I Choose, Therefore I Am

Prelude

I make no claim of originality in what follows. Almost every question in this essay is ancient, and most of the individual arguments have recognizable ancestors in philosophy, physics, mathematics, cognitive science, or theology. What frustrates me is not the absence of thought about these questions, but often the language in which the thought is expressed.

Contemporary philosophy frequently strikes me as unnecessarily vague precisely where greater precision has become possible. Questions about reality, causality, time, determinism, information, consciousness, and free will can no longer be discussed responsibly while remaining largely indifferent to quantum mechanics, statistical mechanics, general relativity, computation, information theory, or what we have learned about complex adaptive systems. Hawking and Mlodinow notoriously declared philosophy “dead,” arguing that philosophers had not kept pace with modern science.¹1. The phrase appears in Stephen Hawking and Leonard Mlodinow, The Grand Design (2010). I do not adopt their conclusion. The point here is narrower: many ontological questions change character once modern physics is taken seriously. Physicists themselves have repeatedly criticized Hawking’s dismissal as philosophically self-defeating: the claim that ontology is dispensable is itself a philosophical claim. I do not share the conclusion. I do share part of the irritation behind it.

But there is an equal and opposite failure on the scientific side. Too many scientists implicitly adopt some version of shut up and calculate: construct the model, derive predictions, compare them with experiment, and regard questions about what the mathematical objects might mean as excursions beyond professional competence. Ontology becomes “above our pay grade.” I find that position equally unsatisfactory. The refusal to discuss ontology does not eliminate ontology. It merely leaves implicit ontological assumptions unexamined. To say that the wavefunction is only a calculational device is already a philosophical position. To say that only observables are meaningful is a philosophical position. To say that two mathematically equivalent formulations describe the same reality is a philosophical position. Even the declaration that it is meaningless to ask which representation is “really” true is a claim about what can be known and what should count as real. One cannot escape philosophy by declining to name it.

This essay is an attempt to occupy the uncomfortable territory between the two attitudes. I want to formulate several old ontological questions using as precise a language as I can borrow from contemporary science, and to combine arguments due to others with my own reflections on them. Equations do not magically settle philosophy, but they often expose distinctions that ordinary language lets us conceal.

The central question is free will. More precisely, I am interested in the extraordinary subjective impression that we are agents: several futures appear before us, we deliberate among them, and eventually we choose one. I suspect that this experience is more fundamental to our impression of being a self than cognition alone.

Descartes wrote cogito, ergo sum — I think, therefore I am. I want to replace this, not as a deductive proof but as a phenomenological proposition, by eligo, ergo sum — I choose, therefore I am.

Thoughts arrive uninvited. Perceptions happen to us. Memories surface. Dreams contain cognition. What most forcefully creates the impression of an “I” may be something more structured: alternatives appear as my possible futures; they are evaluated according to my memories, values and goals; one of them becomes my action.

My working hypothesis is that this impression of agency is an emergent physical phenomenon, in something like the sense in which temperature is emergent. No individual molecule possesses the thermodynamic temperature of a gas. Yet temperature is neither fictitious nor dispensable. It is a stable higher-level variable describing a particular organization of microscopic states. Perhaps selfhood, deliberation, choice and subjective openness have a comparable status.

This is also where, for me, the question of god becomes interesting. I deliberately write god with a lower-case letter and refer to it as it. The choice is methodological rather than provocative: I want to remove from the word as much historically accumulated baggage as possible and ask whether there remains an irreducible concept worth examining. ²2. Here god is a deliberately stripped variable rather than shorthand for any particular religion. Institutional authority, ritual, scripture, mythic narrative, moral lawgiving, personality, omnibenevolence, incarnation, revelation, and historical miracles are all factored out unless explicitly reintroduced. The residue under examination is whatever irreducible ontological or causal posit might remain once empirical and sociological layers are removed. This stipulation is intentionally thinner than classical theism, deism, pantheism, or the god of Abrahamic theology; conclusions reached about this minimal posit should therefore not be advertised as refutations of every theological concept bearing the same word. Institutional religion is factored out. As an organized human institution it belongs largely to politics, history, and the study of power. Traditions and rituals are factored out as well; they belong principally to sociology and anthropology and can bind communities or create meaning independently of any supernatural ontology. Mythology is different again. Religious mythology has contributed immeasurably to human culture, as have Homer, Greek mythology, Dante, the Mahabharata, Norse sagas and the tales collected by the Brothers Grimm. Cultural importance, however, does not by itself confer evidential privilege in an ontological argument.

Science has no particular difficulty contradicting empirical claims embedded in mythology when those claims conflict with evidence. A literal young-Earth reading of biblical chronology, for example, places creation only some six thousand years ago. That is not a subtle interpretive dispute with modern science: radiometric dating places the Earth at roughly 4.54 billion years old, while cosmology places the age of the universe at about 13.8 billion years.³3. The young-Earth example illustrates the narrower claim that science can refute empirical claims embedded in mythology. The familiar date 4004 BCE is James Ussher’s seventeenth-century chronology, not a doctrine shared by all Jewish or Christian traditions. The relevant target is the literal young-Earth empirical claim. Radiocarbon dating is limited to roughly $5\times10^4$ years and therefore does not date the Earth or universe; its role here is merely to show that datable organic material already exceeds a six-thousand-year chronology. The Earth’s age, about $4.54\times10^9$ years, comes primarily from U–Pb and related radiometric systems applied to terrestrial minerals, meteorites, and lunar samples; modern cosmology gives an age of about $13.8$ billion years for the universe. See G. B. Dalrymple, The Age of the Earth (1991), and Planck Collaboration VI, Astronomy & Astrophysics 641, A6 (2020). But that is precisely the easy target, and not the god I am interested in. Refuting Genesis as cosmology no more settles the ontological question than refuting Homer's geography would settle the existence of beauty. I want to remove every empirically exposed layer first: miracles offered as physical explanations, creation chronologies, interventions, and the familiar god of epistemic gaps that occupies whatever mechanism we have not yet understood. Lightning, disease, planetary motion and biological complexity have all occupied such gaps. As causal knowledge advances, they contract. This kind of god is reducible: it is a name attached to an unknown mechanism.

The more difficult question begins only after that pruning. Is there an irreducible notion of god left over: one so thin that it does not compete with any empirical theory and perhaps cannot be established or eliminated by theoretical reason at all? Kant is an obvious landmark here.⁴4. Kant is relevant here because he sharply limits what theoretical reason can legitimately claim beyond possible experience. In the Critique of Pure Reason he attacks the traditional ontological, cosmological, and physico-theological proofs and argues that theoretical cognition cannot legitimately extend beyond the conditions of possible experience. He does not infer atheism: in his practical philosophy he later gives god a role within moral or “rational” faith. I use only the critical restriction: if a putative god is defined so as to lie wholly outside possible experience, theoretical reason cannot treat it like an ordinary empirical object. That protects such a notion from straightforward empirical refutation, but at the price of making its epistemic status radically different from a physical hypothesis. See the Stanford Encyclopedia of Philosophy, “Kant’s Philosophy of Religion”, especially the discussion of the Transcendental Dialectic. I do not mean a hidden mechanism that better science might eventually uncover; that would still be an epistemic gap. I mean the minimal residue, if any, that remains once every claim capable of colliding with observation has been factored out.

My tentative thesis is that one of the last serious footholds for faith in such a god lies in agency: the impression that a nonphysical chooser must somehow close the gap between alternatives and action. The essay asks whether that gap survives a sufficiently crisp physical description. If it does not, the irreducible god becomes thinner still; if it does, we should be able to say much more precisely what explanatory work it performs. Consciousness will remain a separate, harder loophole rather than being smuggled into the free-will question.

I should also state my own prejudice before trying to reason past it. I am a convinced atheist. I do not, however, want atheism to function as a premise of this essay or as the conclusion toward which every argument is quietly engineered. Where the evidence or the concepts do not warrant a conclusion, I would rather leave the question open. I will therefore try, as far as I can, to stay above my own conviction and adopt a neutral position—not because I am personally undecided, but because epistemic neutrality is the more honest standard. The relevant question is not what I believe, but what can actually be inferred.

This essay also has a more personal origin. It has been prompted by nearly a decade of conversations with my friend and colleague David Silver, an Orthodox Jew, about agency, determinism, physics and what—after everything contingent, historical and empirically reducible has been stripped away—either of us could still reasonably mean by god. We were looking, in a thermodynamic and information-theoretic sense, for something like a maximum-entropy definition of god: the widest, least constrained notion to which we could both assent. Maximum entropy here does not mean a midpoint between belief and disbelief, nor a Bayesian estimate of which view is more probable. It means imposing only the constraints on which we agree and otherwise leaving the space of possibilities as large as possible—stripping away disputed attributes until only a common irreducible core remains. The aim is to ask what, if anything, survives that distillation.

The future, or so it seems

There is a particular feature of subjective existence so immediate that we rarely notice how strange it is. The future appears open. Before making a consequential decision, I can entertain alternatives, imagine consequences, revise preferences, and sincerely report that I do not yet know what I will do.

It is tempting to transform that phenomenology directly into metaphysics: to treat experienced uncertainty as evidence for ontological indeterminism, and then to treat indeterminism as the opening required for freedom. The implication does not follow. It conflates an epistemic statement with an ontological one. The fact that an embedded agent cannot know its own future state does not establish that no physical fact determines that state.

A useful conceptual separation is therefore that epistemic openness is not ontological openness.

Our subjective lives establish the first with great force. They do not, by themselves, establish the second. ⁵5. The canonical incompatibilist challenge is Peter van Inwagen’s Consequence Argument: if determinism is true, present actions are consequences of the remote past together with the laws of nature; the remote past is not up to us, and the laws are not up to us; therefore their consequences are not up to us. The argument has generated a large literature because each phrase—especially “up to us” and the relevant modal rule for transferring non-control—is contestable. David Lewis’s famous compatibilist response distinguishes a weak counterfactual ability to do something such that, had one done it, the actual laws would not have held, from the absurd strong ability literally to violate a law. I do not attempt to settle that debate in the main text; the causal-provenance proposal is aimed at a different notion of authorship. See van Inwagen, An Essay on Free Will (1983), ch. 3; SEP, “Free Will”, §2.2. For Lewis’s reply, see D. Lewis, “Are We Free to Break the Laws?”, Theoria 47, 113–121 (1981).

Before interpretation

Quantum mechanics is often invoked as the obvious escape from determinism, but one must first distinguish the extraordinarily successful mathematical formalism from claims about what that formalism represents.

A closed quantum system is represented by a state in Hilbert space. Writing the time dependence of the state implicitly, its isolated evolution in ordinary quantum mechanics is unitary, $$\text{i}\hslash {\partial }_t|\Psi ⟩=H|\Psi ⟩$$ and therefore deterministic: specifying the state and Hamiltonian fixes the state at every other time.⁶ The evolution is invertible: given the Hamiltonian, complete knowledge of the state at one instant fixes the state at every other instant. The unitary propagator and its inverse are useful technical details, but the conceptual point here is simply that ordinary closed-system quantum evolution is deterministic and reversible at the level of the state.

The conceptual difficulty enters with the textbook measurement rule. For a state such as $|\psi ⟩=\alpha |A⟩+\beta |B⟩\text{,}$ the Born rule assigns the alternatives probabilities given by the squared amplitudes, while an actual measurement is said to yield one definite result. Whether this apparent stochasticity is fundamental depends on the interpretation. In the von Neumann formulation, the state is then projected onto the corresponding eigenspace. Quantum theory appears to contain two different dynamical rules: continuous deterministic unitary evolution and stochastic projection during “measurement.”

