When Logic Became Dangerous: Russell, Zermelo, and the Discipline of Totality

This is the second part of a series developed through the Department of Philosophical Theology at the Institute of Lutheran Theology's Christ School of Theology, exploring major results in modern logic and their significance for philosophical and systematic theology.

The great achievements of Frege, Peirce, and Cantor vastly enlarged the expressive resources available to logic and mathematics. Quantification made it possible to speak formally about all or some objects satisfying a condition; the logic of relations permitted systematic treatment of structures involving two or more objects; Cantor showed that infinity itself could be mathematically articulated and that infinite collections could differ in cardinality. Yet precisely this increase in expressive power produced a new problem, for once logic could speak about collections defined by conditions, what prevented us from forming a collection corresponding to any condition whatsoever?

The answer, discovered with particular force by Bertrand Russell, was contradiction.

Consider the apparently innocent idea of the collection of all collections that are not members of themselves. Let us call this collection R. We can describe it this way:

R = {x : x ∉ x}.

Read: R is the collection of all objects x such that x is not a member of itself.

Now ask whether R itself belongs to R. By the very condition defining R, we obtain:

R ∈ R if and only if R ∉ R.

Read: R is a member of itself if and only if R is not a member of itself.

Either answer produces its opposite. If R belongs to itself, then by definition it must not belong to itself; but if R does not belong to itself, then it satisfies the condition for membership in R and therefore does belong to itself.

This was not merely an amusing puzzle. Russell communicated the paradox to Frege in 1902 while the second volume of Frege's Grundgesetze der Arithmetik was in press, and Frege immediately recognized the seriousness of the difficulty. His project had aimed to show that arithmetic could be derived from logical principles, but the paradox exposed a defect in the assumptions governing the formation of extensions or classes. The new logical machinery had become powerful enough to undermine one of its own foundational constructions.

The philosophical lesson is easy to state but profound in its consequences: not every condition that can be expressed determines an object corresponding to that condition.

Suppose we can specify a condition F and say intelligibly what it would be for something to satisfy F. It does not follow merely from this that there exists an object consisting of all and only the things satisfying F, for the movement from a condition to a corresponding totality requires justification. This distinction between specification and object formation became one of the central lessons of twentieth-century logic.

Zermelo and Restricted Set Formation

One response came through Ernst Zermelo and the subsequent development of axiomatic set theory. Instead of assuming a general principle according to which every condition determines a set, Zermelo restricted the circumstances under which sets may be formed. One does not simply move from a condition F to “the set of all Fs”; rather, set formation proceeds according to specified axioms.

The dangerous principle can be expressed simply as:

For every condition F, form the set {x : Fx}.

Read: for any condition F whatsoever, there exists a set containing exactly those objects that satisfy F.

Russell's paradox showed that this principle cannot be accepted without restriction. Zermelo's alternative was more cautious: begin with a set already given, and then select from it those members satisfying a specified condition. Thus, given a set A, one may form:

{x ∈ A : Fx}.

Read: the set of those members x of A that satisfy the condition F.

The difference is crucial because one is no longer permitted to range freely over absolutely everything and then collect into a set whatever satisfies an arbitrary condition. Set formation takes place relative to sets already available within an axiomatic framework, so that the transition from a predicate to a set is controlled rather than automatic.

Russell and the Theory of Types

Russell pursued a different strategy through the theory of types. The underlying intuition was that certain forms of self-reference arise because expressions belonging to different logical levels have been allowed to interact indiscriminately. Individuals occupy one level; predicates of individuals another; predicates of predicates another still. On such an approach, a predicate should not simply be allowed to take itself as an argument.

The slogan is crude but useful: things of one logical type cannot simply be treated as things of every logical type. Russell's solution therefore imposes hierarchy where unrestricted logical construction had permitted self-application, and the point is not merely technical. Logical grammar itself must be disciplined if expressions are not to generate combinations that the theory cannot consistently sustain.

These developments suggest a distinction that remains philosophically important: expressibility is not the same thing as admissible predication, and admissible predication is not the same thing as objecthood. The fact that we can describe something does not yet show that the description determines a genuine object, nor does the grammatical availability of an expression settle the ontological commitments of a theory.

Why This Matters for Theology

The theological relevance is greater than it may first appear because theology regularly speaks in terms that invite totalization: all truths, all possibilities, everything God knows, everything God can do, the totality of creation, or even everything that is not God. Russell's paradox does not show that such expressions are illegitimate, but it does force a distinction between quantifying over things and reifying the domain of quantification into another thing.

Suppose, for example, that we say:

For every x, if x is a creature, then God knows x.

Symbolically:

∀x (Cx → Kgx).

The symbols are simply an abbreviated way of saying: for every object x, if x is a creature, then God knows x.

Nothing in that assertion requires there to be an additional object called the set of all creatures, for the quantifier may range over creatures without thereby packaging the domain over which it ranges into a further entity. The same point applies when theologians speak of divine omniscience. One may say:

For every truth p, God knows p.

That claim does not by itself commit us to the existence of a further object called the set of all truths. Similarly, one may say:

For every creature x, x depends upon God.

Again, nothing in the quantificational structure of the sentence requires that there be one further object called the totality of everything other than God. Quantification alone does not force reification.

The methodological lesson can therefore be stated compactly: quantification should not be confused with reification. To say something of every member of a domain is not yet to say that the domain itself exists as one additional member of one's ontology, and theology is especially susceptible to overlooking this distinction because its characteristic subject matter repeatedly calls forth universal expressions.

There is a deeper theological resonance as well. Christian theology has long had to distinguish between what can legitimately be said of God and what ontological assumptions may be smuggled in by the forms of language used to say it. Russell, Zermelo, and type theory remind us that grammatical or logical form may tempt us into constructing objects that our theory neither requires nor can consistently sustain.

The suspect inference has this form: we can specify what it is to be an F; therefore, there exists one object consisting of all Fs. Yet the first statement does not entail the second. To put the point more carefully, being able to determine of each object whether it is F does not entail the existence of a set containing all and only the Fs. That is precisely the gap Russell's paradox forces us to notice.

The foundational crisis thus yielded a constructive philosophical lesson. Modern logic had acquired enormous power through Fregean quantification and Cantorian set theory, but Russell's paradox demonstrated that expressive power requires discipline. Zermelo supplied axiomatic restrictions upon set formation, while Russell supplied logical hierarchy through types; both responses forced philosophers to distinguish more carefully among language, predication, collection, and existence.

For theology, these distinctions are invaluable precisely because theology regularly attempts to speak about the ultimate, the universal, and the all-encompassing. Whenever theology speaks about all, it should therefore ask a further question: have we merely quantified over everything in some domain, or have we quietly turned that domain into one more thing?The question matters whenever theology attempts to speak of God, creation, possibility, truth, or totality.

Bibliographical Note

The classic primary source for the paradox is Bertrand Russell's 1902 letter to Gottlob Frege, together with Frege's discussion in the appendix to the second volume of Grundgesetze der Arithmetik (1903). Russell developed the theory of types most fully with Alfred North Whitehead in Principia Mathematica (1910–1913). Ernst Zermelo's “Untersuchungen über die Grundlagen der Mengenlehre I” (1908) provided the first major axiomatization of set theory designed in part to avoid the paradoxes generated by unrestricted set formation. For historical orientation, Jean van Heijenoort's From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 remains invaluable.

