Hans Halvorson Physics, Logic, Philosophy

Alumni Lecture 2026

Princeton Alumni Lecture, 2026


The Question

Science and religion are often portrayed as being at war with each other — two rival authorities issuing incompatible verdicts on the deepest questions. But is the conflict real? And if so, what exactly are they fighting about?

This lecture takes a stance: the tension between science and religion is genuine, philosophically serious, and not easily dissolved — but it is also widely misunderstood. The real conflict is not primarily about particular facts (did the universe begin? did species evolve?) but about who has the authority to settle questions, and what counts as a legitimate answer.

One popular way to dissolve the tension is Stephen Jay Gould’s doctrine of Non-Overlapping Magisteria (NOMA): science covers the empirical realm of fact and theory, religion covers questions of ultimate meaning and moral value, and the two need never collide. It is a tidy solution — and, I will argue, ultimately an evasion. The magisteria overlap constantly, and any serious engagement with both science and religion has to reckon with that.


Where Science and Religion Seem to Conflict

Some of the sharpest pressure points:

Darwinian evolution. Natural selection produces the appearance of design without a designer. If the diversity and complexity of life are fully explicable by mindless variation and selection, what work is left for a Creator to do — and what becomes of the idea that human beings occupy a special place in the order of things?

The determinism of physical law. If the state of the universe at any moment is fixed by the laws of physics operating on prior states, there seems to be no room for divine intervention, answered prayer, or even human free will. The universe runs like clockwork — or like a quantum probability distribution — with no gaps for agency to enter.

Miracles. A miracle is precisely a claim that the normal causal order has been suspended or overridden by divine action. This puts miracles in direct tension with the scientific picture of a universe governed by exceptionless natural laws. Hume’s argument — that no testimony could ever make it more probable that a miracle occurred than that the testimony was mistaken — sharpens the conflict: the very regularity that makes science possible seems to make miracles antecedently incredible. More fundamentally, miracle-claims appear to make empirical assertions, which puts them squarely within science’s domain and threatens to undermine any clean separation of the two magisteria.

Relativity and the nature of time. Einstein’s special relativity suggests that the universe is a four-dimensional block in which past, present, and future all equally exist. There is no objective “now,” no moment of creation that is specially present, no unfolding story with a beginning and an end. This sits uneasily with religious narratives built around creation, providence, and eschatology.

The scale and indifference of the cosmos. The observable universe is 93 billion light-years across and 13.8 billion years old. Homo sapiens has existed for roughly 0.02% of that time, on a planet orbiting an ordinary star in an unremarkable galaxy. The sheer scale makes it difficult to sustain the idea that the cosmos was made for us — or that its author is particularly interested in us.

The neuroscience of religious experience. Mystical experiences, feelings of divine presence, and near-death visions correlate with identifiable neural states and can be induced chemically. Does this debunk them — or merely describe the mechanism through which something real is perceived?

The multiverse. Some physicists argue that our universe is one of countlessly many, each with different physical constants. If so, it is no surprise that we find ourselves in a universe fine-tuned for life — we couldn’t find ourselves anywhere else. This undercuts one of the most sophisticated contemporary arguments for God’s existence: the fine-tuning argument. If there is no need for a designer to explain why the constants are life-permitting, a major bridge between science and theism collapses.

Moral psychology. Evolutionary game theory and experimental psychology explain many of our deepest moral intuitions — altruism, fairness, in-group loyalty, disgust — as adaptations selected for their fitness benefits rather than their truth-tracking properties. If our sense of right and wrong is a product of natural selection rather than moral perception, it is hard to maintain that morality is objectively grounded in a divine order. The authority of conscience begins to look like the authority of evolution.


Three Ways of Responding

Faced with these pressure points, there are essentially three philosophical responses — and all three are represented by serious contemporary thinkers, including two at Princeton.

The separationist response holds that science and religion are simply not in competition, because they represent fundamentally different kinds of human orientation toward the world. On this view, the conflict dissolves once we stop mistaking religion for a rival empirical theory. The most sophisticated recent version is Bas van Fraassen’s The Empirical Stance (2002), which argues that science and religion are best understood not as competing bodies of doctrine but as different stances — structured ways of engaging with experience. A stance is not the kind of thing that can be refuted by evidence, so there is no genuine collision. This is the contemporary descendant of Kierkegaard’s and Nielsen’s double-truth position — and it faces the same fundamental objection: if religious commitments have no empirical content whatsoever, it is hard to see what makes them religious rather than merely aesthetic.