The expression Copenhagen interpretation hides important historical differences.⁶6. The label “Copenhagen” needs care because there was no single doctrine jointly codified by Bohr, Heisenberg, and Born under that name. Born supplied the probabilistic interpretation of amplitudes; Bohr emphasized complementarity, experimental context, and the classical description of recorded outcomes; Heisenberg used somewhat different epistemic and collapse language. The now-familiar textbook package—unitary Schrödinger evolution plus a stochastic projection postulate associated with measurement—is historically closer to the von Neumann–Dirac formalism than to a literal transcription of Bohr. The criticism in the main text is therefore directed at a measurement-privileging collapse scheme, not at every subtlety of Bohr’s philosophy. See SEP, “Copenhagen Interpretation of Quantum Mechanics”. For a closed system, with the time dependence of the state left implicit, unitary evolution obeys $\text{i}\hslash {\partial }_t|\Psi ⟩=H|\Psi ⟩\text{,}$ where $i$ is the imaginary unit, $\hslash$ the reduced Planck constant, and $H$ the Hamiltonian. For $|\psi ⟩=\alpha |A⟩+\beta |B⟩\text{,}$ the Born probabilities are $P\text{(}A\text{)}={\left|\alpha \right|}^2$ and $P\text{(}B\text{)}={\left|\beta \right|}^2\text{,}$ with complex amplitudes $\alpha$ and $\beta$ normalized so that their squared moduli sum to one. For our purpose, the target is not Bohr’s entire philosophy but the idea that a physically privileged class of interactions called measurements requires a rule absent from ordinary Schrödinger evolution. Decoherence explains why macroscopic interference becomes inaccessible, but it does not by itself delete all but one term of the global state.⁷7. The role of decoherence here is precise but limited. Environment-induced decoherence drives reduced density matrices toward approximate diagonality in a robust pointer basis because the environment becomes differently correlated with macroscopically distinct alternatives. The global state nevertheless remains entangled. Thus decoherence explains effective classicality and suppression of interference; whether it also solves the “single outcome” problem depends on interpretation. See M. Schlosshauer, Rev. Mod. Phys. 76, 1267 (2005). For a system entangled with an environment, $|\Psi ⟩=\sum _i^n{c}_i|s_i⟩|E_i⟩\text{,}$ the reduced state of the system is obtained by tracing out the environment, ${\rho }_S={\mathrm{Tr}}_E|\Psi ⟩⟨\Psi |\text{.}$ Here $c_i$ are amplitudes, $s_i$ system states, $E_i$ correlated environmental states, and ${\mathrm{Tr}}_E$ the partial trace over environmental degrees of freedom. When the environmental records become nearly orthogonal, the off-diagonal terms of ${\rho }_S$ are strongly suppressed in the selected pointer basis. This explains effective classicality of records but, without an additional interpretive step, does not select one unique global outcome.

That distinction is the measurement problem in its cleanest form: what, in the ontology, makes a measurement different from an ordinary interaction?

Everett refuses to collapse

Everett’s move is radical largely because it is conservative mathematically: remove fundamental collapse and apply the unitary theory to the measuring apparatus, observer and environment as well.

Suppose an apparatus begins in a ready state and becomes correlated with the measured system. Linearity gives the essential branching structure. Here $\to$ denotes state evolution rather than causal contribution.⁸8. More explicitly, $X(t_1)\to X(t_2)$ means that the physical state at one value of the time coordinate is related by the chosen dynamical description to the state at another. The arrow asserts temporal/state evolution only; it does not by itself assert a causal relation. Thus $$\left(\alpha \right|A⟩+\beta |B⟩)|M_0⟩\to \alpha |A,M_A⟩+\beta |B,M_B⟩$$ Everett retains this unitary branching structure and adds no fundamental collapse.⁹ Including observer and environment enlarges the same entangled state; decoherence makes the macroscopic alternatives effectively autonomous without selecting one of them as the unique surviving component.

Everett’s 1957 “relative-state” theory was explicitly pure wave mechanics without a fundamental collapse process.⁹9. Everett’s 1957 relative-state proposal supplies the cleanest version of the no-collapse move used in the main text: universal wave mechanics is taken literally, and the quantum state never undergoes a fundamental collapse. Measurement entangles system, apparatus, observer, and environment; later decoherence theory explains why certain coarse-grained components become dynamically autonomous for all practical purposes. Modern “many-worlds” language is a later interpretation of this branch structure, not terminology Everett needed for the formal proposal. The hard residual issue is probability: if all decoherent outcomes occur, what exactly do Born weights mean for an observer? See H. Everett III, “Relative State Formulation of Quantum Mechanics,” Rev. Mod. Phys. 29, 454–462 (1957), and D. Wallace, The Emergent Multiverse (2012). For a two-alternative measurement the unitary correlation can be written exactly as $\text{(}\alpha |A⟩+\beta |B⟩\text{)}|M_0⟩\to \alpha |A,M_A⟩+\beta |B,M_B⟩\text{,}$ where $M_0$ is the apparatus ready state and $M_A$, $M_B$ are the correlated records. If the universal quantum state is the complete ontology and always evolves unitarily, its fundamental dynamics is deterministic. The hard Everettian problem is not dynamical randomness but probability: if all decohered alternatives remain present, what exactly does a Born probability mean?¹⁰10. Removing collapse does not remove the separate problem of explaining the Born weights in Everettian quantum mechanics. Everett removes stochastic collapse; it does not by itself derive why rational expectation should be weighted by $|\alpha_i|^2$ Several programs address this. Gleason’s theorem constrains noncontextual probability measures on Hilbert-space projectors (for dimension $>2$) to the trace-rule form; Deutsch–Wallace decision theory argues that rational preferences over quantum gambles enforce Born weighting; Zurek’s “envariance” uses symmetries of entangled states; typicality and self-locating accounts give related readings. Each route has substantive premises, so it is safer to say that Everett has a probability problem with sophisticated proposed solutions, not that the Born rule follows trivially from branching. See Gleason (1957), Wallace (2012), and Zurek, Phys. Rev. A 71, 052105 (2005).

Bohmian mechanics reaches determinism by a very different ontology: particles have actual positions, the wavefunction evolves by Schrödinger’s equation, and the configuration follows a deterministic guidance equation.¹¹11. Bohmian mechanics is the clearest reminder here that Bell’s theorem does not eliminate deterministic quantum theories: it supplements the wavefunction with an actual configuration whose trajectory is determined by a first-order guidance equation; the wavefunction itself obeys Schrödinger evolution. Thus standard quantum statistics are compatible with a deterministic ontology. Bell’s theorem does not rule out determinism: under its assumptions it rules out locally causal hidden-variable completions reproducing the quantum correlations. Bohmian mechanics survives by being explicitly nonlocal. The point needed here is only logical: “quantum mechanics is empirically probabilistic” does not entail “every empirically adequate ontology must be fundamentally stochastic.” See D. Bohm, Phys. Rev. 85, 166–193 (1952), and J. S. Bell, Physics 1, 195–200 (1964). Objective-collapse models such as GRW instead deliberately add real stochastic dynamics.¹²12. The opposite possibility is that collapse is not merely interpretive language but a real modification of the dynamics. GRW/CSL-like theories alter Schrödinger dynamics so that macroscopic superpositions are dynamically suppressed by genuine stochastic localization. Unlike a merely interpretive collapse rule, such modifications are physical hypotheses and in principle experimentally testable. See SEP, “Collapse Theories” (rev. 2025). The original GRW model is G. C. Ghirardi, A. Rimini & T. Weber, Phys. Rev. D 34, 470–491 (1986). Quantum phenomena do not logically require an indeterministic ontology.

The coin we cannot predict

A coin toss provides the elementary model of how a future can be epistemically open while dynamically fixed. We may rationally assign equal odds to heads and tails while an ordinary macroscopic coin remains, to excellent approximation, governed by deterministic classical dynamics. With sufficiently exact initial conditions — position, velocity, angular momentum, forces, collisions, air resistance and geometry — the final face is determined. Probability represents our coarse knowledge of the microscopic state and our practical inability to propagate it exactly. Chaotic sensitivity can make this impossibility spectacularly severe without introducing fundamental randomness. Unpredictability is not indeterminism.

The analogy with deliberation is direct. “I do not yet know what I will choose” does not entail “no physical state determines what I will choose.” A human brain is vastly more complicated than a tossed coin, and there is an additional self-reference: the system trying to predict the answer is partly the system computing the answer. There is no reason for the output of a computation to be available to the computer before the computation occurs.

This gives two distinctions that will recur: being determined is not the same as being known in advance, and being determined is not the same as being produced without deliberation.

The deliberation may itself be the physical process through which the determined outcome is produced.

Everett is not merely a quantum coin: in the classical coin only one microtrajectory actually occurs, while in Everett multiple decohered successor records remain in the universal state. But for our philosophical argument the shared lesson is enough: observer-level probability can coexist with deterministic fundamental law.

Randomness is not freedom

Suppose Everett is wrong and collapse is genuinely stochastic. Would this rescue free will? Imagine that a genuinely random quantum event selects between two possible actions with specified probabilities. The randomness makes the outcome indeterministic; it does not by itself make either outcome authored.

If a radioactive atom decays I choose coffee; otherwise tea. The result is physically indeterministic. Yet it has not become more mine.

Indeed, if I deliberate carefully and conclude that one action is best, but an independent quantum random number generator makes me perform the other, agency has apparently been diminished. Randomness is not freedom.¹³13. The reason indeterminism does not automatically help agency is the familiar luck problem. The objection is standard in the free-will literature and is often called the luck, rollback, or Mind argument. If two worlds have exactly the same complete history up to an undetermined choice and then diverge, the critic asks what makes the agent the controller of which branch occurs rather than the beneficiary of luck. Libertarians have serious answers: event-causal theorists such as Robert Kane locate indeterminism inside the agent’s effort, while agent-causal theorists hold that the agent exercises an irreducible causal power at choice. The modest claim in the essay is therefore not “libertarianism has been refuted”; it is that randomness by itself cannot supply the missing authorship. See SEP, “Free Will”, §2.5, and A. Mele, Free Will and Luck (2006). The formal point can be made with a stochastic policy. If an internal state $X$ produces actions according to a conditional distribution $P\text{(}a|X\text{)}\text{,}$ nonzero conditional entropy of the action does not by itself identify the random component with control by the agent. The philosophical question is about the provenance and reasons-responsiveness of the mechanism generating that distribution, not merely whether the distribution is degenerate.

This exposes a persistent difficulty for libertarian free will. If my choice is determined by my reasons, values, memories and character, then those antecedent states causally explain it. If they do not determine it, some further factor must distinguish the action I perform from the one I do not. Merely making that factor random does not supply authorship. The desired third category is often called agent causation: the choice is neither determined nor random but authored by the agent. The phrase names a desideratum; it does not by itself supply a mechanism.

Galen Strawson’s “Basic Argument” presses the deeper problem of ultimate responsibility.¹⁴14. A deeper challenge to ultimate responsibility comes from Galen Strawson’s Basic Argument, whose target is ultimate moral responsibility. In compressed form: what one intentionally does depends on how one is mentally; to be ultimately responsible for what one does, one would therefore need to be ultimately responsible for how one is; yet any deliberate attempt to shape how one is already issues from an antecedent mental constitution for which one was not ultimately responsible. Random origination would not help, because luck is not self-authorship. Strawson concludes that the kind of responsibility requiring literal causa sui is impossible. This does not by itself eliminate ordinary agency, legal responsibility, praise, blame, or reasons-responsiveness. See G. Strawson, “The Impossibility of Moral Responsibility,” Philosophical Studies 75, 5–24 (1994). To be ultimately responsible for the character from which I choose, I would somehow have to choose that character. But the act of choosing it would already require an earlier chooser with a prior character. Literal self-creation demands that I precede myself.

Ultimate causa sui therefore looks impossible under both deterministic and stochastic physics.

Eligo, ergo sum

Descartes sought an irreducible certainty in cogito, ergo sum. “Thinking,” however, encompasses too much that is passive. A thought can occur without invitation; perception arrives from outside; memory intrudes; dreaming contains cognition.