Two Revolutions in Modern Logic: Quantification and the Infinite

This essay is part of a series developed through the Department of Philosophical Theology at the Institute of Lutheran Theology’s Christ School of Theology, exploring major results in modern logic and their significance for philosophical and systematic theology.

Most theologians who have studied logic have encountered quantifiers and perhaps heard that Georg Cantor proved that there are different sizes of infinity. What is easier to miss is just how revolutionary these developments were. In the final decades of the nineteenth century, logic ceased to be primarily a theory of propositions of the Aristotelian sort—“All men are mortal,” “Some Greeks are philosophers”—and acquired the resources needed to describe indefinitely complicated structures of objects and their relations. At roughly the same time, mathematics learned that the infinite was not a single undifferentiated beyond, but possessed an articulated internal structure.

Both developments matter for theology, although neither proves anything theological. What they do is enlarge the conceptual space within which theological claims can be formulated, distinguished, and assessed, making it possible to ask with much greater precision what follows from what, what sorts of relations are being asserted, and what kind of infinity is actually at issue.

1. Frege, Peirce, and the Revolution in Quantification

The decisive breakthrough associated with Gottlob Frege’s Begriffsschrift of 1879 was not simply the invention of some new logical symbols. Frege supplied a new analysis of the logical structure of propositions, replacing the limitations of traditional subject-predicate analysis with a framework of functions, arguments, variables, and quantification.

Consider a simple statement:

Every human being is mortal.

In contemporary notation we write:

∀x(Hx → Mx).

Read aloud, this says: for every object x, if x is human, then x is mortal.

The statement does not name some peculiar object called “every human being.” Rather, it says that anything whatsoever in the relevant domain that is human is also mortal, so that its logical form becomes visible only when we distinguish the predicates—being human and being mortal—from the variable over which the quantifier ranges.

The real power of quantification appears when quantifiers are nested. Compare:

∀x∃y Rxy

with

∃y∀x Rxy.

The first reads: for every x, there is some y such that x bears relation R to y.

The second reads: there is some single y such that every x bears relation R to that y.

The difference lies only in the order and scope of the quantifiers, yet the difference in meaning can be enormous. “Everyone loves someone” does not entail “There is someone whom everyone loves,” and once this machinery becomes available logic can represent patterns of dependence that traditional syllogistic logic could scarcely express. Mathematics, science, metaphysics, and theology thereby acquire a far more exact language for describing structures.

Frege was not alone in bringing about this transformation. Charles Sanders Peirce and his collaborators, especially Oscar Howard Mitchell, independently developed powerful systems of quantification during roughly the same period, while Peirce’s work on the logic of relations deserves particular notice. Aristotelian logic had been especially comfortable with one-place predicates such as “is human,” “is mortal,” or “is wise,” whereas Peirce emphasized relations among two, three, or more objects.

Thus:

Rxy

can be read simply as: x bears relation R to y.

A three-place relation,

Rxyz,

says that x, y, and z stand in some specified three-place relation. One might represent “x gives y to z,” for example, by such a structure.

This sounds elementary to us precisely because the revolution succeeded.

For theology the significance is immediate, since Christian theological vocabulary is saturated with relations: the Father begets the Son; the Son is begotten of the Father; the Spirit proceeds; God creates the world; God justifies the sinner; Christ assumes a human nature; believers participate in Christ; promise is addressed to hearer. Such claims cannot adequately be represented merely by assigning properties to isolated objects, for their logical articulation requires relations, often asymmetric relations, and sometimes relations whose formal properties themselves become doctrinally significant.

Consider merely the difference between saying that each divine person is God and saying that the divine persons stand in particular relations to one another. The first set of claims concerns predication, whereas the second concerns relational structure. No piece of predicate logic solves the doctrine of the Trinity, but modern quantificational and relational logic allows theologians to see with far greater precision what kinds of claims they are making and where apparently similar formulations differ logically.

There is another consequence that may be even more important. Quantification makes explicit the distinction between what is true of some object and what is true of every object, and theology constantly moves among existential, universal, and uniqueness claims: there is a God; everything other than God depends upon God; there is exactly one God; every human being is a creature; some human beings believe; every justified sinner stands in a particular relation to Christ. The logical differences among these claims are not stylistic variations, for they determine what follows from them and what further commitments they carry.

The theological payoff, then, is not that Frege or Peirce secretly supplied Christian doctrine with its proper metaphysics. It is rather that modern logic makes possible a level of structural clarity that theological argument badly needs, since quantifier scope, relational order, dependence, uniqueness, and identity can all be made explicit. Much theological disagreement that appears initially to concern “concepts” turns out, upon examination, also to concern logical form.

2. Cantor and the Discovery of Different Infinities

The second revolution came from Georg Cantor. Before Cantor, philosophers and mathematicians had certainly discussed infinity, but infinity was commonly treated as though it were a single notion: the indefinite, the unbounded, or that which simply exceeds every finite magnitude. Cantor showed that infinite collections can themselves differ in size.

The key idea is deceptively simple. Two sets have the same cardinality when their members can be paired one-to-one: every member of the first set is paired with exactly one member of the second, and none is left over. For finite sets this seems trivial. A set containing five books has the same cardinality as a set containing five chairs because each book can be paired with exactly one chair.

Cantor applied the same criterion to infinite sets. Consider the natural numbers:

1, 2, 3, 4, …

and the even numbers:

2, 4, 6, 8, …

At first the even numbers seem to form a smaller collection, since they constitute only part of the natural numbers. Yet every natural number n can be paired with exactly one even number, namely 2n: 1 with 2, 2 with 4, 3 with 6, and so on without end. Thus the natural numbers and the even numbers have the same cardinality, and infinity therefore behaves differently from finite magnitude because a proper part of an infinite set can have the same number of members as the whole.

Cantor’s deeper result was more startling. Not all infinite sets have the same cardinality. His diagonal argument establishes that the real numbers cannot be paired one-to-one with the natural numbers. In ordinary language: there are strictly more real numbers than natural numbers, even though both collections are infinite.

Cantor proved something stronger still. Given any set S, form its power set, written:

P(S),

which simply means the set of all subsets of S. Cantor’s theorem tells us that:

|S| < |P(S)|.

Read in words: the set of all subsets of S is always strictly larger than S itself.

This means that there can be no greatest cardinal number. Begin with any infinity whatsoever, and one can specify a still greater infinity. Cantor’s discovery therefore forced philosophy to reconsider what it meant by “the infinite,” since there is no single mathematical infinity but rather an ordered hierarchy of infinite cardinalities.

The theological temptation at this point is obvious and should generally be resisted. Cantor’s transfinite mathematics does not provide a mathematical model of divine infinity, and God’s infinity should not simply be identified with some enormously large cardinal number. Indeed, because Cantor proved that there is no greatest cardinality, saying that God possesses “the largest mathematical infinity” would not even make mathematical sense.

Precisely here, however, Cantor becomes theologically useful, because his mathematics teaches theologians to distinguish different senses of infinity rather than allowing the word infinite to do undisciplined work. Mathematical infinity concerns the cardinality or ordering of mathematical structures, whereas divine infinity has traditionally concerned the absence of creaturely limitation in God. To say that God is infinite is not ordinarily to say that God has infinitely many parts, occupies infinitely many locations, or instantiates some transfinite cardinality.

Cantor therefore offers theology a conceptual warning: do not infer from the single word “infinite” that two uses of the term belong to the same logical or ontological category. At the same time, his work expands our imagination, for human reason can rigorously distinguish structures beyond every finite magnitude without thereby collapsing into incoherence. The infinite need not simply mean “something too large for us to think,” since certain infinities can be precisely defined, compared, and ordered.