The demythologization response accepts that traditional supernatural religion is indeed in conflict with science — and resolves the tension by reinterpreting religion rather than abandoning it. The move goes back at least to Feuerbach, who argued that theology is really anthropology in disguise: what we project onto God is the idealized essence of humanity itself. Bultmann carried the same impulse into 20th-century Protestant theology, arguing that the mythological framework of the New Testament — miracles, resurrection, apocalypse — must be demythologized and reread as an existential call to authentic self-understanding. The most philosophically rigorous recent version is Mark Johnston’s Saving God (2009), which argues that the personal, interventionist God of orthodox theism is not merely scientifically untenable but theologically confused — a form of idolatry that mistakes the divine for a very large human being. Johnston proposes rescuing what is essential in religion by identifying the sacred with the structure of existence itself: “the Highest One” as the self-outpouring of being rather than a supernatural agent. The result is religion without miracles, providence, or answered prayer — religion, one might say, without the parts that conflict with science. Whether what remains deserves the name is precisely what is at issue. (How close this tradition comes to the position of Brøchner — who also sought a “religiously reconciled humane consciousness” beyond both orthodoxy and atheism — is a question the lecture leaves open.)

The conflict-denial response argues that the apparent conflict between science and religion is an illusion generated by a misreading of both — and that when each is properly understood, they are not merely compatible but mutually supporting. Alvin Plantinga’s Where the Conflict Really Lies (2011) presses this case with full philosophical force. The real conflict, Plantinga argues, is not between science and religion but between science and naturalism: a commitment to evolution plus the denial of any guiding intelligence is self-undermining, because evolution selects for fitness rather than truth, giving us no reason to trust the cognitive faculties on which science itself depends. Theism, by contrast, provides exactly the metaphysical underwriting that science requires. On this view, religion does not merely coexist with science — it rescues it.

Each of these responses has genuine philosophical force. The lecture argues that none is fully adequate — and that the 19th-century Danish debate remains the sharpest place to see why.


A 19th-Century Test Case: Denmark in the 1860s

These questions are not new. A remarkably sharp version of the same debate erupted in Copenhagen in the 1860s, and the arguments made then remain among the clearest on record.

The story begins with Søren Kierkegaard, whose Concluding Unscientific Postscript (1846) argued that faith and objective knowledge are not merely different but categorically incommensurable — uensartede Størrelser, heterogeneous quantities that cannot be measured on the same scale. Faith is a subjective, existential commitment; science deals in objective, publicly verifiable results. They belong to different registers of human existence entirely.

Rasmus Nielsen (1809–1884), professor of philosophy at the University of Copenhagen, took Kierkegaard’s insight and tried to turn it into a systematic philosophical position: faith and scientific reason occupy completely separate, incommensurable domains — a “double-truth” position meant to let both science and Christianity flourish without interference. His critics — above all the Hegelian philosopher Hans Brøchner (1820–1875) and the cultural critic Georg Brandes (1842–1927) — argued that the separation was philosophically incoherent and morally dangerous.

The debate was triggered by Darwin’s reception in Denmark and set the stage for the Sædelighedsfejde (the 1880s controversy over sexual morality). The underlying question is perennial: who — or what — writes the moral and epistemic rules? God, or nature and reason?

The most important figure for assessing the debate is one who lived through it from the inside — who initially took a side, was publicly converted to the opposite position, and spent the next three decades working out what the conversion implied. Harald Høffding (1843–1931) is that figure.

Phase One: Nielsen and Kierkegaard (1865–1867)

Høffding came of age in the crucible of the controversy. A student of both Nielsen and Brøchner at the University of Copenhagen, he had prepared for the ministry and undergone a spiritual crisis in his student years — a crisis precipitated not by science but by Kierkegaard. Reading the Concluding Unscientific Postscript and the Journals, Høffding became convinced that Kierkegaard was right: the original demands of Christianity — absolute self-renunciation, total existential commitment, willingness to suspend the ethical itself on the authority of revelation — are categorically incompatible with life in the modern world of family, state, art, and science. The church had betrayed Christianity by making it comfortable. If one was honest, one had to admit the incompatibility and choose. Høffding chose the world — and abandoned his plans for ordination.