What most forcefully generates the subjective impression of a persisting self may instead be the architecture of choice. A system represents several possible futures, evaluates them according to its internal state and goals, and commits to one of them. The internal process unfolds from represented possibilities through evaluation and deliberation to commitment and action. The important point is not the notation but the organization: the action is produced by the system's own machinery for comparing counterfactual futures.

“I choose, therefore I am” is not offered as a Cartesian logical proof. Grammatically, “I choose” already presupposes an “I.”¹⁵15. The Latin formulation is not decorative: its grammar fits the intended claim unusually well. eligo is the first-person singular present active indicative of eligere, “to choose” or “to select.” Latin is a pro-drop language: the personal pronoun ego is normally unnecessary because the verbal ending already specifies the subject. Thus eligo does not merely mean “choose”; it already means “I choose.” The same is true of sum, which already means “I am.” An explicit ego would usually add emphasis or contrast — roughly, “I choose.” So eligo, ergo sum carries the first person twice in its grammatical morphology while never having to name the I separately. This makes the Latin formulation particularly apt for a thesis in which the self is not posited in advance as an independent substance but revealed through the grammatical form of agency itself. It is a phenomenological thesis: agency may be the most fundamental ingredient in our subjective construction of selfhood. The internal indexical structure matters. These are not merely possible futures. They are represented as my futures, evaluated by my memories, values and goals, and connected to my body. A stable “I” is useful computationally because it binds temporally dispersed information and counterfactual control into one local model. ¹⁶16. Frankfurt’s earlier analysis of personhood gives a useful vocabulary for the kind of self-governance invoked here. In “Freedom of the Will and the Concept of a Person” (1971), Frankfurt distinguishes first-order desires—desires to perform actions—from second-order desires, including desires about which first-order desire should become one’s effective will. His point is not that this hierarchy solves determinism, but that personhood and freedom of the will involve identification with, and reflective endorsement of, some motives rather than merely having motives. That supplies an important antecedent to the claim here that an agent is not just a locus where competing impulses occur: the architecture includes a model of which motives count as mine and should govern action. See H. G. Frankfurt, “Freedom of the Will and the Concept of a Person,” Journal of Philosophy 68 (1971), 5–20.

Emergent agency

The naturalistic hypothesis I want to entertain is not that agency is an illusion, but that it is emergent.¹⁷17. Jenann Ismael’s How Physics Makes Us Free is probably the closest single antecedent to the broad architecture developed here. It treats the self as a self-governing physical system, analyzes the Consequence Argument, develops an interventionist account of causation, and devotes a chapter to the physical asymmetries that make the future practically and epistemically “open” to embedded decision-makers. Her central move is not to find a breach in physics but to understand how control looks from inside a physically realized system that represents and exploits causal pathways. The present essay differs mainly in what it subsequently does with thermodynamic memory, god, atemporal grammar, and duality. See J. T. Ismael, How Physics Makes Us Free (Oxford, 2016), especially chs. 4–7.

Temperature provides a useful archetype. In equilibrium statistical mechanics, temperature is not a primitive property assigned independently to each molecule. It is a macroscopic variable characterizing a distribution over microscopic states; in suitable ensembles it has an exact thermodynamic definition.¹⁸18. The temperature analogy is useful only if its limits are kept explicit. In equilibrium thermodynamics, temperature is a state variable; in the microcanonical ensemble one may write $T^{-1}=(\partial S/\partial E)_{N,V,\ldots}$. For sufficiently small or far-from-equilibrium systems a unique scalar temperature may be unavailable, so the analogy should not be overextended. The point is structural: a higher-level variable can be objective, measurable and explanatorily indispensable without being a primitive microscopic degree of freedom. “Emergent” here means multiply realizable and dependent on lower-level organization, not supernatural or causally autonomous in violation of microphysics. There is no microscopic “temperature particle.” Nevertheless temperature is real, measurable and causally useful at the thermodynamic level. The statement that a pressure difference drives flow is not made false by the existence of a deeper molecular account.

Perhaps the self, agency, intention, choice and subjective openness have the same logical status: higher-level variables describing organized patterns in a lower-level physical state. Emergent does not mean unreal. ¹⁹19. Christian List develops a nearby account in which free will is treated as a genuinely higher-level phenomenon. He distinguishes physical possibility from agential possibility: a maximally fine-grained deterministic physical state may permit only one physical future, while a coarser-grained state used by a valid psychological theory can be compatible with several action-level futures. He argues that agency, alternative possibilities, and causal control should be assessed at this higher level rather than searched for among fundamental physical variables. This is stronger than the temperature analogy in the main text because it is explicitly modal. It is also controversial: critics can ask whether coarse-graining creates genuine alternatives or merely epistemic multiplicity. The present essay does not need to settle that modal question; it needs only the more modest claim that higher-level agency can be objectively real. See C. List, “Free Will, Determinism, and the Possibility of Doing Otherwise,” Noûs 48, 156–178 (2014), and Why Free Will Is Real (2019). This blocks a common false dichotomy. Either there is a metaphysically uncaused chooser, or agency is fake. There is a third possibility: agency is a real causal architecture realized by physical degrees of freedom, just as computation is realized by transistors without being identical to a list of transistor voltages. ²⁰20. Calling agency emergent immediately raises Jaegwon Kim’s causal-exclusion challenge: if a physical event already has a sufficient physical cause, what independent causal work remains for a higher-level mental cause without systematic overdetermination? One response—closer to the interventionist language used in this essay—is to reject the demand that a higher-level cause be an additional microscopic force. A coarse variable can be causally informative when interventions or counterfactual changes at that level systematically change the outcome, even though every realization is physical. Barry Loewer, among others, has argued that Kim’s exclusion principle depends on a stronger and more metaphysically loaded account of causation than such counterfactual accounts require. The essay therefore claims real higher-level causal organization, not a second causal substance acting over and above microphysics. See J. Kim, Physicalism, or Something Near Enough (2005), and B. Loewer, “Mental Causation, or Something Near Enough,” in Meaning, Mind, and Matter (2011), 215–234.

A deterministic chess player provides a useful toy model: the move can be fixed by the position and the player’s decision procedure without making the intervening search or evaluation causally idle.²¹21. A deterministic chess program makes the distinction between being predetermined and being precomputed concrete. Consider a deterministic chess program in a fixed position. With a fixed search rule, evaluation function, tie-breaking convention and hardware state, its eventual move is fixed. But it does not follow that the move exists inside the machine as an already available answer before the search. In a minimax-style program, candidate continuations are generated, evaluated and propagated back through the game tree; pruning and heuristics may determine which branches are inspected. The final move is the output of that internal computation. Counterfactually changing the evaluation function, search depth, position or explored branches can change the move. Thus the search is not bypassed by determinism; it is part of the deterministic causal mechanism that produces the move. One could replace the computation by a gigantic lookup table or an oracle, but that would merely substitute a different physical mechanism. The point is conceptual: from the output is uniquely determined it does not follow that the computation producing it is explanatorily or causally dispensable. The same distinction matters for deliberation: a deterministic agent may have to perform the very process we call deciding before its decision exists as an accessible internal result. This is why predetermined should not be confused with precomputed or with causally independent of deliberation.

Where the cause lives

Can we make this less metaphorical? Divide the physical world, approximately, into an agent subsystem and its environment. The boundary is functional rather than metaphysically absolute: it identifies the machinery whose internal organization realizes perception, memory, valuation, counterfactual simulation and action. No real agent is causally isolated. The environment supplies sensory input, food, language, threats, education and physical perturbations. So authorship cannot mean “having no external causes.”

Instead, ask where the proximate counterfactually decisive computation producing an action occurs.²²22. Unlike the ordinary temporal arrow, $\Rightarrow$ is introduced here for causal contribution rather than material implication. Let $X_E$ denote ordinary environmental input, $R_A$ internal reasons or valuations, $C_E$ an external controller, and $A$ the action. The contrast is schematically$$X_E\Rightarrow R_A\Rightarrow A\qquad\text{versus}\qquad C_E\Rightarrow A$$The localization claim concerns causal provenance rather than causal insulation. In Woodward-style interventionist terms, reasons-responsiveness requires that relevant interventions on $R_A$ alter the distribution of $A$ through the normal mechanism, for example$$P(A\mid do(R_A=r_1))\ne P(A\mid do(R_A=r_2))$$External commandeering is the contrasting case in which an intervention on $C_E$ fixes $A$ while screening off or bypassing the normal dependence on $R_A$. This is only a schematic causal model: subsystem boundaries and variable choices are scale-dependent, and human agency is not captured by one scalar intervention. The philosophical proposal is that authorship tracks the provenance and organization of the action-producing mechanism, not causal isolation. Compare J. Woodward, Making Things Happen (2004).

In an ordinary intentional action, environmental input is processed through the agent's sensory state, internal world model, valuation and counterfactual machinery before producing a decision and an action. The causal path runs through the deliberative organization of the agent rather than bypassing it.²² The outside world supplies evidence and constraints, but the transformation from evidence into action runs through the agent’s own internal reasons-responsive machinery.

Under direct external control, the structure differs: an external controller can bypass or override the agent's deliberative machinery and directly determine the action.

This suggests a physically meaningful notion: Authorship is approximately the localization of the action-generating causal relation within the agent’s subsystem. ²³23. Fischer and Ravizza’s notion of guidance control is the closest established analogue to the present proposal. They distinguish regulative control—having genuinely accessible alternatives—from guidance control, which can exist even when only one action is available. On their account an action can ground responsibility when it issues from the agent’s own, moderately reasons-responsive mechanism. “Ownership” is historical: the mechanism must have become the agent’s in the appropriate way, not merely be located inside the skull. This is very close to the present emphasis on actual causal provenance. The difference is one of formulation: I am trying to recast sourcehood in a physical subsystem/interventionist language, not claiming to have discovered the underlying philosophical intuition. See Fischer & Ravizza, Responsibility and Control (Cambridge, 1998), especially chs. 3, 7–9.

Localization is necessary to this picture, not sufficient. A mechanism can operate entirely inside the agent and still have been installed, engineered, or commandeered in a way that undermines ownership; the history by which the reasons-responsive mechanism became the agent’s own therefore matters as well. The qualification approximately is essential. Subsystem boundaries are not metaphysically sharp, and causes reach across them continually. The proposal is that the dominant causal mechanism that converts information, reasons and values into action is locally integrated within the agent rather than imposed by an external controller.

Interventionist causal language can sharpen this proposal: changing an agent’s internal reasons or valuations should change the action through the agent’s normal mechanism, while an external controller can destroy authorship by fixing the action while bypassing that dependence. The point is not causal isolation, but counterfactual sensitivity to reasons processed through the agent’s own mechanism. An externally commandeered action can therefore be fixed by the controller while bypassing the normal dependence on the agent's reasons-responsive internal state. This is not yet a complete mathematical theory of moral agency, but it gives “authorship” causal content rather than a mystical residue.

The notion naturally becomes graded. A reflective adult, a coerced person, an addict undergoing compulsion, a child, and a patient with frontal damage can all possess different degrees and architectures of local causal integration. Law and ordinary morality already recognize this graded structure without requiring a metaphysical switch labeled FREE WILL.

The Frankfurt interpretation

Call this, with a deliberate nod to Copenhagen, the Frankfurt interpretation. Harry Frankfurt’s famous 1969 counterexamples to the Principle of Alternative Possibilities become especially transparent in this language.²⁴24. The Frankfurt example targets the Principle of Alternative Possibilities (PAP), which says, roughly, that a person is morally responsible for an act only if the person could have done otherwise. Frankfurt argued that responsibility may survive when alternative action is impossible, provided the mechanism preventing the alternative never actually produces the choice. See H. G. Frankfurt, “Alternate Possibilities and Moral Responsibility,” Journal of Philosophy 66 (1969), 829–839; and SEP, “Moral Responsibility and the Principle of Alternative Possibilities”.