This has interesting consequences for classical theological discussions of divine knowledge. Suppose we say that God knows every natural number, every real number, every subset of the natural numbers, and every mathematical truth. The point is not that divine knowledge thereby acquires some particular cardinality, but rather that Cantorian mathematics demonstrates how quickly apparently simple talk of “all things” becomes structurally complicated. A theology of omniscience must therefore take seriously the logical character of the totalities over which its claims range.

Cantor also helps us resist an old rhetorical maneuver in theology: invoking infinity whenever conceptual analysis becomes difficult. “God is infinite” cannot function as a license for contradiction, for Cantor’s work is a striking historical demonstration that infinity and rigor are not opposites. Modern mathematics became more rigorous precisely by refusing to leave infinity unanalyzed.

Why These Two Revolutions Belong Together

Frege, Peirce, and Cantor transformed different areas of mathematics and logic, yet the two revolutions belong together. Fregean and Peircean logic gave us vastly more powerful ways of saying what is true of objects and structures, while Cantor revealed that the domains over which our variables range may themselves possess unsuspected structure.

Together they prepared the ground for twentieth-century model theory. Once we possess quantifiers ranging over a domain, predicates and relations interpreted over that domain, and a mathematically disciplined conception of infinite structures, questions that would previously have been nearly impossible to formulate become natural: Which sentences are true in a structure? Can two different structures satisfy exactly the same sentences? Must an infinite theory have models of different cardinalities? Can a formal language uniquely characterize the structure it is intended to describe?

Those questions lead eventually to Löwenheim, Skolem, Gödel, Tarski, compactness, and some of the most philosophically unsettling results of modern logic. What begins with the enrichment of logical language therefore becomes a problem about the relationship among language, theory, model, and world.

For theology, however, the first lesson is already substantial. Modern logic teaches us that form matters, because who quantifies over what, which relations hold between which objects, what depends upon what, and what sort of infinity is being invoked are not technical details added after theology has finished its real work. They belong instead to the work of determining what theological claims actually say and what follows from them.

Bibliographical Note

For Frege, the obvious starting point is Gottlob Frege, Begriffsschrift: A Formula Language, Modeled upon That of Arithmetic, for Pure Thought (1879), conveniently available in translation in Jean van Heijenoort, ed., From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 (Harvard University Press, 1967). Van Heijenoort’s volume remains especially valuable because it allows readers to encounter many of the foundational texts of modern logic themselves.

The parallel American development should not be overlooked. See Oscar Howard Mitchell, “On a New Algebra of Logic” (1883), and Charles S. Peirce, “On the Algebra of Logic: A Contribution to the Philosophy of Notation” (1885). For the importance of Peirce and his circle in the development of quantification and the logic of relations, see Geraldine Brady, From Peirce to Skolem: A Neglected Chapter in the History of Logic (North-Holland, 2000).

For Cantor, the classic sources include his 1874 paper establishing the non-denumerability of the real numbers and his 1891 diagonal argument, “On an Elementary Question of the Theory of Manifolds.” Both are widely reprinted and translated. A particularly accessible philosophical introduction remains Michael Hallett, Cantorian Set Theory and Limitation of Size (Oxford University Press, 1984). For the broader historical setting, see Joseph W. Dauben, Georg Cantor: His Mathematics and Philosophy of the Infinite (Princeton University Press, 1979).

Where Have the Theologians Gone? Christ School of Theology and the Changing Geography of Doctoral Theological Education

I recently asked myself what I thought was a fairly straightforward question: How large is the PhD program at Christ School of Theology (CST) when compared with doctoral programs at the institutions that have traditionally trained systematic, philosophical, and historical theologians?

The question arose because CST has 42 PhD students enrolled in 2026–27. They are concentrated in three areas: Philosophical Theology, Systematic Theology, and Historical Theology. Forty-two seemed to me like a substantial number, but substantial compared with what?

When I entered academic theology, the geography was familiar. Yale, Chicago, Harvard, Princeton, Duke, Notre Dame, and the Hyde Park consortium immediately came to mind. If one wanted to become a systematic theologian, historian of theology, or philosopher of religion, these were among the places one considered. They possessed distinguished faculties and large communities of doctoral students. Their graduates populated university and seminary faculties throughout North America.

I assumed that CST's 42 students would still constitute a relatively small program measured against these older centers. That assumption appears to be wrong.

Comparing the Same Thing

One has to be careful with the numbers. A PhD in Religion is not necessarily a PhD in theology.

Consider Duke. Duke currently reports 45 students in its entire PhD program in Religion. Those students are distributed among Asian Religions, Christian Theological Studies, Early Christianity, Hebrew Bible/Old Testament, History of Judaism, Islamic Studies, New Testament, Religion, Aesthetics & Society, and World Christianity. CST has forty-two students in three areas of theology alone.

Harvard supplies another revealing comparison. Harvard Divinity School currently reports 63 students in the PhD program. Yet this is the Harvard Graduate School doctorate administered through the Committee on the Study of Religion, encompassing the broader academic study of religion rather than sixty-three students doing Christian theology.

Yale has undergone a similar development. Its Religious Studies doctorate now contains ten fields of study. Theology remains one of them, and Philosophy of Religion remains another. Indeed, Yale's Philosophy of Religion program explicitly includes philosophical theology and requires engagement with both analytic and continental philosophical traditions.

These remain extraordinary doctoral programs. The point concerns what they are programs in. Much of what was once concentrated in theology has become part of the broader academic study of religion. That changes the comparison.

Notre Dame Is Particularly Interesting

Notre Dame provides a cleaner case because its doctorate remains explicitly a PhD in Theology. Its current public roster lists 77 PhD students. I counted the students according to Notre Dame's own classifications. Twenty-two are in Systematic Theology and twelve are in History of Christianity. That gives 34 students in the two fields most directly comparable with CST's Systematic and Historical Theology programs. CST currently has 42 across Systematic Theology, Historical Theology, and Philosophical Theology.

This does not tell us that CST has somehow overtaken Notre Dame. It tells us something much more precise and, to my mind, more interesting. The concentration of doctoral students at CST in these traditional theological disciplines is already on the same numerical order as the corresponding concentration at one of North America's premier departments of theology. I did not expect that.

Princeton and Chicago

Princeton Theological Seminary remains another important comparison because its doctorate still bears a recognizably theological shape. Its current students work in Theology, Ethics, and Politics; History and Ecumenics; Biblical Studies; Practical Theology; and Religion and Society. Current profiles confirm active doctoral work in systematic and constructive theology as well as the several historical fields.

Our preliminary count of Princeton's current public profiles produced roughly eighteen students across Theology, Ethics, and Politics and the broadest possible construction of History and Ecumenics. Even that comparison is generous, since Religion in the Americas and World Christianity do not always constitute historical theology in the sense in which CST uses the term.

Chicago may display the historical shift still more dramatically.

The University of Chicago Divinity School remains one of the world's distinguished places for the study of religion. Its current PhD describes itself as interdisciplinary research into the “human phenomenon of religion,” encompassing constructive, historical, social-scientific, literary, and other approaches. Its current directory shows students across a wide range of areas. Theology and Philosophy of Religions continue, but they now occupy places within a much broader conception of the discipline.