But he did not, at first, follow Brandes and the naturalists in concluding that religion itself must be given up. Instead he was drawn to Nielsen’s position, which seemed to offer a principled way to honor both his scientific conscience and his residual sense that religion expressed something permanently important about human existence. Nielsen’s double-truth — faith and knowledge are heterogeneous quantities, incommensurable by design — promised to give science complete authority over the empirical domain while preserving religion from its jurisdiction.

In 1866, aged 23, Høffding published his first book: Philosophie og Theologie: en historisk-kritisk Afhandling (Philosophy and Theology: A Historical-Critical Treatise). He signed it Cand. theol. The book is a comprehensive survey of the science–religion controversy from medieval scholasticism through the present day — covering the duae veritates evasion of the late scholastics, Hegel’s attempted synthesis, the left-Hegelian critique of Strauss and Feuerbach, Kierkegaard’s radical separation, Nielsen’s appropriation of Kierkegaard, and Brøchner’s nascent objections. And he concluded, explicitly, in Nielsen’s favor. The double-truth position was, he argued, the only tenable outcome of the entire historical development: faith and scientific reason are categorically incommensurable, and any attempt to force them into dialogue results in either making theology a pseudo-science (Martensen’s error) or reducing Christianity to a naturalism that is no longer Christian (Strauss’s and Feuerbach’s error).

Phase Two: Brøchner’s Critique and the Conversion (1867)

Within a year of publication, Høffding had changed his mind. In a letter to his fiancée dated November 1867 — just twelve months after the book appeared — he wrote that he could “no longer agree with Rasmus Nielsen.” What had happened was Brøchner.

Brøchner’s argument against Nielsen, developed in his lectures at Copenhagen and eventually published as Problemet om Tro og Viden (1868), drove home a point that Høffding could not answer. The double-truth position, Brøchner argued, is not a stable philosophical standing but a concealed contradiction. When faith makes claims — about God’s existence, about miracles, about resurrection — it uses the same concepts of existence, causation, and event that reason uses. It cannot both employ those concepts and declare itself immune from the norms that govern their use. The attempt to seal faith off from rational scrutiny does not protect religion; it evacuates it of content. A faith that cannot say anything that could in principle be challenged by reason has nothing to say.

Moreover — and this was the point that struck Høffding most directly — Nielsen’s double-truth required an intellectually dishonest compartmentalization that corroded the integrity of the individual who adopted it. One could not simultaneously be a person of rigorous scientific conscience and hold religious beliefs in a hermetically sealed compartment labelled “not subject to the same conscience.” Kierkegaard himself had seen this, and had demanded radical honesty: choose. Nielsen’s synthesis was not a resolution but an evasion — worse, a comfortable evasion that prevented the honest reckoning Kierkegaard demanded.

Høffding accepted this critique completely. He wrote in the same 1867 letter that “Christianity will — of this I am fully convinced — always be for me the highest truth.” But that conviction did not survive long. What Brøchner’s critique had done was close off the comfortable middle ground; it forced Høffding to confront whether the religious significance he still felt could be given a philosophically honest account — or whether it had to be abandoned.

Phase Three: Positivism and the Problem of Religion (1868–1882)

On Brøchner’s advice, Høffding went to Paris in 1868–69, where he encountered Comte’s positivism, Spencer’s evolutionary philosophy, and Taine’s naturalism. These were the intellectual resources of the Moderne Gennembrud — the cultural movement Brandes would launch in 1871. Høffding became Denmark’s main philosophical interpreter of this tradition, publishing Filosofien i Tyskland efter Hegel (1872) and Den engelske Filosofi i vor Tid (1874).