Consider Alice, deciding whether to perform action A. Unknown to Alice, Bob has a device monitoring her decision process. If Alice begins to decide B, Bob will intervene—perhaps by directly manipulating Alice's brain—and force A. If Alice decides A on her own, Bob does nothing. Alice deliberates for her own reasons and chooses A. Bob never intervenes.

In the actual history, Alice's beliefs and evaluation produce her intention, which produces action A. In the counterfactual history in which Alice starts toward B, Bob intervenes and produces A instead.

The final action is the same and, given Bob's device, Alice cannot robustly bring about B. Yet the causal provenance of A differs completely between the two histories.

This is exactly what the local-authorship proposal captures. In the actual history, the decisive causal computation resides inside Alice’s subsystem. In the intervention history, a decisive edge crosses the subsystem boundary from Bob into Alice. Freedom may be primarily a property of causal provenance, not metaphysical indeterminacy. ²⁵25. Manipulation cases show why a simple “the cause was internal” criterion is too permissive for authorship. Manipulation arguments imagine an external designer who engineers an agent’s desires, values, or reasons-responsive mechanism so thoroughly that the later action flows internally and reflectively—yet still seems unfree because of its history. Pereboom’s Four-Case Argument gradually moves from moment-to-moment neural manipulation toward ordinary deterministic causation; Mele’s Zygote Argument imagines a creator selecting a zygote whose deterministic development is known to produce a later act. These cases motivate history-sensitive notions of ownership. The present subsystem account should therefore be understood as local causal provenance plus an appropriate history of how the local mechanism became the agent’s own, not mere anatomical localization. See SEP, “Arguments for Incompatibilism”, §3.2; A. Mele, Free Will and Luck (2006), ch. 7; D. Pereboom, Free Will, Agency, and Meaning in Life (2014), ch. 4.

There is a vast literature on whether Frankfurt cases genuinely eliminate every “flicker” of alternative possibility. We need not settle it. The narrower point is robust: two physically identical overt actions can differ in authorship because their internal causal histories differ. ²⁶26. P. F. Strawson supplies a complementary reason not to make responsibility practices wait for a final metaphysical verdict. His “Freedom and Resentment” (lecture delivered 1962; published in Proceedings of the British Academy 48) shifts the problem in another direction. Rather than deriving responsibility practices from a prior metaphysical verdict about determinism, he begins from the interpersonal reactive attitudes—resentment, gratitude, forgiveness, indignation and related responses through which we ordinarily treat one another as participants in relationships. This does not prove compatibilism, and it does not identify authorship with social practice. It does show why the question “is the action really the agent’s?” matters independently of whether an ultimate self-creating cause can be found. The present essay is mainly about authorship rather than moral desert, but Strawson is an important warning against assuming that the latter must stand or fall with metaphysical indeterminacy.

Distilling god

The exercise begun in the Prelude can now be made precise. By a maximum-entropy definition of god I mean the widest, least constrained notion left after removing every attribute that the argument does not require. We therefore introduce only the minimal extra posit needed to ask whether something outside the physical description does explanatory work. We can now strip the notion of god down to what is ontologically relevant here. Remove institutional religion, ritual, tradition and mythology. Remove also the ordinary god of epistemic gaps—the placeholder inserted wherever our current causal model has a missing edge.

For compactness, let $G$ denote the minimal residual proposal: some entity or principle not already included in a causally sufficient physical description, invoked because physical causation is said to be insufficient for agency. Let $X$ denote the complete physical state relevant to the agent, and let the phenomena to be explained include deliberation, reports, decisions, actions, regret and self-control. Either the physical description of $X$ is sufficient to account for those phenomena, or one claims that an additional factor—$G$—is required. The immediate question is whether $G$ makes any physical difference.

If it acts

If $G\Rightarrow X$, the physical account is incomplete: the presence of $G$ changes some physical state or observable correlation. The mathematical form of that new coupling is deliberately left open; it need not resemble any familiar interaction.²⁷27. The causal gap can be written compactly. Let $\mathcal A$ denote the observable and experienced phenomena of agency. A causally sufficient physical account says$$\mathcal A=F(X)$$whereas the proposed extra posit says$$\mathcal A=F(X,G)$$If that extra argument changes physical outcomes, then $G\Rightarrow X$. At the level of a generic dynamical model one could write$$\dot X=f(X,G)$$or, only as a mnemonic in quantum language, a deliberately schematic “god Hamiltonian”$$i\hbar\partial_t|\Psi\rangle=(H_{\mathrm{phys}}+H_G)|\Psi\rangle$$Here $H_G$ is not a proposed literal interaction Hamiltonian; it stands only for whatever additional coupling changes empirical predictions. Genuinely new physics could instead be nonlinear, nonunitary or stochastic. The question raised in the main text has an established analogue in philosophy of divine action, usually called the problem of the “causal joint.” The question “where does a nonphysical cause enter the physical order?” has a substantial science-and-religion literature under the label causal joint. Modern proposals have variously placed special divine action in quantum indeterminacy, chaotic amplification, emergent mind, or other loci thought compatible with scientific law. The general pressure mirrors the mental-causation problem: if physical effects already have sufficient physical causes, an additional independent cause risks causal overdetermination; if they do not, one should identify the empirically incomplete causal structure. Importantly, “causal closure/completeness of the physical” is itself a substantive philosophical and empirical thesis, not a theorem of logic. See SEP, “Mental Causation”, §2, and S. L. Ritchie, Divine Action and the Human Mind (2019), ch. 2.

Those differences are, in principle, scientific data. Whatever metaphysical name we give their source, a reproducible coupling belongs to an enlarged empirical theory. This does not prove that the source is not god; it means that calling it god adds no scientific content unless the word imposes additional constraints. ²⁸ 28. A classical theist can object at this point that divine causation need not compete with physical causation at all. A Thomist or other classical theist may reject the whole “extra force” picture. On Aquinas’s primary/secondary-causation framework, god is not one efficient cause among others inserted between physical events. Created causes are genuine secondary causes, while divine primary causation is supposed to underwrite their very existence and causal power. Contemporary theological writers therefore describe such divine and natural causation as noncompetitive. This is a serious objection to treating every form of theism as a missing term in a Hamiltonian. My response is limited: a noncompetitive god is no longer being invoked to explain why one physically possible neural transition occurred rather than another instead of the complete physical account; it has moved from event-level causal completion to a different metaphysical relation such as dependence or grounding. That may be coherent, but it is no longer the free-will gap targeted here. See I. Silva, “Causal and non-causal explanations in theology: the case of Aquinas’s primary–secondary causation distinction,” Religious Studies (2025; first published online 2024), and Ritchie (2019), ch. 7.

If it does not act

If $G\nRightarrow X$, by contrast, every physical observation is unchanged whether $G$ exists or not. A completely decoupled god can be postulated metaphysically, but the god-containing and god-free descriptions are empirically equivalent.

The conclusion is not atheism. It is empirical equivalence and explanatory redundancy with respect to the physical phenomena under discussion.

Later we will question whether a fundamental theory even contains a primitive causal arrow. The same fork can then be restated without dynamics: if adding god changes the theory's observable relational structure, the difference is empirical; if it changes nothing observable, it adds no distinguishable physical content.

A byproduct of inference

There is a more reflexive possibility. Human cognition is extraordinarily good at seeing an effect and inferring a hidden cause. When the inference is correct, causation runs from the hidden cause to the observed effect; the mind's inference runs epistemically in the opposite direction, from the observed effect to a hypothesis about its cause. When a pattern looks intentional, we similarly infer a hidden agent whose goals might causally explain the behavior.

This ability is indispensable to social life. Predicting another person from a microscopic description is, for any realistic case, computationally hopeless; attributing beliefs, goals and intentions is efficient. Dennett called this the intentional stance.²⁹29. Dennett’s intentional stance provides a useful methodological comparison here: systems can often be predicted efficiently by treating them as rational agents with beliefs and desires, even when those states are physically realized. The stance need not imply an immaterial mind. See D. Dennett, The Intentional Stance (MIT Press, 1987).

Cognitive science of religion has explored whether supernatural agency concepts recruit ordinary agency-detection and teleological reasoning.³⁰30. The cognitive-science literature on agency detection supports only a limited claim and should not be turned into a debunking theorem. Guthrie, Barrett, Kelemen and others have studied anthropomorphic attribution, “hyperactive” agency detection, and teleological explanation. The empirical literature is more nuanced than the slogan that religion is merely an overactive predator detector. The modest claim used here is only that causal and agent-inference mechanisms plausibly contribute to supernatural concepts. Explaining why a belief is cognitively natural does not logically show that its object is unreal.

This suggests a recursive possibility. A system evolved to infer hidden causes from observed effects, and hidden agents from apparently purposeful behavior, may apply the same explanatory grammar outside the domain in which those heuristics were learned. Because our own actions are naturally represented in agentive language — I formed an intention; my intention caused an action — the analogous move from a structured world to a hidden world-agent can feel almost compulsory. But this is an inference made by an inference machine, not yet evidence that the inferred agent exists.

This is not proof against god. An evolved tiger detector can detect real tigers. But it changes the evidential burden by separating two questions: Why do humans believe in god? and Does god exist?

A naturalistic answer to the first removes the inference itself as uncomplicated evidence for the second.

The consciousness loophole

Agency may be functionally reducible while phenomenal consciousness remains much harder. One can imagine an epiphenomenalist model in which physical brain states generate phenomenal experience while phenomenal experience never causally affects physics.³¹31. Writing $X$ for the relevant physical brain state and $C$ for phenomenal consciousness, strict epiphenomenalism has the asymmetric structure$$X\Rightarrow C,\qquad C\nRightarrow X$$Physical state may determine or accompany experience, while experience makes no physical difference. Epiphenomenalism preserves physical causal closure only by accepting a severe explanatory cost. Phenomenal facts can then accompany physical facts but cannot explain any physical report about themselves. The view is logically coherent, but it creates a severe epistemic puzzle—if consciousness never affects neural processing, why should our physical utterances about consciousness reliably track it? This is one reason the consciousness problem should not be casually identified with the free-will problem. See SEP, “Epiphenomenalism”.

This preserves physical causal closure, yet creates a peculiar consequence. My sentence “I am conscious” is a physical event. If phenomenal consciousness has no effect on physical state, my consciousness cannot be why my body reports consciousness. A physically identical zombie would generate the same words. Under strict epiphenomenalism, I report consciousness, but my consciousness is not causally responsible for my reporting it.

This is logically possible and deeply strange. It is one reason I separate the problem of consciousness from libertarian free will. We have a plausible functional and causal architecture for agency. Whether, and why, that architecture carries phenomenal experience remains genuinely difficult.

The working hypothesis of this essay is nevertheless that subjective experience may itself be emergent, analogous in logical status to temperature. That analogy is a hypothesis about ontology, not an explanation of consciousness.

A universe without verbs

Time is so deeply built into thought and language that an atemporal universe is difficult even to imagine. Augustine captured the difficulty long before modern physics: “If no one asks me, I know; if I wish to explain it to him who asks, I know not.” The problem is not merely defining a coordinate called time. Our verbs, memories, explanations and decisions already divide experience into what has happened, what is happening and what may happen. ³²32. Augustine's line is from Confessions XI.14 (c. 397–400 CE), in the middle of an extended analysis of time. The surrounding passage is philosophically sharper than the aphorism alone: Augustine notes that time is among the most familiar things we speak about, yet past and future are puzzling because the past is no longer and the future is not yet; an ever-present present, he argues, would be eternity rather than time. Nothing here anticipates modern relativity or quantum gravity. Its relevance is phenomenological: temporal concepts are so constitutive of ordinary thought that removing fundamental time is harder to conceive than merely deleting a variable from an equation. See Augustine, Confessions, XI.14.