Anyone who remembers Hyde Park several decades ago will recognize how significant the change is. The Chicago theological ecosystem once concentrated an extraordinary number of theologians within a few blocks. The institutions remain, but the distribution of doctoral work has changed.

So What Has Happened?

I think at least two developments are visible.

First, many of the strongest university programs have moved toward the academic study of religion conceived very broadly. That move has intellectual justification. Religion is a global human phenomenon, and serious scholarship cannot simply identify the study of religion with the study of Christianity.

Yet there is an institutional consequence. Forty or sixty doctoral students distributed among Christianity, Judaism, Islam, Asian religions, biblical studies, anthropology, ethics, history, philosophy, and other fields do not constitute forty or sixty systematic, philosophical, and historical theologians.

Second, seminary contraction has reduced the number of institutions maintaining large research doctorates in the classical theological disciplines. Programs have closed, contracted, consolidated, or broadened their purposes.

The result is a curious situation. There may now be fewer places in North America where a substantial number of doctoral students gather specifically to do theology. However, CST has moved in precisely the opposite direction.

What CST Has Accidentally—or Deliberately—Become

Our forty PhD students are concentrated in three neighboring disciplines. A student working in philosophical theology regularly encounters systematic theologians. A systematician encounters historians of doctrine. Historical work raises constructive questions; constructive work encounters philosophical ones. That density matters.

There is a considerable difference between enrolling forty people pursuing doctorates and possessing a community of forty doctoral theologians. The latter can become an intellectual environment. But what follows from the numbers?

Certainly not that CST is now “better than” Yale, Harvard, Princeton, Chicago, Duke, or Notre Dame. Such a claim would be silly. These institutions possess resources accumulated over generations: great libraries, endowed faculties, enormous universities, selective admissions, funding structures, placement networks, and reputations generated through thousands of graduates. Reputation is real, and so is institutional capital. But another fact is real as well:

Christ School of Theology has achieved doctoral scale before it has achieved commensurate reputation. That is what surprised me in looking at the numbers.

I think we can now say, with reasonable caution, that CST has developed one of the larger concentrated communities of PhD students in North America working specifically in systematic, philosophical, and historical theology.

Perhaps further research will reveal several programs we have overlooked. I would welcome the correction. This is an empirical question. One must count the students, identify their fields, and compare like with like.

But Duke has forty-five doctoral students in its entire Religion program. Harvard has sixty-three. Notre Dame has thirty-four in Systematic Theology and History of Christianity combined. Yale organizes its doctorate across ten fields. Once those facts are placed beside forty students concentrated in CST's three theological fields, something worth noticing has happened.

Scale Is Only the Beginning

Numbers do not produce scholarship, because 42 disconnected students are simply 42 students. The next question for CST is therefore more important than the enrollment question: What must happen for these students to become a genuine community of theological scholarship?

They must read one another's work. They must present dissertation chapters and defend arguments before colleagues. Philosophical theologians must learn enough historical theology to know when a supposedly new problem is an old one. Historical theologians must be pressed about what follows from the texts they study. Systematic theologians must learn to state clearly what they claim, what makes the claim true, and what follows if it is.

They should meet major scholars. They should publish. They should participate in conferences. Their dissertations should matter. Their graduates should eventually teach the next generation. At this point enrollment begins to generate intellectual capital.

This also suggests why CST should be cautious about proliferating doctoral concentrations. There is nothing inherently wrong with PhDs in practical theology, leadership studies, biblical studies, missiology, or other fields. But institutional identity comes partly from decisions about what one will not do. CST presently possesses something unusual: a large doctoral program centered quite deliberately upon theology. We ought to know what we have.

A Changed Map

The most interesting conclusion therefore concerns neither CST nor enrollment statistics by themselves. The map has clearly changed.

The great institutions remain great. Yale is still Yale. Harvard is still Harvard. Notre Dame, Princeton, Duke, and Chicago remain institutions with extraordinary scholars and enormous intellectual resources. Yet the concentration of doctoral students within the classical theological disciplines is no longer distributed as it once was.

New centers can consequently emerge. Whether CST becomes one of them will not be settled by enrollment numbers. It will be settled by the quality of the scholarship produced by its faculty and students, by the rigor of its dissertations, by publications, by intellectual exchange, and ultimately by the scholars its PhD program sends into the church and academy.

But one necessary condition is already present. There are enough theologians in the room, and that is something I had not fully realized until I counted them.

Model Theory in Theology: From Descartes to Luther

This short talk given on August 12, 2026, at the 15th International Luther Congress in Aarhus, Denmark, introduces model theory to historians. Like all my papers, it arises from work done at the Department of Philosophical Theology, ILT Christ School of Theology. 

Two Problems We Have Not Escaped

I want to begin some distance from model theory, with two problems associated above all with Descartes. The first is the problem of the external world. How do I know what the world is like apart from my representations of it? The second is the problem of other minds. How do I know what another person thinks, means, intends, believes, or experiences when I never occupy that person’s consciousness?

Descartes formulated these problems with unusual clarity. Four centuries later, we have not made them disappear. We have mostly learned how to live intelligently with them. We do not solve either problem by somehow getting outside ourselves. Rather, we encounter something over against us, something that resists us, and we try to render it intelligible. The world does not always behave as our theories predict. Other persons say and do things our accounts of them do not anticipate. Our interpretations can fail because something confronts us that is not simply at our disposal.

We cannot solve either problem by looking down at reality from nowhere, as though we could step outside ourselves and check our account against the thing itself. But we are remarkably good at a more modest maneuver: looking left and right, comparing one account with another and both with what resists them. That is the maneuver this essay is about.

Historians Live with the Problem of Other Minds

Historians confront the second Cartesian problem every day. At a Luther Congress we ask what Luther meant, what Melanchthon believed, what a late-medieval logician was doing with suppositio, or what theological possibilities were available to an author in 1517. But we cannot climb into Luther’s mind. We have texts, vocabulary, grammatical practices, controversies, other authors, institutional settings, manuscripts, and subsequent writings.

What historians actually do is reconstruct. We construct an account under which this evidence becomes intelligible together. Different historians may agree about the words on the page and nevertheless disagree about the best account of what those words are doing. The text and its historical setting constrain us: they possess what, borrowing loosely from Charles Peirce’s language of Secondness, I shall call an over-and-againstness or “bump-up-againstness.” They do not allow us responsibly to make them say whatever we wish.

This means that the mens auctoris need not function as an independently accessible semantic court of appeal. Authorial intention remains a legitimate historical hypothesis, but what we can reconstruct is the intentionality of a textual act from publicly available historical evidence. Our reconstruction may be excellent without becoming incorrigible.

The Special Sciences Face the External-World Version

The special sciences confront an analogous problem from the other Cartesian direction. The physicist does not have uninterpreted physical reality sitting on one side of the laboratory and a theory on the other. The biologist does not inspect life in itself. Scientists encounter phenomena, measurements, regularities, anomalies, and recalcitrant observations, and they construct theoretical structures that make these intelligible.

The historian’s problem and the scientist’s problem are not identical. A manuscript, another mind, and a physical process are not the same kind of object. But structurally the inquiries share something important: neither historian nor scientist possesses a God’s-eye standpoint. Both construct accounts of something that confronts them and is capable of proving those accounts inadequate. Theories are answerable to what they seek to understand without our having to suppose that finite knowers can compare their theories with an entirely uninterpreted world.

