems, and proofs in formal notation. Published in: Collected Works, Vol. III (Oxford, 1995).

  2. Christoph Benzmüller & Bruno Woltzenlogel Paleo — Computer-checked proof of Gödel’s ontological argument (2013–2016)

    They fed Gödel’s proof into automated theorem provers (Isabelle, Coq) and computationally checked its logical structure. They also discovered that Gödel’s axioms entail modal collapse (everything true is necessarily true), which is theologically problematic. Key paper: “Automating Gödel’s Ontological Proof of God’s Existence with Higher-order Automated Theorem Provers” (2014).

  3. Alvin Plantinga — The Nature of Necessity (1974), Chapter X

    Plantinga reformulated the ontological argument using S5 modal logic (the system where “possibly necessary” implies “necessary”). More rigorous than popular presentations suggest. The key move: if maximal greatness is even possible, God exists in every possible world.

  4. Jordan Howard Sobel — Logic and Theism: Arguments For and Against Beliefs in God (Cambridge, 2004)

    This is probably closest to what you want as a single comprehensive reference. Sobel (a logician) systematically formalizes virtually every major argument for and against God’s existence — ontological, cosmological, teleological, from miracles, from evil — using extensive symbolic logic and Bayesian probability. Each chapter has formal appendices. It is rigorous, technical, and thorough.

  5. Graham Oppy — Ontological Arguments and Belief in God (Cambridge, 1995)

    A rigorous formal analysis of the entire family of ontological arguments, from Anselm through Gödel and Plantinga.

The Bayesian / Probabilistic Tradition#

  1. Richard Swinburne — The Existence of God (1979, revised 2004)

    Swinburne systematically applies Bayesian probability theory to theistic arguments. He assigns prior probabilities, calculates likelihoods, and builds a cumulative probabilistic case. This is the most sustained attempt to treat theology as a problem in Bayesian epistemology.

  2. Stephen Unwin — The Probability of God: A Simple Calculation That Proves an Ultimate Truth (2003)

    A more accessible Bayesian treatment. Less rigorous than Swinburne but explicitly mathematical.

The Analytic Theology Movement (Contemporary)#

  1. Oliver Crisp & Michael Rea (eds.) — Analytic Theology: New Essays in the Philosophy of Theology (Oxford, 2009)

    The founding manifesto of the analytic theology movement, which explicitly advocates applying formal logical methods to theological doctrines (Trinity, Incarnation, Atonement, etc.).

  2. T&T Clark Handbook of Analytic Theology (2017)

    Comprehensive survey of the field, with chapters on formal methods applied to specific doctrines.

  3. A.C. Anderson & Michael Gettings — work on formal axiomatizations of theology at St Andrews and elsewhere

    There is an active John Templeton Foundation project on Formal Approaches to Philosophy of Religion and Analytic Theology that specifically develops formal logical tools for theological questions.

Bridging Works#

  1. Ladislav Kvasz — “The Invisible Link Between Mathematics and Theology” (Perspectives on Science and Christian Faith, 2004)

    Argues that mathematics and theology share deep structural parallels in their methods of reasoning about non-empirical objects.

  2. Edward Nelson — “Mathematics and Faith” (Princeton, 2002)

    A Princeton mathematician reflecting on the foundational parallels between mathematical and theological epistemology.

Assessment#

  • Sobel’s Logic and Theism is the best single starting point if you want to see what “mathematical theology” looks like in practice — real formalizations with real proofs.

  • Gödel’s ontological proof (and the Benzmüller/Paleo computational proof-checking) is the purest example of theorem-proving applied to theology.

  • Swinburne is the best entry for the Bayesian/probabilistic approach.

  • Spinoza remains the most radical historical attempt at the axiomatic-deductive approach you describe.

  • The analytic theology movement is where the most active current work is happening, though it varies in how formally mathematical (vs. merely logically careful) individual contributions are.

A true, unified “mathematical theology” as a recognized discipline — with its own journals, standard axiom systems, and accumulated body of proven theorems — does not yet exist. But the pieces are all there, and the Templeton-funded projects suggest it may be coalescing.

Note

Caveat from Opus: I’m moderately confident about the major works listed above (Gödel, Sobel, Swinburne, Plantinga, Spinoza) but less certain about some of the details of newer projects. I’d recommend verifying publication details before purchasing.

Sources consulted by AI#

The first concrete axiom system to emerge from this survey was a set of 14 axioms for pan-en-theistic mathematical theology, proposed by Claude Opus on 2026-03-11 and subsequently refined through poster review on 2026-03-14/15. That work now lives in its own section at PET Model for Pan-En-Theism.



If you wish to extend such analyses and to explore many more such questions to replace eschatological warfare between nuclear and other nations on Earth with mathematical clarity, then please consider supporting this work by buying in towards scaling up a ResearchCity that can actually do it (see box below).