Everything so far has therefore been phrased in a local temporal grammar: the world is narrated as a succession of states, with one state evolving into the next. That grammar is natural for differential equations, prediction and ordinary causal explanation—and perhaps inevitable for an agent that remembers one temporal direction and acts toward the other. But a useful representation of physics need not always have this form. A theory may characterize an entire admissible structure by relations or constraints rather than by a privileged story in which one event locally produces the next. That does not show that time is unreal, nor that causal language is mistaken at the scales where it works. It only warns against assuming that the grammar most natural to embedded agents must also be the grammar of the fundamental description.

This matters for the argument about god. If a future fundamental theory is atemporal, the question cannot depend on the phrase “does god cause a later physical change?” The representation-independent question is whether introducing the additional posit changes the observable relational structure at all.

The next two sections make this less abstract from opposite directions. Gravity gives a striking example of a global restriction linking geometry and information; thermodynamics and memory then show how a pronounced temporal asymmetry can emerge inside laws that are far less asymmetric than our experience. Neither example proves a timeless ontology. Together they loosen the intuition that reality must fundamentally be written as a sequence of verbs.

Gravity and information

If atemporal structure sounds too abstract, physics already contains global constraints whose content is awkward to narrate as one event causing another. Gravity and information provide a particularly sharp example. For an ordinary local quantum field theory regulated at a short-distance cutoff, one naively expects the number of independent local degrees of freedom available in a region to grow with its volume. Gravity gives us a radically different clue.

For a stationary black hole, the Bekenstein–Hawking law makes the essential scaling transparent: the leading semiclassical entropy is proportional to the horizon area rather than to the enclosed volume.³³ Quantum and higher-curvature corrections can modify the simple area formula, so this should be understood as the leading result for Einstein gravity in its semiclassical regime. This is one of the clues behind holography: once gravity is included, the maximum information that can be associated with a region appears to be constrained far more severely than naive volumetric field-theory counting suggests. Bousso's covariant entropy bound is the careful modern form of this idea, formulated on appropriate null light-sheets rather than as an unrestricted statement about every spatial volume.33. For a stationary black hole in semiclassical Einstein gravity, the leading entropy formula is$$S_{BH}=\frac{k_BA}{4\ell_P^2}$$The area scaling in the main text can also be motivated by combining an entropy bound with the requirement that the system has not already collapsed into a black hole. For a bounded, weakly self-gravitating system, Bekenstein's bound is $$S\le\frac{2\pi k_BER}{\hbar c}$$ Here $S$ is entropy, $E$ is total energy, $R$ is the effective radius, $k_B$ is Boltzmann's constant, $\hslash$ is the reduced Planck constant, and $c$ is the speed of light. Requiring that the system not lie inside its own Schwarzschild radius gives, parametrically, $$E\lesssim\frac{c^4R}{2G}$$ where $G$ is Newton's gravitational constant. Combining the two inequalities gives an entropy scale proportional to $R^2\text{,}$ or equivalently to the spherical area $A=4\pi R^2\text{.}$ With ${\ell }_P$ denoting the Planck length, ${\ell }_P=\sqrt{\frac{\hslash G}{c^3}}$, this becomes $$S\lesssim\frac{\pi k_Bc^3R^2}{G\hbar}=\frac{k_BA}{4\ell_P^2}$$ A Schwarzschild black hole saturates the corresponding area scale. This is a motivating argument under stated assumptions, not a theorem that every arbitrary region contains exactly this number of states; the Bekenstein bound itself has a substantial technical history and domain of validity. See Bekenstein, Phys. Rev. D 7, 2333–2346 (1973); Bekenstein, Phys. Rev. D 23, 287–298 (1981); and Bousso, Rev. Mod. Phys. 74, 825–874 (2002). ³⁴34. For a codimension-two surface $B$ and an appropriate null light-sheet generated from it, the covariant entropy bound is schematically$$S_L\le \frac{k_B A(B)}{4\ell_P^2}$$where $S_L$ is the entropy on that light-sheet. The qualification “appropriate” is essential. That clue should not be overstated: several increasingly strong claims are often grouped under the word holography. The Bekenstein–Hawking area law for stationary black holes is a central semiclassical result. Entropy bounds go further and suggest that the information associated with gravitating systems can be limited by boundary area rather than spatial volume. Naive spacelike versions fail in sufficiently general geometries, which is why Bousso's covariant entropy bound is formulated on suitable null light-sheets generated from a surface. The still stronger holographic principle is a proposal about the fundamental organization of quantum gravity; AdS/CFT is its clearest concrete realization. None of this establishes a general theorem that an arbitrary region in our cosmological spacetime literally possesses a Hilbert space of dimension $e^{A/\text{(}4{\ell }_P^2\text{)}}\text{;}$ here the Hilbert-space dimension means the number of independent quantum basis states available to the region. See R. Bousso, Rev. Mod. Phys. 74, 825–874 (2002).

The philosophical point is structural. There need be no temporal story in which a surface acts on an interior and deletes states. A quantum theory of gravity may simply restrict the admissible joint configurations of geometry and information. The relation is then a property of the allowed total structure, not an event imposed at an earlier time.

Landauer's principle becomes relevant at this point because it destroys the temptation to treat information as something that floats free of matter. Erasing information has a thermodynamic cost: resetting an unknown bit in a thermal environment must dissipate heat even in the ideal quasistatic limit. The qualification resetting matters; measurement and logically reversible computation need not pay this cost at each logical step.³⁵35. The qualification about resetting is exactly where Landauer’s principle becomes precise. The bound concerns logically irreversible information processing: resetting an unbiased bit maps two logical possibilities to one and therefore requires an entropy increase of at least $k_{B}ln2$ outside the logical degree of freedom in the ideal isothermal setting. Multiplying by the reservoir temperature $T$ gives the heat bound $Q\ge k_{B}Tln2\text{.}$ It is therefore a category error to attach that cost to every measurement, logic gate, or act of computation. Bennett showed that logically reversible computation and measurement can in principle be performed with arbitrarily small dissipation in the quasistatic limit; a cyclic device with finite memory eventually pays when information is discarded or memory is reset. Real devices dissipate much more because they operate at finite speed and must suppress errors. See C. H. Bennett, “The Thermodynamics of Computation—a Review” (1982) and “Notes on Landauer’s Principle…” (2003). Black-hole thermodynamics adds a much stronger statement: physical information, entropy, and geometry are not independent. The leading semiclassical black-hole area law is robust in its domain; the extrapolation from it to a universal microscopic state count for arbitrary regions is the stronger holographic claim and requires additional structure.

So the hierarchy of claims should be kept straight: Landauer says that information processing is physically instantiated; the Bekenstein bound links entropy, energy and size; gravity limits how much energy can occupy a region without collapse; black-hole thermodynamics saturates the resulting area scale; and holography asks whether this scaling reveals the microscopic organization of quantum gravity. We do not yet possess a generally accepted microscopic account of gravitational entropy, nor do we know in general what its underlying microstates are.³⁶36. What counts as a gravitational microstate is theory-dependent. String theory famously reproduces the Bekenstein–Hawking entropy for important classes of supersymmetric and near-supersymmetric black holes by counting microscopic states, while loop-quantum-gravity and other approaches provide different microscopic constructions. These successes do not yet amount to a universal microscopic definition of gravitational entropy for arbitrary spacetimes or cosmological regions. The restrained inference used here is therefore structural: an entropy that scales with area, together with gravitational entropy bounds and holographic examples, is evidence that the independent microscopic degrees of freedom of a gravitating universe are much more constrained than a naive local volume count suggests. The essay does not assume a particular microscopic ontology. Yet the area scaling strongly suggests that gravity imposes a severe microscopic constraint on the admissible states of the universe. In the atemporal language developed here, that constraint need not be pictured as a later boundary acting on an earlier bulk. It can instead be a structural restriction on the possible configurations of the entire bulk universe itself.

Memories of the future

Our subjective world is violently asymmetric in time. We remember yesterday and not tomorrow. Eggs scramble and do not spontaneously unscramble. Radiation disperses. Organisms consume free-energy gradients. Yet much microscopic dynamics is reversible in a much stronger sense than our macroscopic experience suggests. First, invertibility and time-reversal symmetry are different claims. Unitary quantum evolution is mathematically invertible; true time-reversal symmetry additionally requires the appropriately transformed reversed history to obey the same dynamics. The weak interaction violates time-reversal symmetry, but those microscopic violations are not what explains the enormous everyday thermodynamic arrow.³⁷37. Unitarity and time-reversal invariance are different properties. Unitarity says that closed-system evolution is invertible: $U^{-1}=U^\dagger$ A time-reversal symmetry requires more: there must be an antiunitary operator $\Theta$ mapping a solution into the appropriately momentum/spin-reversed history and leaving the dynamics invariant (schematically $\Theta H\Theta^{-1}=H$ for a time-independent Hamiltonian with no $T$-odd parameters). The Standard Model contains genuine $T$ violation associated with weak interactions; by CPT symmetry, observed CP violation entails corresponding T violation under the standard framework. This microscopic asymmetry is not the explanation of the thermodynamic arrow: the everyday arrow is vastly larger and is successfully modeled through statistical mechanics plus special boundary conditions. Direct T violation has been observed in the neutral-B system; see the BABAR Collaboration, Phys. Rev. Lett. 109, 211801 (2012).