Theology Has Both Problems at Once

Theology inherits both problems. Theologians are historians. We ask what Paul meant, what Augustine meant, what Luther meant, what Nicaea meant, and what inherited doctrinal language was doing in its original settings. But theologians also make assertions about reality: God raised Jesus from the dead; God justifies the ungodly; Christ is present in the Supper.

Theology therefore interprets witnesses to other minds while also speaking about a world in which God is soteriologically ingredient. It asks both what inherited theological assertions meant and what account of God, world, Christ, sinner, promise, sacrament, and salvation renders the subject matter intelligible. The two Cartesian problems meet inside theological inquiry.

This is why theology cannot simply borrow its method from the historian or the scientist alone. It needs a single account of inquiry general enough to cover both tasks at once—one that tells us what we are doing when we build a model of a mind we cannot enter and a model of a God we cannot view from above. That is the account model theory can supply, and it is why I turn to it now.

A Small Luther and Trutvetter Example

Let me give one small example from another paper I presented here. Luther entered the University of Erfurt in 1501, the year Jodocus Trutvetter’s Summule totius logice appeared. We possess Trutvetter’s texts and Luther’s texts. The historical question is not merely whether Luther remembered particular sentences from Trutvetter. It is what semantic and inferential possibilities belonged to the intellectual world within which Luther’s later disputation became intelligible.

Consider a Trinitarian inference discussed by Trutvetter:

This divine essence is the Father.
This divine essence is the Son.
∴ The Son is the Father.

If I assign the copula est strict numerical identity throughout, the inference is valid. If this divine essence is numerically identical with the Father and numerically identical with the Son, then Father and Son are numerically identical with one another. There is no problem with the logic, but the theology is disastrous.

So what must est, essentia, Father, and Son be doing semantically for Trutvetter’s discussion to become intelligible? And when Luther later reasons with inherited scholastic logical vocabulary, what larger structure of interpretation makes both Trutvetter and Luther intelligible?

Here I need to point out that I am using the word interpretation in a way different from its hermeneutical use familiar to many of us. In formal semantics an interpretation assigns semantic values to the non-logical vocabulary of a language—in the simplest cases, the things to which its terms apply. Two readers may agree completely on the visible words and disagree about the meanings being assigned to them.

In historical work we are not pretending that Trutvetter’s or Luther’s prose is itself a formal language. We construct structured interpretations of the texts, and where useful we can regiment selected claims formally. One historian may model the relevant predication one way, another differently. We can then ask which model makes more of Trutvetter’s text, Luther’s text, and the historical relation between them intelligible. We can even ask whether a larger space of intelligibility can accommodate both without erasing their differences.

Theological Language Presents the Same Problem

The same issue appears when we turn from the historical reconstruction of theologians to the theological tradition and the Word of God that confront us. People of good will can agree on the language of theology while interpreting its terms very differently.

Lutherans may say, “We are justified by grace through faith.” But what is the semantic work of justification? What is grace? What sort of relation between God and the sinner is being asserted? Or Christians may agree that “Christ is present in the Eucharist” while operating with very different understandings of Christ, presence, body, sign, promise, and sacrament.

Theological disagreement therefore frequently occurs because the same sentences are satisfied under different models. A model may preserve familiar vocabulary while changing the larger structure in which the vocabulary functions. The question then becomes whether one model preserves more of the theological subject matter, whether another changes the subject, and whether several admissible models remain possible.

Model Theory Makes the Structure Explicit

Only now do I want to introduce model theory in its technical sense—and I will keep the symbols to the minimum that actually does work for us.

A theory, syntactically understood, is simply a set of sentences. Call it T:

T={φ1​,φ2​,φ3​,…}

Read this as: T is just the set of claims the theory makes.

An interpretation assigns semantic values to the non-logical terms of a language. A model is a structure under such an interpretation in which the relevant sentence or theory is true. When a structure M makes a sentence φ true under the interpretation supplied by M, we say that M satisfies φ, and we write:

$$M\models \phi$$

Read ⊨ simply as “satisfies” or, less technically, “makes true.”

A model of a theory satisfies every sentence in it. The collection of all such models is what logicians call Mod(T):

$$Mod(T)=\{M\mid M\models T\}$$

Read this as: Mod(T) is the class of models that make all of T’s sentences true.

And now we can state formally something historians and theologians encounter constantly. One theory can admit more than one model:

M1​⊨T

and

M2​⊨T,

while

~(M1​ = M2​).

The final expression says only that the two models are not numerically identical. More importantly for our purposes, they may differ substantially in the structures under which the same sentences are true. Both can satisfy the theory without representing its subject matter in the same way.

Satisfaction alone therefore does not tell us which model should be preferred. Some candidate models can be excluded because they violate constraints constitutive of the subject matter. An interpretation of a text that cannot accommodate its actual wording may cease to be an interpretation of that text. A theological model that preserves the word resurrectiononly by abandoning the identity of the one said to have been raised may have changed the subject rather than merely offered a less attractive account.

Among the models that remain admissible, we compare. We ask about consistency, coherence, explanatory scope, fecundity, parsimony, applicability, historical adequacy, capacity to accommodate recalcitrant evidence, and sometimes elegance or beauty. These virtues are not mechanically commensurable. There is no algorithm that adds them together and announces the correct model.

This is where I find Kant’s reflektierende Urteilskraft—reflecting judgment—useful. We compare, discriminate, and judge without pretending that an antecedently possessed universal rule mechanically determines the result. I call the structured field within which such comparative judgments occur teleo-space.

The position is fallibilist. Further texts, evidence, experiences, arguments, or distinctions may force us to reorder the models. But fallibility does not imply that every model has equal epistemic standing. We can give reasons why one is better than another.

Nor do we need a God’s-eye standpoint from which model and uninterpreted reality can be placed side by side. We cannot look down from nowhere. But we are remarkably good at looking left and right. We can compare models. We can see that one explains something another leaves obscure, preserves a distinction another destroys, or accommodates an obstinate text or experience another must suppress.

Model theory therefore does not solve Descartes’ problems by giving finite creatures access to reality without mediation. It does something more useful. It clarifies the structure of responsible inquiry when such access is unavailable.

The historian constructs models of other minds from texts that resist interpretation. The scientist constructs models of a world that resists theory. The theologian does both: we interpret witnesses, and we make claims about a reality in which God is soteriologically ingredient.

Our models are fallible. More than one may satisfy the assertions with which we begin. Some can nevertheless be excluded; others can be comparatively ordered. We can offer what I would call a reasoned account: a publicly criticizable, corrigible judgment about how the subject matter may be independently of our present act of modeling it.

We cannot look down from nowhere. But we can look left and right. And perhaps model theory can help theology become clearer about what it is doing when it does.

Reality Does More than Resist; It Corrects

This essay continues an ongoing series in philosophical theology from the Department of Philosophical Theology at Christ School of Theology. The series asks a few basic but demanding questions: What makes reality intelligible? How does theological language work? What philosophical assumptions support Christian belief? Behind it stands a simple conviction: theology exists because these questions exist, and its first task is to make Christian doctrine intelligible without reducing, replacing, or explaining away the reality to which that doctrine points.

The previous essay argued that reality has the first word. Inquiry does not begin because an isolated subject decides to direct its attention toward an otherwise indifferent world. It begins because something has already presented itself, interrupted our expectations, resisted our descriptions, or called our understanding into question. Before we formulate a hypothesis, devise an experiment, or construct a theory, something has already occasioned the inquiry.