This positivist period pulled Høffding in two directions at once. On one hand, it confirmed Brøchner’s central argument: religion could not be kept insulated from the empirical demands of the scientific spirit. On the other hand, the purely naturalist resolution — Feuerbach’s reduction of theology to anthropology, Comte’s replacement of religion with the Religion of Humanity — left something undone. Brøchner himself, who died in 1875, had never produced the positive philosophy of religion he had promised; his critique of Nielsen was decisive, but his own alternative — a Hegelian notion of religion as “the religious in its unity with the human” — was more programmatic than substantive. And the positivist alternatives seemed to Høffding to dissolve religion rather than account for it. Feuerbach’s “what theology projects onto God is really humanity idealized” is a genealogical explanation of religion, not a philosophical assessment of its validity. The positivist who says “religion is nothing but consolation for social suffering” may be correct, but has not addressed whether the religious impulse points toward something real.

The tension crystallized in the lecture Høffding gave at the inaugural meeting of the new Studentersamfund in 1882: “Realisme i Videnskab og Tro” — “Realism in Science and Faith.” This was his first public statement of the mature position he had been working toward. Against both the separationists and the reductionists, Høffding argued for a realism in religion: the religious question is a genuine question about reality, not a pseudo-question to be dismissed or a merely existential commitment to be protected from scrutiny. But a realist approach to religion, combined with scientific integrity, requires taking seriously both the evidence and the limits of evidence.

Phase Four: The Religionsfilosofi (1885–1901)

The essays collected in Mindre Arbejder (1899) trace Høffding’s development across this period. “Forholdet mellem Tro og Viden i dets historiske Udvikling” (1885) returns directly to the historical survey he had made in 1866 — but now reaches a sharper conclusion. The lesson of history is not Nielsen’s double-truth but something more unsettling: “the riddle of the world is equally great for faith and for science.” Neither science nor religion can claim to have resolved the fundamental questions about existence, causality, and value. This is not a concession to religion; it is an insistence that science, honestly pursued, reveals its own limits. We cannot ultimately understand why the law of causality holds, why there is something rather than nothing, or what gives value its claim on us. Religion, rightly understood, lives in that space — not as a rival explanation, but as an orientation toward the inexplicable that sustains rather than blocks inquiry.

The Religionsfilosofi (1901; 2nd ed. 1906) is the systematic statement of this position. Its epigraph — Alte dubitat, qui altius credit, “he doubts more deeply who believes more deeply” — announces the dialectical character of the entire enterprise. The book is organized around three questions: the epistemological (can religious beliefs be rationally grounded?), the psychological (what is the phenomenology of religious experience?), and the ethical (what does religion contribute to a fully human life?).

Høffding’s answer to the epistemological question preserves the core of Brøchner’s critique: religious claims cannot be insulated from rational scrutiny, and traditional dogmas — creation ex nihilo, the personal God who intervenes in history, bodily resurrection — cannot survive scientific and philosophical examination in their literal form. But his answer does not stop there. He argues that the essential content of religion is not its doctrinal shell but the attitude it expresses and sustains toward existence: the conviction that value is not negated by the scientific picture of the world, that what is highest in human experience does not disappear into physical process. This is the sætningen om værdiens bestaaen — the persistence of value — which Høffding takes to be the proposition that every religion, in its own idiom, is trying to assert.

The sætningen is not itself a scientific claim, but neither is it protected from rational scrutiny in Nielsen’s fashion. It is a hypothesis — Høffding uses this word deliberately, following the positivist vocabulary — that can be assessed against experience but never definitively confirmed or refuted. It is the religious equivalent of the working assumptions a scientist must make in order to do science at all: unprovable, but not arbitrary. Høffding’s reading of the Stoics (in “Hedenske Sandhedssøgere,” 1892) is part of this argument: figures like Epictetus and Marcus Aurelius reached genuine religious depth without any dependence on Christian doctrine, which suggests that the underlying impulse is universal and not tied to a particular revelation.

What Høffding Inherits from Brøchner — and What He Adds

The relationship between Høffding and Brøchner is not merely one of intellectual influence. It was a personal conversion: Brøchner’s critique destroyed the Nielsen position Høffding had publicly defended, and forced him to find a different answer to the same problem. Brøchner gave Høffding the negative result — Nielsen’s double-truth is philosophically incoherent — but not the positive one. What Høffding adds is the sustained attempt to articulate what religion is for once the separationist shelter has been demolished.