The clean standard statistical-mechanical account instead puts the large asymmetry in a boundary condition: the observable universe occupied an extraordinarily special low-entropy macrostate toward what we call its early boundary—the Past Hypothesis in one influential formulation. Given that boundary and a suitable typicality measure, entropy-increasing histories dominate away from it. For cosmology, the qualification is important: the early universe was smooth, and gravitational entropy makes “low entropy” subtler than simply “cold” or “ordered.” ³⁸38. The thermodynamic arrow invoked in the main text requires a low-entropy boundary condition, usually formulated as the Past Hypothesis. Boltzmannian statistical mechanics does not obtain an arrow merely from reversible microscopic equations. One specifies a low-entropy macrocondition at one boundary and a probability/typicality measure over compatible microstates. For almost all such microstates in the relevant measure, coarse-grained entropy rises away from the low-entropy boundary for a very long interval. The cosmological case is subtle because the early plasma was close to local thermal equilibrium: its low entropy is associated mainly with the extraordinary smoothness of the gravitational field. Gravitational clumping—especially black-hole formation—opens an enormous entropy reservoir. No universally accepted local gravitational-entropy density exists for general spacetimes, so statements that “the early universe had low gravitational entropy” are well-motivated but not summarized by one general formula. See Albert (2000), Price (1996), and SEP, “Thermodynamic Asymmetry in Time.” In ordinary evolutionary language we say that entropy was extraordinarily low in the early universe and is much higher later. In an atemporal or block description, the same statement can be read as a property of the entire history: one part of spacetime has exceptionally low entropy and the complete structure contains a large entropy gradient away from it. Nothing external has to push entropy “forward.” The informational asymmetry available to an embedded agent can be made explicit in a minimal toy universe. ³⁹39. This might still sound too abstract. I myself have always been frustrated by the fact that every discussion stopped short of actually producing a mathematical example. So here is mine. Let $X_t$ be a coarse-grained world variable taking values on a large odd cycle of $N$ sites. Couple neighboring values of the coordinate $t$ by the symmetric nearest-neighbor kernel $K\text{(}x,y\text{)}=\frac{1}{2}$ when $y=x\pm 1$ (on the cycle), and zero otherwise. The local law itself has no orientation: $$K\text{(}x,y\text{)}=K\text{(}y,x\text{)}\text{.}$$ Equivalently, the weight of a finite bulk configuration is built from symmetric edge factors $\prod _{s=0}^{T-1}K\text{(}{x}_s,x_{s+1}\text{)}$; at equilibrium, with the uniform distribution $\pi \text{(}x\text{)}=1/N$, the path statistics are invariant under reversal of the $t$ coordinate. Now add the only directional ingredient: the boundary condition $p_0\text{(}x\text{)}={\delta }_{x,0}$. Let $H_t=H\text{(}{X}_t\text{)}$ be its Shannon entropy, playing here the role of a toy coarse-grained thermodynamic entropy. The exact $H_t$ can be written explicitly, but all we need is that this doubly stochastic walk makes it nondecreasing from $H_0=0$ and, because the odd cycle mixes, it asymptotically approaches ${\text{log}}_{2}N$. Thus the arrow is not in the local law but in the low-entropy boundary condition and the asymmetric statistics it imprints on the bulk $\text{{}{X}_t:t\ge 0\text{}}$. Call one coordinate $t$ now. For $0<\Delta \le t$, the conditional uncertainties on its two sides satisfy $$H\text{(}{X}_{t+\Delta }|X_t\text{)}-H\text{(}{X}_{t-\Delta }|X_t\text{)}=H_t-H_{t-\Delta }\text{.}$$ The side of now toward the low-entropy boundary is therefore more tightly constrained by the present than the equally distant side away from it, by exactly the entropy gained over the intervening interval. In this toy model that is the analogue of the thermodynamic arrow emerging from otherwise perfectly time-symmetric microscopic laws. As equilibrium is approached, $H_t-H_{t-\Delta }\to 0$, and this bare statistical distinction disappears. For an embedded agent, call inference in either direction estimation. An ideal estimator that knows the exact bulk statistics and uses $X_t$ alone is left with the baseline residual uncertainties $E_t^{\pm }\text{(}\Delta \text{)}=H\text{(}{X}_{t\pm \Delta }|X_t\text{)}$. Their asymmetry is exactly the entropy-gradient term above. Now let $M_t$ denote additional local record degrees of freedom available to the agent. Define the record information they add about either side by the reduction in uncertainty $$R_t^{\pm }\text{(}\Delta \text{)}=H\text{(}{X}_{t\pm \Delta }|X_t\text{)}-H\text{(}{X}_{t\pm \Delta }|X_t,M_t\text{)}\text{.}$$ Thus $R_t^{-}>0$ means that local records reduce uncertainty about the lower- $t$ side, while $R_t^{+}>0$ is an equally well-defined record of what we call the future. In an atemporal bulk there is nothing incoherent about correlations of either kind. The uncertainty left after ideal estimation and records is $U_t^{\pm }=E_t^{\pm }-R_t^{\pm }$, so $$U_t^{+}-U_t^{-}=\underset{\text{thermodynamic / estimation asymmetry}}{H_t-H_{t-\Delta }}+\underset{\text{record asymmetry}}{R_t^{-}-R_t^{+}}\text{.}$$ In this operational sense, $U_t^{+}>U_t^{-}$ is the information-theoretic signature of a comparatively open future and closed past. It does not require zero correlation, or even zero record information, on the future side. If $R_t^{-}=R_t^{+}$, the record contributions cancel and the thermodynamic term alone fixes the orientation. Future-pointing records can weaken that orientation without reversing it; reversal requires $R_t^{+}-R_t^{-}>H_t-H_{t-\Delta }$. At equilibrium the first term vanishes, so any remaining orientation must reside in asymmetric records. The toy model therefore separates two questions. The low-entropy boundary derives the estimation asymmetry; it does not by itself prove that real agents satisfy $R_t^{-}>R_t^{+}$. That is a further statistical-mechanical claim about physical records. Sidenote 41 connects this abstract record term to real memory formation; sidenote 42 states the important qualifications. Despite the temporal vocabulary, nothing here requires time literally to flow: all of these inequalities are properties of correlations and conditional uncertainties already imprinted in the complete bulk structure. The classical toy is doing more work than it first appears: replacing it by a fully quantum atemporal bulk already exposes much of the problem of time. ⁴⁰40. One might ask why this toy universe was made stochastic rather than quantum. If we allow an external time parameter, the replacement is straightforward. Let the closed state evolve unitarily with $U={\text{e}}^{-\text{i}H\delta t/\hslash }$, so $\text{|}{\psi }_{t+1}\text{⟩}=U\text{|}{\psi }_t\text{⟩}$, and obtain observable probabilities from the Born rule. By entangling each step with unobserved ancillas and tracing them out, the reduced diagonal dynamics can even reproduce the classical random-walk kernel exactly. The total closed evolution remains deterministic and unitary; the apparent stochasticity belongs to the reduced description. But this construction has quietly restored precisely what the main text is trying not to assume: an external parameter telling us which state comes next. Moreover, the entropy of the global pure state does not increase; only reduced or coarse-grained entropies can do so. The atemporal classical toy was easier because it supplied a single positive joint distribution over all coordinates. A naive quantum analogue instead assigns a complex amplitude to a history, $$𝒜\text{(}{x}_0,\dots ,x_T\text{)}={\psi }_0\text{(}{x}_0\text{)}\prod _{s=0}^{T-1}\text{⟨}{x}_{s+1}\text{|}U\text{|}{x}_s\text{⟩}\text{.}$$ We cannot in general turn these amplitudes into an ordinary probability distribution over all unmeasured intermediate alternatives by simply squaring each history separately, because different histories interfere. For an endpoint outcome the amplitudes over unresolved intermediate alternatives must instead be summed before applying the Born rule: $$P\text{(}{x}_T\text{)}={\text{|}\sum _{x_1,\dots ,x_{T-1}}𝒜\text{(}{x}_0,\dots ,x_T\text{)}\text{|}}^2\ne \sum _{x_1,\dots ,x_{T-1}}{\text{|}𝒜\text{|}}^2\text{.}$$ Sequential measurements can of course define joint probabilities for a specified measurement protocol, and sufficiently decohered alternatives can behave classically; what fails in general is the innocent classical assumption that every intermediate alternative already belongs to one positive Kolmogorov distribution independent of how it is interrogated. There is nevertheless a beautiful way to package ordinary unitary evolution into a single static quantum object. Introduce a clock degree of freedom and form the finite history state $$\text{|}\Omega \text{⟩}=\frac{1}{\sqrt{T+1}}\sum _{t=0}^T{\text{|}t\text{⟩}}_C\otimes U^t\text{|}{\psi }_0\text{⟩}\text{.}$$ Conditioning on the clock reading $t$ recovers the relative state $U^t\text{|}{\psi }_0\text{⟩}$. This is a finite-clock cousin of the Page–Wootters construction discussed in sidenote 47: evolution has become correlation inside a stationary state. But the price is now visible. The global state is pure and stationary, so the thermodynamic arrow must be reconstructed from conditional reduced states, entanglement, decoherence, coarse-graining and a special low-entropy boundary; classical records and even a usable internal clock must themselves emerge from that same structure. Our classical stochastic toy therefore cheats in exactly the places where an atemporal quantum theory of the universe becomes difficult.

To connect the abstract record term of the toy model to physical memory, consider the smallest possible recorder. A binary event meets a bit prepared in a standard ready state, and an ideal interaction correlates the two. Such elementary correlation can be reversible. A useful macroscopic memory, however, is not a bare correlation: it must be prepared and made sufficiently stable to survive noise, usually through amplification, redundancy or error correction; finite reusable storage must eventually be recycled. These requirements draw on low-entropy resources and free-energy gradients. ⁴¹41. Sidenote 39 treated memory abstractly as a local reduction of conditional uncertainty. Real physical memories add a thermodynamic layer. The elementary act of making a correlation need not itself be irreversible: for a classical bit, the ready-state map $\text{(}e,0\text{)}\mapsto \text{(}e,e\text{)}$ can be embedded in the reversible controlled-NOT map $\text{(}e,m\text{)}\mapsto \text{(}e,m\oplus e\text{)}$. A useful macroscopic recorder, however, must normally begin in controlled ready states and make records sufficiently stable to survive noise; realistic memories use amplification, redundancy or error correction, and finite reusable storage eventually requires recycling or reset. Such implementations draw on free energy and export entropy. Landauer's bound applies specifically to logically irreversible operations such as reset or erasure, not to correlation as such. With a one-sided low-entropy boundary, these physical requirements provide a natural route to record asymmetry: robust lower- $t$ records can be supported by ordinary low-entropy resources, whereas, for ordinary robust record architectures, a higher- $t$ record requires the specially coordinated correlations characteristic of the time-reflected ensemble. As equilibrium is approached and exploitable free-energy gradients are exhausted, the sustained formation and maintenance of new robust records becomes increasingly difficult—not because correlations are mathematically impossible, but because prepared resources for amplification, protection and recycling cease to be generically available. This is a physical mechanism that can make the record term of sidenote 39 satisfy $R_t^{-}>R_t^{+}$. Sidenote 42 gives the important qualification: generic alignment is a statistical-mechanical claim about physical record systems, not a logical consequence of the abstract definition of memory. As equilibrium is approached and exploitable free-energy gradients are exhausted, sustained formation and maintenance of new robust memories becomes increasingly difficult.

The time-reflected record-forming structure is nevertheless allowed by the microscopic laws. Under the same one-sided low-entropy boundary, however, generic robust records are expected to align toward the low-entropy side; future-pointing records require the specially coordinated correlations of the time-reflected ensemble. Thus actual records can reinforce the baseline estimation asymmetry of the toy model: the densely recorded side feels comparatively closed, while the side with greater residual uncertainty feels open. ⁴² 42. Sidenote 39 and sidenote 41 separate two claims that should not be conflated: the low-entropy boundary produces an asymmetric conditional-information structure, while the physics of record-forming systems can make actual memories align with it. The second claim is powerful but not logically compulsory. Mlodinow and Brun argue that, wherever a robust thermodynamic arrow exists, a generic physical memory should align its psychological arrow with it—even if the memory device itself is reversible and nondissipative—provided the recorder is not specially fine-tuned to the system being recorded. Wolpert and Kipper give a broader formal analysis: some physically defined memory systems are time-symmetric and can provide information about either past or future states, whereas others exhibit an epistemic arrow; the relation to the Second Law depends on the architecture of the memory system rather than on correlation alone. There is also explicit philosophical dissent: Gołosz (2025) argues that thermodynamic explanations of trace asymmetry risk presupposing a more fundamental temporal orientation. Accordingly, the text treats $R_t^{-}>R_t^{+}$ as a physically motivated typicality claim, not as a theorem that thermodynamics uniquely explains every notion of temporal direction. See Mlodinow & Brun, Phys. Rev. E 89, 052102 (2014); Wolpert & Kipper, Entropy 26, 170 (2024); Gołosz, Minds and Machines 35, 48 (2025).

Ted Chiang's Story of Your Life is a useful literary counterexample to our intuition that this linguistic asymmetry is inevitable. Its heptapods use a written language conceived as a complete, nonsequential form; as Louise Banks acquires it, she comes to experience her life nonsequentially, producing what our grammar can only call “memories of the future.”⁴³43. Ted Chiang’s 1998 novella “Story of Your Life” is useful here as a thought experiment rather than as evidence. In the story (collected in Stories of Your Life and Others, 2002), the heptapods' language and cognition are explicitly associated with variational descriptions of physics, especially Fermat's principle. Heptapod B is semasiographic and globally composed rather than a linear transcription of speech. The story is fiction, not evidence that language can grant access to the future or for a strong Sapir–Whorf thesis. Its value here is conceptual: it makes vivid how deeply human grammar presupposes sequence, tense and becoming, and how hard it is even to formulate an atemporal perspective without smuggling temporal words back in. Our ordinary language is saturated with before and after, tense and aspect, becoming and remaining. Even “the future already exists” sabotages itself: already imports temporal becoming into the attempted description of a timeless block. We may therefore be trying to think atemporal ontology with a cognitive and linguistic apparatus built for organisms whose memories and controls are aligned with an entropy gradient.