That claim reverses an order of explanation deeply embedded in modern thought, which imagines us first as active knowers who subsequently turn toward reality as an object of intellectual activity. The actual experience of inquiry suggests otherwise. Reality does not enter the process only after we have begun asking questions; the questions arise because reality has already refused to remain unnoticed.

From resistance to correction

Resistance alone, however, does not explain inquiry. A locked door resists the body. A steep hill resists the traveler. A malfunctioning machine resists its operator's intentions. Such resistance may frustrate us, delay us, or force a change of behavior, but it does not yet constitute correction.

Intellectual inquiry requires something more: reality must be capable not merely of impeding our purposes but of showing that an account of it is inadequate. A scientist whose prediction fails does not conclude that nature has simply been uncooperative; she asks whether the theory, the measurement, or the experimental design was mistaken. A historian who discovers a document inconsistent with a familiar narrative does not treat it as an obstacle to a preferred interpretation; he asks whether the narrative must be revised. A philosopher who finds a contradiction within an argument does not treat it as an unfortunate collision of equally acceptable possibilities; she recognizes that something has gone wrong. In each case, reality does more than resist. It corrects.

To be corrected is not merely to be pushed in a different direction. It is to discover that one ought to think differently because one's previous account has failed to do justice to its object. This "ought" is already present in every serious inquiry. We do not prefer a revised theory merely because it is newer; we judge it more adequate. We do not abandon a historical interpretation because another has become fashionable; we abandon it because the evidence no longer supports it. We do not reject an argument because it is rhetorically inconvenient; we reject it because its conclusion does not follow or its premises cannot be sustained.

Inquiry is therefore normative from the beginning, for it distinguishes better from worse descriptions, more and less adequate explanations, responsible from irresponsible judgments. Without such distinctions there may still be curiosity, experimentation, or invention, but there is no disciplined search for understanding.

The limits of construction

This is where many contemporary accounts of knowledge become unstable. They rightly emphasize that human knowing is historically situated, linguistically mediated, socially conditioned, and conceptually structured. No one encounters reality from nowhere; every observation occurs within practices of interpretation, and every judgment employs concepts inherited from particular traditions. Yet none of this explains how those practices, concepts, and traditions can themselves be corrected. A community may share an interpretation and still be mistaken. An inherited narrative may organize experience powerfully while concealing what actually occurred. A conceptual scheme may be internally coherent while systematically misdescribing its object. Even a theory of knowledge that insists all knowledge is socially constituted must distinguish a more adequate account of that constitution from a less adequate one.

The language of construction, then, cannot be the final word. Human beings undoubtedly construct theories, models, narratives, and conceptual frameworks. The planetary model, the economic model, the historical narrative, and the theological system all result from acts of selection, abstraction, and representation; no model reproduces its object without mediation. Construction is therefore not the enemy of realism—it is one of the conditions under which finite beings become capable of understanding anything at all. The relevant question is not whether our models are constructed, but whether they remain answerable to what they seek to understand.

The difficulty arises when the constructed character of a model is taken to mean that it owes nothing beyond itself. At that point coherence replaces adequacy, usefulness replaces truth, and a model's capacity to organize discourse matters more than its capacity to disclose its object. A model may be coherent and still false. It may be useful and still distort what it represents. It may secure agreement among those who employ it while excluding every consideration that would expose its inadequacy. That a model works for some purpose does not establish that it has understood the reality with which it deals.

This becomes especially clear when models meet anomalies. An anomaly is not simply something unexpected; it is something that ought not to have occurred if the model were adequate. Its significance lies in the tension between what the model permits us to expect and what reality actually presents. Yet even anomalies do not automatically correct us—human beings are remarkably skilled at protecting favored explanations from inconvenient evidence, whether by dismissing exceptions, redefining terms, altering standards of evidence, questioning a critic's motives, or introducing auxiliary explanations whose real function is to prevent the original account from being tested. A model becomes intellectually responsible only when it permits reality to count against it.

That sentence sounds obvious, but much depends on it. Inquiry requires more than the availability of evidence; it requires a willingness to let evidence exercise normative force. Reality must be granted the authority to expose not only that our expectations have failed, but that our descriptions must change.

The third partner

This is why inquiry always includes what might be called a third partner. There is the knowing subject, with a history, language, community, and set of intellectual practices. There is the theory, model, or interpretation through which the subject seeks understanding. And there is the reality the model intends to disclose.

This third partner cannot be absorbed into either of the others. It is not merely a projection of the knowing subject, because it continually resists what the subject would prefer to find. Nor is it identical with the model, since competing models may address the same reality, and every model remains open to correction by what it fails to preserve.

Once this third partner disappears, inquiry changes character. Disagreement becomes a contest between perspectives rather than a shared attempt to understand something that exceeds them both. Theories are assessed by the identities they sustain, the interests they serve, or the effects they produce, and questions of truth are gradually redescribed as questions of power, coherence, usefulness, or social location. These considerations are not illegitimate—intellectual practices do involve power, interpretations do arise from particular social locations, theories do have consequences—but none of them explains why an account of power, location, or consequence should itself be accepted as more adequate than its alternatives. Even the critique of truth must present itself as a truthful critique.

This inescapability suggests that correction belongs more deeply to inquiry than any particular theory of knowledge does. Before we decide whether we are realists, idealists, pragmatists, or constructivists, we have already distinguished claims that illuminate reality from claims that obscure it, and assumed that inquiry can disclose why one judgment should replace another. The phenomenon is familiar enough that we scarcely notice it: a physician changes a diagnosis because the patient's condition does not fit the original account; a mechanic abandons one explanation of an engine failure because the parts do not behave as predicted; a child revises an assumption about another person because that person's actions keep contradicting it. In each case, understanding advances when the object is permitted to instruct the one seeking to understand it.

This instruction need not arrive as a complete answer. Reality seldom interprets itself in finished form; it confronts us through anomalies, contradictions, absences, patterns, and unexpected relations. We must still reason, imagine, compare, and construct. Correction does not eliminate the active work of the knower—it places that work under judgment.

Creativity and humility

Genuine inquiry therefore requires both creativity and humility. Creativity, because reality does not hand us ready-made conceptual schemes; we must devise models capable of rendering its order intelligible. Humility, because no model can claim immunity from the reality it seeks to understand. The deepest intellectual failure occurs when creativity is preserved but humility is lost—when inquiry becomes the art of producing ever more sophisticated constructions without allowing anything outside those constructions to judge them. The result may be ingenious, influential, even institutionally successful. It will not be understanding.

What correction requires of reality

The claim that reality corrects us goes beyond asserting that a world exists independently of human thought. A merely independent reality could remain mute, chaotic, or wholly unintelligible; it might resist our actions without providing any basis for distinguishing a better description from a worse one. Correction requires more than independence. It requires order.

Reality must possess determinate features and relations that our descriptions can preserve or distort. It must be stable enough that inquiry can discover patterns, rich enough that our first descriptions remain incomplete, and intelligible enough that failure can become the occasion for improved understanding. The normativity of inquiry is not imposed on reality from outside; it arises within the encounter between finite understanding and an order that exceeds it. We discover that we ought to revise our judgments because reality has shown them to be inadequate.

None of this makes correction final. Later inquiry may expose weaknesses in what presently appears to be the better account, and reality does not speak unambiguously—evidence must be interpreted, and reasonable people may disagree about what a given anomaly requires. But fallibility does not abolish correction; it makes correction necessary. The possibility of error presupposes a difference between what we believe and what is the case. The possibility of learning presupposes that this difference need not remain permanent. Inquiry inhabits the space between them—the space in which reality can unsettle our judgments and call forth more adequate ones.