Brøchner’s own positive account — religion as “the religious in its unity with the human,” a Hegelian synthesis that had dissolved the supernatural into the immanent — gestures toward demythologization without completing it. Høffding’s contribution is to ask the further question: if we strip away the doctrinal shell and the supernatural claims, what remains, and is it enough to justify calling the residue religion rather than simply ethics or aesthetics? His answer — that what remains is the specifically religious conviction that value persists in the face of the natural order’s apparent indifference to it — is philosophically richer than anything Brøchner left behind.

Whether it is rich enough to answer the charge that it is just another version of the NOMA evasion — whether “value persists” is a substantive claim or a comforting gesture — is the question the lecture raises but does not presume to settle. What is clear is that Høffding understood the difficulty more deeply than almost anyone before him: he had lived through the dialectic from inside, had been wrong once in a published book, and had spent thirty years working out what it meant to be right.


Primary Sources in Translation

The following texts are provided in new English translations from the Danish originals.

Hans Brøchner

Problemet om Tro og Viden (1868) The Problem of Faith and Knowledge: A Historical-Critical Treatise. Brøchner’s major critique of Nielsen’s double-truth position, originally delivered as lectures at the University of Copenhagen in the autumn of 1867.

(Further chapters forthcoming.)

Om det Religiøse i dets Enhed med det Humane (1869) On the Religious in its Unity with the Human. The constructive “positive supplement” to the 1868 critique, in which Brøchner develops his own Hegelian alternative.

(Translations forthcoming.)

Rasmus Nielsen

Om det oprindelige Forhold mellem Religion og Videnskab (1881) On the Original Relationship between Religion and Science. Delivered as a university festival address at the University of Copenhagen, 8 April 1881. Nielsen’s most direct and systematic treatment of the faith–science relationship, written at the height of his influence. The central argument is that revelation-faith is essentially miracle-faith, and that miracles, as objects of faith, are constitutively inaccessible to scientific cognition — placing the two domains in principled, irresolvable separation.

(Further sections forthcoming.)

Georg Brandes

(Translations forthcoming)


Background Reading

Høffding: Primary Sources

  • Harald Høffding, Philosophie og Theologie: en historisk-kritisk Afhandling (1866) — Høffding’s first book, written aged 23 as Cand. theol. A comprehensive survey of the philosophy–theology controversy from medieval scholasticism through the present day, concluding — explicitly — in Nielsen’s favor. The starting point for tracing his intellectual development.

  • Harald Høffding, Mindre Arbejder (1899) — collected essays from 1882–1898, assembled by Høffding himself as preparation for the Religionsfilosofi. The most directly relevant pieces are: “Realisme i Videnskab og Tro” (1882), his inaugural statement of the mature position; and “Forholdet mellem Tro og Viden i dets historiske Udvikling” (1885), which revisits the 1866 survey with the sharper conclusion that “the riddle of the world is equally great for faith and for science.” Full text available on Wikisource.

  • Harald Høffding, Religionsfilosofi (1901; 2nd ed. 1906) — the systematic culmination of three decades of thought. The key sections for the lecture are the epistemological chapters on the sætningen om værdiens bestaaen (the persistence of value) and the psychological chapters on religious experience. Translated into English as The Philosophy of Religion (1906).

  • Harald Høffding, Erindringer (1928) — memoir written in his eighties; invaluable for his account of the Kierkegaard crisis, his relationship with Brøchner, and the atmosphere of the 1860s controversy.

On the Danish Debate

  • Carl Henrik Koch, Den danske idealisme 1800–1880 (2004) — the standard scholarly treatment of the Nielsen–Brøchner controversy and its intellectual context.

  • Niels Henrik Gregersen & Peter Kjaergaard, eds., Darwin og den danske debat (2010) — the Danish reception of Darwin, including its intersection with the faith-and-knowledge controversy.


Notes on the Translations

The translations are made from OCR transcriptions of the original printed editions, digitized by the Royal Danish Library (kb.dk). The originals are in the public domain. The long-s (ſ) convention of 19th-century Danish typography has been normalized to s throughout. Translations aim to be accurate and readable rather than literal; Brøchner’s Hegelian terminology is glossed on first occurrence.


Page maintained by Hans Halvorson. Corrections and comments welcome.