A timeless quantum gravity

This local temporal grammar may itself fail to be fundamental. General relativity already rejects Newton’s fixed spacetime stage: spacetime geometry is itself dynamically coupled to matter.⁴⁴44. General relativity makes spacetime geometry dynamical rather than prescribing a fixed metric background on which matter evolves. But “background independence” has several inequivalent technical meanings—absence of nondynamical geometric structures, diffeomorphism invariance, relational observables, or stronger requirements on boundary data—and there is no universally accepted single definition applicable to every candidate quantum-gravity theory. The safe point is narrower: GR deprives coordinate labels and a fixed Newtonian metric of direct physical status, and the canonical constraints encode this gauge freedom. See SEP, “Quantum Gravity,” especially §§3.2 and 5.2, and De Haro, Mayerson & Butterfield (2016) on background independence in gauge/gravity duality. A complete solution can be represented as one four-dimensional geometrical object with no mathematically privileged universal “now,” although relativity by itself does not settle every metaphysical debate about temporal passage. ⁴⁵45. Relativity motivates the block representation used here without by itself proving a block-universe metaphysics. Relativity eliminates a preferred observer-independent global simultaneity structure of the Newtonian kind. A complete relativistic solution is naturally represented as a four-dimensional spacetime with entire worldlines. That mathematical representation is congenial to “block universe” or eternalist readings, but the stronger metaphysical thesis that past, present, and future are equally real is not itself an experimentally isolated theorem of Einstein’s equations. The essay needs only the weaker claim: fundamental relativistic physics does not contain a unique global present sweeping through the solution, so ordinary tensed language should not be read directly into the formalism. Quantum gravity sharpens the tension because ordinary quantum mechanics normally uses an external time parameter, whereas general relativity makes the geometry defining clocks and durations dynamical. In canonical quantization this tension appears schematically in the Wheeler–DeWitt constraint $\hat{H}\Psi =0\text{,}$ rather than in an ordinary external-time Schrödinger evolution. This is one face of the problem of time.⁴⁶46. The Wheeler–DeWitt equation makes the canonical version of the problem of time mathematically explicit. In canonical GR the Hamiltonian is built from constraints; after Dirac quantization, physical states are required to satisfy the corresponding operator constraints. The Hamiltonian constraint is written schematically as $\widehat{\mathcal H}\Psi=0$ Unlike the ordinary Schrödinger equation it carries no external $t$ This is only one facet of the “problem of time”: one must also define gauge-invariant observables and recover the experienced temporal ordering of subsystems. The formula is schematic, ordering and regularization are nontrivial, and canonical quantum gravity is not experimentally established as the final theory. It is therefore evidence for a conceptual problem, not proof that time is an illusion. See SEP, “Quantum Gravity,” §3.2.2.

One relational strategy is to use a physical subsystem as a clock and describe the rest conditionally on its reading. “Evolution” is then encoded in correlations among parts of the total state; the total object need not itself evolve in a second, external meta-time. ⁴⁷47. The finite history-state construction in sidenote 40 is a discrete toy version of this same relational idea. Page and Wootters provide a concrete example of how effective evolution can arise without an external global time parameter. They consider a globally stationary closed system and partition it into a clock $C$ and the rest $S$ Conditional on the clock indicating a value $t$ the relative state of $S$ can exhibit ordinary dynamical evolution even though the joint state is stationary with respect to an external parameter. In simplified versions one writes a global constraint such as $$(H_C+H_S)|\Psi\rangle=0$$ and recovers the Schrödinger evolution of $S$ in correlations with suitably ideal clock states. The construction is a proof of concept for relational time, not a complete solution of quantum gravity: realistic clocks are imperfect and constrained systems raise additional issues. See Page & Wootters, Phys. Rev. D 27, 2885–2892 (1983). In such a theory, “the universe is deterministic” may itself be secondary language. The deeper statement may be that a global quantum-gravitational object satisfies constraints and contains subsystems whose correlations admit an effective temporal description. The entropy gradient, record asymmetry and local agents can all be structures inside that whole.

From Newtonian to Lagrangian grammar

Even familiar mechanics warns us not to read ontology directly from grammatical form. I will call the local, step-by-step description Newtonian grammar: a state at one instant evolves into another according to differential equations. I will call the global variational description Lagrangian grammar. In Lagrangian grammar an entire admissible history is characterized by an action functional, and the physical history satisfies the compact stationarity condition $\delta S=0\text{.}$ Under the usual regularity assumptions the resulting Euler–Lagrange equations recover the same local mechanics. “Least action” is therefore a potentially misleading name: the action is stationary, not necessarily minimal.⁴⁸48. The relation between Newtonian and Lagrangian grammar can be made exact for regular mechanical systems. For a regular finite-dimensional system with Lagrangian $L(q,\dot q,t)$ stationarity of $S[q]=\int_{t_1}^{t_2}L\,dt$ under variations with fixed endpoints yields the Euler–Lagrange equations $d(\partial L/\partial\dot q_i)/dt-\partial L/\partial q_i=0$ With appropriate regularity and initial/boundary data these encode the same classical trajectories as Newtonian or Hamiltonian evolution. The variational statement therefore does not entail backwards causation, teleology, or a timeless ontology. Its philosophical value here is representational: identical empirical structure can be expressed either by local evolution from data on a slice or by a constraint on a complete history.

The variational form can sound teleological, as if a particle knew its endpoint and selected the best route. That is a grammatical temptation, not a physical conclusion. No intention or backwards signal is required.

Quantum mechanics deepens the global language. Feynman’s path-integral formulation assigns a transition amplitude by combining contributions from whole histories rather than narrating one classical trajectory step by step. The slogan that “the particle explores all paths” is a heuristic, not automatically an ontology. ⁴⁹49. The path-integral formulation should not be read as particles literally trying every route. Formally, a transition amplitude can be represented as a functional integral $K(b,a)\sim\int\mathcal Dq\,e^{iS[q]/\hbar}$ over histories satisfying the boundary conditions. Where both formulations are well defined, this is equivalent to operator quantum mechanics. In continuum interacting quantum field theory, however, “the path integral” is often a formal object requiring discretization, gauge fixing, analytic continuation, renormalization, or another limiting definition. Individual integration histories therefore need not be interpreted as simultaneously existing classical trajectories. The point used in the essay is only that quantum theory admits a successful whole-history mathematical grammar. What matters philosophically is that local temporal propagation and global constraint can be mathematically equivalent descriptions. Our preference for “cause followed by effect” may reflect the informational situation of agents who carry records of one temporal direction, forecasts of the other, and local control interfaces. Newtonian grammar may be our natural grammar without being the unique grammar in which reality itself must be written.

Reality up to duality

Modern physics provides an even sharper warning about ontology. Two formulations can use radically different primitive ingredients and yet, if an exact duality holds, encode the same physical theory. Gauge/gravity duality is the striking example: a gravitational description in a higher-dimensional spacetime can be equivalent to a lower-dimensional nongravitational quantum field theory. Philosophical work on duality makes the exact structural requirement precise.⁵⁰50. Schematically, the exact-equivalence claim used here is$$T_{\mathrm{grav}}\cong T_{\mathrm{QFT}}$$meaning a structure-preserving correspondence between the state spaces, quantities and dynamics of the two formulations—not literal identity of their primitive vocabularies. The ontological use of duality in the main text requires a stronger notion than mere empirical similarity. De Haro, Mayerson, and Butterfield model a theory by a state space, quantities, and dynamics, and an exact duality by a bijective structure-preserving map between the corresponding structures. In that bare-theory sense, exact duals are isomorphic representations of a common core. Two cautions matter. First, canonical AdS/CFT is still a conjecture, albeit one with very substantial evidence; the ontological argument here is conditional on exact duality. Second, formal duality need not by itself force interpretive equivalence: Butterfield has emphasized that two dual formulations can be assigned interpretations under which they disagree about the world. The “is gravity fundamental?” argument therefore assumes not merely a formal dictionary but a case in which we treat the dual formulations as physically equivalent descriptions. See De Haro, Mayerson & Butterfield, Found. Phys. 46, 1381–1425 (2016); De Haro & Butterfield, Synthese 198, 2973–3013 (2021); Butterfield, “On Dualities and Equivalences Between Physical Theories” (2018). See also B. Le Bihan & J. Read, “Duality and Ontology,” Philosophy Compass 13, e12555 (2018), for a focused survey of the ontological options generated by duality.

Now let G mean gravity—deliberately, not god. In the bulk description, a dynamical metric, curvature, black holes and gravitons are primitive gravitational language. In the dual boundary description there is no primitive higher-dimensional dynamical metric; bulk gravitational facts are encoded in generally complicated collective structures of the nongravitational theory. So: is gravity real? Gravitational waves and black holes are certainly not hallucinations. But if by fundamental we mean representation-invariant under an exact equivalence, gravity-as-a-primitive becomes less secure. It is explicit on one side and absent as a primitive on the other. What survives the dictionary is the common invariant structure, not necessarily either side's preferred furniture. ⁵¹51. Whether gravity should be called “real” depends on which sense of reality is intended. If it means empirically indispensable at the gravitational descriptive level, then yes: curvature, black holes, and gravitational radiation are robust physical phenomena. If it means primitive and invariant across all exactly equivalent formulations, an exact gauge/gravity duality would undermine that stronger claim: a bulk dynamical metric can be mapped to non-gravitational boundary variables, so “the metric is fundamental furniture” is not invariant under the dictionary. This does not make gravity illusory; it distinguishes phenomenological reality from primitive ontology. De Haro, Mayerson & Butterfield explicitly discuss whether spacetime and gravity are emergent in gauge/gravity duality and stress that exact duality by itself leaves no informational asymmetry from which a direction of emergence automatically follows.

This is why exact duality complicates loose talk of emergence. In useful semiclassical regimes one may say that bulk geometry emerges from boundary degrees of freedom. But if the complete theories are exactly dual, neither contains more physical information than the other; an absolute direction of fundamentality requires some additional criterion beyond exact equivalence.

Only now replace gravity by god. Imagine—not as a claim about any existing physical theory, but as a logical test—that one exact representation contains god as a primitive while a dual representation contains no primitive object resembling it, and every physical state, observable and relation has an exact counterpart across the dictionary.⁵²52. The substitution of god for gravity at this point is deliberately a thought experiment rather than a claim about known physics. No established gauge/gravity duality contains “god” on one side. Its purpose is to test the semantics of an existence claim: if a putative primitive disappears under an exact reformulation with identical physical content, then its primitive status is representation-dependent. The stronger claim—“god is unreal”—does not follow. What follows is that a physically meaningful realist claim should specify what invariant structure the word denotes. Does god exist? In the primitive vocabulary of the first representation, yes; in that of the second, no. The lesson is not a literal contradiction. It is that “god is a primitive constituent of reality” may fail to be a representation-invariant proposition—just as “gravity is fundamental” can fail to be invariant under a gauge/gravity dictionary.

The harder realist question is therefore what survives the dictionary. If every empirically and structurally meaningful fact attributed to god on one side is represented without god on the other, the invariant physical content does not require god as a primitive. To make “god exists” an ontologically substantive claim rather than a choice of coordinates on theory space, one must say what representation-invariant structure the word god denotes.

The “why?” question

I do not want to end by preserving “Why is there something rather than nothing?” as a sacred residual mystery. That would grant, without argument, that the unrestricted why is well defined.

In ordinary use, “Why?” requests an explanatory asymmetry. Often it is causal, but it may instead request a logical derivation, a constitutive reduction, a purpose, or an agent's reason. These are different relations, and I will not overload the causal arrow for them.⁵³53. The word “why” hides several different explanatory relations, so the question must be typed before it is answered. Depending on context it may request (i) an efficient cause, (ii) a mechanistic explanation, (iii) a constitutive reduction (“why is the gas hot?”), (iv) a deductive or mathematical reason, (v) a teleological or functional explanation, or (vi) an agent’s reason for acting. These relations have different directionality and different standards of adequacy. The essay’s objection is therefore not that the word why is meaningless, but that an unrestricted cosmic “why?” is underspecified until we say which explanatory relation is being demanded and why that relation should apply to the totality rather than merely within it. When the explanandum is reality as a whole, it is unclear that this grammar transfers. If “why?” demands an efficacious external cause, then as soon as that cause interacts with the universe, the causally complete object has been enlarged: the alleged outside cause belongs to the larger causal reality under discussion.