Toward the next question

We can now state the advance beyond the previous essay. Reality has the first word because inquiry begins in response to what confronts us. But that first word is not merely the brute announcement of presence—it is also a claim upon our understanding. Reality does not merely say, "I am here." It says, "You have not yet understood me."

That claim gives inquiry its peculiar dignity. Human beings do not merely adjust themselves to their environments; they seek to become answerable to what is real. They recognize, however imperfectly, that an inadequate description ought to be revised, and that understanding bears responsibilities not exhausted by usefulness or success.

The question that now emerges is deeper still. Norms such as truth, adequacy, and explanatory superiority are not objects situated alongside other objects. We do not observe adequacy as we observe a tree, a molecule, or a distant planet. Yet without such norms, no observation becomes evidence and no theory becomes corrigible. What kind of reality can call forth not merely causal reactions but responsible judgments? What must the world be like if it not only resists our constructions but teaches us how those constructions have failed?

Reality has the first word. We must now ask how that word becomes intelligible as correction.

How can God be Present without Ceasing to Be God?

This essay is part of an ongoing series from the Department of Philosophical Theology at Christ School of Theology. The series asks how Christian faith can speak truthfully of God’s presence in the finite, ordinary, and everyday without reducing God to one more feature of the world or removing God into a distance where presence becomes only metaphor. At stake is a basic theological question: how can God be truly present to creatures without ceasing to be the living God who is not contained by what God creates?

One of the unexpected privileges of growing older as a scholar is discovering that a question asked many years earlier was perhaps better than the answer one was then able to give. In 1993, at the American Academy of Religion meetings in St. Paul, I presented a paper on the Lutheran understanding of theosis. The paper arose within the context of the growing interest in the Finnish interpretation of Luther and its insistence that justification involves not merely the imputation of Christ’s righteousness but the real presence of Christ in faith. I recognized at the time that the historical question—whether Luther could speak of deification—could not finally be separated from a philosophical one. What must reality be like if Christ is genuinely present in the believer and the believer thereby participates in the divine life without ceasing to be a creature?

More than thirty years later, I have come to think that the question posed there was substantially correct, even though the conceptual resources available to me were not yet sufficient for answering it. The issue was never simply whether Luther used the language of deification, nor even whether the Finnish interpretation had properly reconstructed the relevant texts. The more fundamental difficulty concerned the ontological structure of divine presence. If the believer participates in the divine essence itself, the distinction between Creator and creature appears endangered. If, on the other hand, participation is restricted to divine effects or energies understood as something less than God’s own presence, it becomes difficult to see how the resulting account constitutes genuine deification. The problem is to affirm a divine presence strong enough to transform the believer without construing that presence in such a way that the believer becomes an instance or portion of deity.

Said of and Present in

The distinction that first allowed me to formulate the problem came from Aristotle’s Categories. Aristotle distinguishes between what is “said of” a subject and what is “present in” a subject. When human being is said of Socrates, Socrates is identified as an instance of humanity. The name and definition of the universal apply to the particular: Socrates is a human being, and what it is to be human applies to him. When whiteness is present in Socrates, however, the relation is different. Socrates is not an instance of whiteness in the same sense in which he is an instance of humanity. Whiteness inheres in him as a property or accident inheres in a substance.

This distinction has immediate theological importance. If God were “said of” the believer in the Aristotelian sense, then the believer would fall under divinity as Socrates falls under humanity. The believer would become a specimen of God, a token of the divine type. Whatever theosis means, it cannot mean this without surrendering the distinction between Creator and creature. The believer does not become a finite instance of a universal deity, nor does salvation elevate the creature into membership within the divine species.

The biblical language of indwelling points instead toward the “present in” relation. Paul does not ordinarily say that the believer becomes an instance of divinity. He says that Christ lives in the believer, that the Spirit dwells in us, and that those who are in Christ have become new creations. The governing structure is not classification but presence. God is not said of the believer as humanity is said of Socrates, bur rather God is present in the believer as that which gives the believer a new life. This is why the language of indwelling is theologically more basic than the language of participation whenever participation is construed as a particular’s falling under a universal.

Yet the analogy with Aristotelian inherence produces its own difficulty. An ordinary accident depends upon the substance in which it inheres. Socrates’ particular whiteness is present in Socrates and cannot continue to exist once Socrates no longer exists. The substance is the locus of the accident, but it is also the ontological ground upon which the accident depends. God’s presence in the believer cannot possess this structure. God is genuinely present in the believer, but God does not depend upon the believer for being. Indeed, the dependence runs in precisely the opposite direction: the believer depends upon the divine presence for the believer’s new mode of existence.

The Inversion of Inherence

This is what I have come to call the inherence inversion problem. The theological case preserves the location characteristic of inherence while reversing its ordinary direction of dependence. God’s presence is located in the believer, but it is not grounded in the believer. Moreover, the believer does not possess God in the way Socrates possesses his whiteness. Divine presence cannot become one more property belonging naturally to a human substance, something accumulated, controlled, or held as the believer’s own. The believer is the locus of the presence but not its owner and certainly not its source. 

I remember speaking about this during a short presentation at the International Luther Congress in Minneapolis in August of 1993. I told the room that this was a problem, and that we were dealing with a theological accident which allows the believer to be the believer that he is apart from the accident -- this is necessary, I said, to avoid collapsing the creature into the Creator -- while nonetheless not depending upon the believer for its being. Far from being simply an aspect of the believer, divine presence transcends the being of the believer, I averred, but cautioned that such a way of being seemed impossible on strictly philosophical grounds. 

The 1996 continuation of the argument approached this problem by examining seven models of the unity between Christ and the believer. In "The Ontology of Deification" written for the Mannermaa Festschrift published the next year, I concluded that the traditional language of the Mystical Personal Union, understood through the category of perichoresis, provided the least inadequate account. The union had to be stronger than juxtaposition or moral association but weaker than merger or identity. Christ could not remain merely external to the believer, since the language of indwelling and transformation would then lose its force. Yet neither could Christ and the believer collapse into one substance or one person, since the difference between Christ and the Christian must remain.

The difficulty was that perichoresis named the required relation without explaining its metaphysical structure. To say that two realities mutually indwell one another is to identify the phenomenon in need of explanation, not yet to provide the explanation. The final footnote of the 1996 paper gestured toward the idea of the “theological accident" I had spoken about at the Luther Congress, but the concept remained undeveloped. I knew that the divine presence must somehow be genuinely present in the believer while not depending upon the believer, but I still did not yet possess a philosophical account capable of holding these affirmations together.

The conceptual resources needed for such an account emerged only gradually through work on questions that initially appeared quite different: Luther’s Christology, trope theory, divine agency, Davidson’s anomalous monism, metaphysical grounding, model-theoretic semantics, and, more recently, constitutive divine causality. Over time it became clear that these investigations shared a common structural question. How can one reality be genuinely present within another without either becoming identical with it or remaining merely externally related to it? The question arises in the union of divine and human natures in Christ, in sacramental presence, in the relation between divine and creaturely agency, and in the indwelling of Christ within the believer. These are not identical theological problems, but they exhibit a common metaphysical form.

Location and Grounding

The distinction that now seems decisive is the distinction between location and grounding. In ordinary cases of inherence, these relations coincide. Socrates’ particular whiteness is located in Socrates and grounded in Socrates. It belongs to the concrete whole that Socrates is and perishes with the dissolution of that whole. The substance is therefore both the locus of the property-instance and the ontological ground upon which it depends. The theological problem arises because divine presence seems to preserve the first relation while reversing the second. God is genuinely present in the believer, but God cannot be grounded in the believer.

A conceptual resource for understanding this structure appears in Edmund Husserl’s account of Fundierung in the Third of his Logical Investigations. Husserl distinguishes relatively independent parts from non-independent parts, or moments. A piece can, at least in principle, be separated from the larger whole of which it is presently a part and continue to exist independently. A moment, by contrast, is what it is only within a more comprehensive whole or in conjunction with other moments. Color, for example, cannot occur except as extended, while sensibly presented extension cannot occur without some qualitative determination. Such moments are not externally connected items accidentally placed beside one another. Their identities include relations of essential dependence.

Husserl’s analysis is particularly helpful because foundation need not possess only one form. Some relations of Fundierung are reciprocal: each moment requires the other if it is to be the kind of moment that it is. Others are one-sided: one reality requires another, although the latter does not correspondingly require the former. Foundation may also be immediate or mediated through more comprehensive relations among moments and wholes. Husserl thereby provides a vocabulary for articulating ontological dependence without reducing it either to efficient causation or to logical implication. To say that one reality is founded upon another is to say that the first cannot be what it is apart from the second, not necessarily that the second caused it at some earlier moment.

This distinction allows the structure of divine indwelling to be stated more carefully. God does not depend upon the believer or upon the union between God and the believer in order to be God. The relation of indwelling, however, cannot be this particular relation apart from both God who is present and the believer in whom God is present. The relation is founded upon its relata without thereby making those relata reciprocally dependent in their being. The believer’s renewed life exhibits a still clearer asymmetry: it is founded upon the divine presence, while God’s being and power are not founded upon the believer’s natural capacities. The believer requires the divine presence for the believer’s new life; God does not require the believer in order to be God.

Husserl therefore clarifies the structure of dependence involved, but his account does not by itself settle the question of ontological source. His principal concern is with the relations among parts, moments, and wholes, rather than with the ultimate ground in virtue of which a particular reality obtains. During the past three decades, contemporary analytic metaphysics has developed a more explicit account of grounding as a primitive relation of ontological dependence. Associated especially with the work of Kit Fine, Gideon Rosen, Jonathan Schaffer, and others, grounding seeks to answer a question distinct from those of causation or logical implication. One thing may obtain because of, in virtue of, or on the basis of another without standing to it either as a causal effect or as a logical consequence. Grounding thus articulates relations of explanatory priority within reality itself. It asks not merely what caused something to occur or what propositions entail it, but what features of reality make it the case that it exists or obtains at all.

Husserl supplies the architecture of dependence; contemporary grounding theory helps identify its direction and ultimate source. Once grounding is distinguished from both causation and location, there is no obvious reason why every property-instance must be located in the same substance in which it is ontologically grounded. The possibility immediately arises that a property-instance might be located in one substance while remaining grounded in another. It is precisely this possibility that proves decisive for the theological problem before us.

Accordingly, I now call a property-instance whose location and grounding belong to different substances an ectopic trope. The adjective ectopic is borrowed from medicine, where it identifies something situated outside its ordinary or expected location. Only the structural feature is intended here. An ectopic trope is present in one substance while grounded in another. Its locus and its ontological home do not coincide.

At this point a brief explanation of trope theory is necessary. Over the past half century, a number of philosophers have proposed that the basic constituents of reality are not abstract universals but particularized properties, or tropes. Rather than speaking of redness as a universal instantiated in many objects, trope theory speaks of this particular redness of this rose and that particular redness of that fire truck—numerically distinct property-instances that resemble one another without being identical. Individual substances are then understood as structured bundles of such particularized properties. Whether or not one accepts trope theory as a complete ontology is not important for the present argument. What matters is that it provides a natural way of speaking about particular instances of properties or presences without treating them either as abstract universals or as independent substances. The divine presence in the believer is not God’s essence abstractly considered, nor is it another substance alongside the believer. It is, rather, a particular presence of God in this believer at this time. Trope theory supplies an ontological vocabulary for describing such particularized presences.

The particular presence of God in the believer can thus be understood as genuinely located in the believer, so that the language of indwelling need not be reduced to metaphor or to the extrinsic attribution of a new status, while the presence remains ontologically grounded in God. It exists and acts in virtue of God’s being and giving, not in virtue of the believer’s natural capacities. The believer is accordingly the site of a divine presence whose source remains beyond the believer. God’s presence conditions and transforms the believer without becoming dependent upon the believer or reducible to one of the believer’s naturally possessed properties.

This account gives philosophical content to the claim that divine-human union is stronger than mingling but weaker than merger. It is stronger than mingling because the divine presence is not merely adjacent to the believer or externally related to the believer. It is genuinely present within the believer and constitutive of the believer’s new life. It is weaker than merger because the location of the presence does not become its ground. God and the believer remain ontologically distinct even within their union. The finite does not become infinite, nor is the infinite diminished through its presence in the finite. Rather, to borrow Luther’s own language, the infinite is truly in, under, around, and beyond the finite. Finitum capax infiniti: the finite is capable of bearing the infinite precisely because the infinite can be genuinely present within it without ceasing to be infinite.

The formula that emerged from the earlier work can now be stated more precisely: God became a human being while remaining God so that a human being might become God while remaining human. The “while remaining” clauses are not pious qualifications attached after the fact; they identify the ontological structure that any adequate account must preserve. The believer remains human because the believer remains a distinct creaturely substance. God remains God because the divine presence continues to be grounded in God even when genuinely located within the believer.

Christ Lives in Me

Galatians 2:20 provides the paradigmatic expression of this structure: “It is no longer I who live, but Christ who lives in me; and the life I now live in the flesh I live by faith in the Son of God.” The verse neither eliminates the human subject nor leaves that subject unchanged. Paul continues to speak of the life that “I now live in the flesh,” but this continuing human life has received a new ground: “Christ lives in me.” The believer remains the subject who lives, believes, acts, suffers, and hopes; yet the believer no longer understands this life as grounded autonomously in the self.

The non ego, sed Christus is therefore not the destruction of the human “I” but the displacement of its claim to self-grounding. Christ is present in the believer in such a way that the believer’s life becomes genuinely new, while the believer continues to live as a finite human being. The divine presence is not possessed as an achievement or a stable spiritual acquisition. It is received and lived by faith. The believer is constituted by what the believer did not make and cannot own.

Whether the language of the ectopic trope will finally prove adequate remains an open question. Philosophical concepts do not master the realities to which theological language refers, and the success of a model must never be confused with the truth of the reality modeled. Yet theology cannot responsibly affirm that God is genuinely present in the believer while refusing every question about what such presence might mean. The first task of philosophical theology is not to replace confession with metaphysics, but to ask what must be true of reality if the confession itself is true.

The question that first appeared in 1993 was therefore not merely a question about the interpretation of Luther or the historical legitimacy of speaking about theosis. It was a question about the ontology of divine presence. How can the infinite be genuinely present in the finite without absorbing it? How can the finite be transformed by the infinite without becoming infinite? The distinction between location and grounding may offer the beginning of an answer. The believer becomes the home of what the believer does not own, the locus of a presence whose source infinitely exceeds its location. Perhaps this is what it means to say that Christ lives in us while we continue to live our lives in the flesh by faith in the Son of God.