If the fundamental description is atemporal, even the causal arrow may be the wrong kind of relation. One might instead seek a deeper principle from which the total structure follows. But then the same explanatory demand can be reapplied to that principle.⁵⁴54. The Principle of Sufficient Reason is a substantive metaphysical thesis rather than a rule of syntax. Leibnizian versions of the Principle of Sufficient Reason (PSR) require, roughly, that every fact or truth have a sufficient reason why it is so rather than otherwise. The formulation and scope of “sufficient reason” are themselves disputed: causal explanation, grounding, demonstration, necessity, and intelligibility are not interchangeable. The PSR is philosophically powerful but neither a theorem of logic nor a result of physics. Rejecting an unrestricted PSR does not prohibit ordinary scientific explanation; it rejects the inference that every totality is guaranteed in advance to admit an explanation of the same type as events within it. See SEP, “Principle of Sufficient Reason”. We are therefore not entitled to infer either that reality must have an ultimate explanation or that it cannot have one. The more cautious statement is that we do not yet know whether the unrestricted question “why does the total structure exist?” denotes a coherent explanatory request. Before answering it, we should specify the relation the word why is supposed to denote. ⁵⁵55. The difficulty becomes sharpest when the explanandum is the whole rather than an event embedded in a wider structure. Scientific explanations normally embed an explanandum in a wider structure: earlier conditions and laws, a mechanism, a more microscopic theory, a variational principle, a symmetry, or a statistical ensemble. If the explanandum is stipulated to be the total physical structure, an explanation of the same kind cannot simply appeal to another causally efficacious physical item without enlarging the totality. One may instead invoke grounding, logical necessity, mathematical uniqueness, or a metaphysical dependence relation—but those are additional philosophical proposals, not automatic continuations of ordinary causal explanation. This is why the essay stops short of either “the universe has no explanation” or “there must be an ultimate explainer.” The semantics of the explanatory demand have to be specified first.

There is a useful warning from logic. Russell’s paradox showed that an expression can be grammatically impeccable and still fail because the operation used to form it has been applied without the restrictions that make it coherent. The analogy is not that an ultimate why? is literally a set-theoretic contradiction. It is that an explanatory predicate that is perfectly well defined for events or objects within a domain need not remain well defined when applied without restriction to the totality that contains the explanatory relation itself.⁵⁶56. Russell’s paradox begins with unrestricted comprehension: for any predicate $P\text{(}x\text{)}$, suppose there is a set $\text{{}x:P\text{(}x\text{)}\text{}}$. Let $R=\text{{}x:x\notin x\text{}}$. Then asking whether $R\in R$ yields $R\in R\iff R\notin R$. Zermelo–Fraenkel set theory avoids this not by declaring sets mysterious, but by restricting set formation. The Axiom Schema of Separation forms subsets of an already given set satisfying a predicate rather than allowing an arbitrary predicate to define a set over an unrestricted universe. The Axiom of Foundation is a separate restriction that, in standard ZF, excludes membership cycles such as $x\in x$; it is not the primary cure for Russell’s paradox. The methodological lesson is modest: syntactic well-formedness does not guarantee that an unrestricted predicate denotes a coherent object. Likewise, before asking for the cause or purpose of everything, one should establish that the explanatory relation remains well defined when its domain is enlarged to include the very structure in which causes and purposes have their meaning. See Russell (1903), Zermelo (1908), and the SEP entry “Russell’s Paradox.”

This closes the loop with causal cognition. A causal-inference machine encounters unexplained events and searches for hidden causes; a social agent encounters apparently purposeful behavior and searches for hidden agents. Applied without restriction, the same machinery naturally asks for a cause or agent behind the totality itself. The demand for an ultimate causal answer may therefore be partly a projection of an explanatory grammar evolved for relations inside the world onto a domain where its semantics have not been established.

Rational machines and sentient beings

There is a danger in stopping here. If purpose is not part of the fundamental vocabulary of physics, if agency requires no exemption from physical law, and if even god can dissolve under a change of representation, one might conclude that the exercise has gradually emptied the world of everything that matters to us. I do not think that follows. It confuses the vocabulary appropriate to a fundamental description with the vocabularies appropriate to creatures who live inside the world.

Here I find Sean Carroll’s poetic naturalism particularly congenial. Carroll summarizes it with the deliberately simple motto that “there is only one world, but there are many ways of talking about it.”⁵⁷57. Carroll develops poetic naturalism in The Big Picture: the natural world is the only world, but higher-level theories, models, vocabularies, and stories can describe real patterns when they are useful and compatible with the underlying physics. Carroll also repeatedly attributes the line about life’s “purpose” being to hydrogenate carbon dioxide to the geochemist Michael J. Russell. For the underlying geochemistry, serpentinization can generate molecular hydrogen, and reduction of dissolved carbon dioxide by such hydrogen is thermodynamically and experimentally well motivated, although the pathways relevant to the origin of life remain an active research problem. See Carroll (2016), Carroll (2021), and McCollom & Seewald (2001). Fundamental physics constrains what can happen and what can consistently exist; it need not be the only useful level of explanation. Temperature is real even though thermodynamic temperature is not normally an intrinsic property of a single molecule. An intention can be real without appearing as a new term in the Standard Model. Love does not become fictitious because it is absent from the Hamiltonian.

The same restraint should apply in both directions. It is a mistake to discard every concept that fails to occur in fundamental physics. It is equally a mistake to take a concept that works beautifully at one level and demand that it do explanatory work at another. God can belong to a human vocabulary—as metaphor, cultural inheritance, poetry, a name for awe, unity, gratitude, moral aspiration, or the limits of comprehension—without thereby becoming an additional variable in microscopic ontology. The problem begins when a word meaningful at one level is smuggled into another and asked to close a physical causal or explanatory gap. That would be rather like insisting that because temperature explains why a gas expands, there must be a thermodynamic temperature attached to each individual molecule.

There is a wonderful example of this ambiguity in the word purpose. Carroll likes to quote the geochemist Michael Russell—not, obviously, Bertrand Russell of the set-theoretic paradox a few paragraphs ago—as saying that “the purpose of life is to hydrogenate carbon dioxide.” Behind the joke lies serious thermodynamics. In hydrothermal origin-of-life scenarios, water–rock chemistry can generate molecular hydrogen in the presence of carbon dioxide, creating a redox disequilibrium from which reduced carbon compounds can in principle be formed. The reactions may be thermodynamically favorable while remaining kinetically obstructed; catalysts and increasingly organized chemistry open pathways through those barriers. In this intentionally perverse vocabulary, living matter becomes one of the structures through which an environmental free-energy gradient finds routes toward dissipation.

But nobody who asks about the purpose of their life is asking whether they should improve the kinetics of carbon dioxide reduction. The thermodynamic description can be true without exhausting the phenomenon. Purpose at the scale of a sentient agent is something else. We anticipate, prefer, suffer, love, regret, invent, fear, become attached to other people, and construct projects extending beyond ourselves. None of these introduces a new fundamental force. Yet eliminating them because they are absent from microscopic physics would be as confused as eliminating temperature because molecules have positions and momenta instead.

This is where the word poetic matters. Dirac, commenting on Oppenheimer’s interest in poetry, is reported to have said: “In science you want to say something nobody knew before, in words which everyone can understand,” and then dismissed poetry as doing essentially the reverse.⁵⁸58. The remark is anecdotal rather than a published aphorism by Dirac. A version appears in Robert Jungk’s Brighter Than a Thousand Suns (1958, trans. James Cleugh), in the context of Dirac’s conversations with Oppenheimer at Göttingen; later biographies reproduce closely related wording. The contrast is memorable precisely because it is so Dirac-like, but its transmission should be treated as recollection rather than a verbatim statement from a Dirac publication. He meant it as criticism. I am less sure. Telling us what nobody knew is one extraordinary human activity; finding a new form for what, at some level, everyone already knows is another. Physics can tell us that we are finite arrangements of matter in a universe with no externally assigned purpose. It cannot replace the vocabulary in which being finite, loving someone, losing someone, fearing death, or finding something beautiful is experienced from the inside. Poetry does not compete with physics here. It operates at another level of description.

This is also why I have deliberately avoided grounding the argument of this essay in neuroscience, in Libet-style timing experiments⁵⁹59. Libet and colleagues asked subjects to make simple self-initiated movements while reporting, from a rapidly rotating clock, the moment at which they first became aware of the urge or intention to move. The EEG readiness potential began several hundred milliseconds before this reported W time; in their 1983 data the main negative shift typically preceded reported conscious intention by roughly 350 ms in the more spontaneous trials, and sometimes substantially more. This was widely read as showing that the brain had already “decided” before consciousness became aware of the decision. That inference is much stronger than the experiment warrants. The task concerns arbitrary timing of simple movements, the conscious time is itself a retrospective subjective report, and the interpretation of the readiness potential remains disputed. Schurger, Sitt & Dehaene (2012) showed that an RP-like buildup can arise from stochastic neural fluctuations conditioned on threshold crossing, while Maoz et al. (2019) found the classical readiness potential strongly diminished or absent for deliberate consequential choices. Libet is nevertheless relevant here for a different reason: it demonstrates that the phenomenology of when I decided need not transparently reveal the underlying physical organization of decision-making. That is precisely why this essay avoids using the subjective timing of intention as an ontological primitive. See Libet et al. (1983), Schurger et al. (2012), and Maoz et al. (2019)., or even in the phenomenology of the self. These are fascinating questions, but they concern particular implementations of machinery whose more invariant structure I have been trying to isolate. I know first-hand how little pharmacology is required to disturb that implementation: a dose of LSD on the order of 80 μg can wreak havoc not merely with perception but with the apparently self-evident boundaries, continuity, and even conceptual coherence of one’s own self. I do not take that experience as evidence for any particular metaphysics. Almost the opposite. It makes me reluctant to elevate the phenomenology generated by one nervous system, in one biochemical state, into an ontological primitive.

The aim here has therefore been deliberately subtractive: to make the ontological questions as human-invariant as I could. The relevant question about agency was not how choosing feels, but where the organization producing a choice resides. The question about time was not primarily why time feels as though it flows, but what statistical structure distinguishes the two sides of an embedded observer. And the question about god was not what the word evokes in a human mind, but whether anything invariant remains when representation-dependent descriptions are stripped away.

That subtraction has limits. We are not only rational machines trying to infer the invariant structure of reality. We are sentient beings to whom things matter. Once that fact is admitted, purpose re-enters the vocabulary—not as a boundary condition imposed on the universe from outside, but as something instantiated locally by creatures capable of caring. The universe need not have a purpose for there to be purposes in the universe.

Seen this way, naturalism does not require us to impoverish our language. Quite the contrary. We can afford an extravagant vocabulary precisely because we no longer have to confuse vocabulary with ontology. We can speak of selves, choices, beauty, love, purpose, and even god, provided we remember the domains in which those words earn their meaning. Physics constrains the stories we may consistently tell; it does not require the fundamental equations to be the only language in which a human life may be understood.

I have purposefully left those higher-level questions largely outside this essay. They deserve more than an epilogue to an ontological exercise, and I will surely write another essay devoted entirely to purpose, meaning, value, and what a naturalistic universe can mean to sentient beings. The present exercise was meant to discover what remains when our contingent human perspective is factored out. It was never meant to suggest that what was factored out is worthless. Quite often, it is the part we care about most.

Epilogue

The path of the argument was deliberately narrow. The first step was to localize free will rather than to search for it in determinism or indeterminism. Randomness does not create authorship, and determinism does not abolish it. Agency can instead be an emergent causal organization of a physical system: the place where reasons, memories, values, counterfactuals, and deliberation are turned into action. Eligo, ergo sum. The choice need not escape physics to be mine.

The second step was to loosen the causal grammar in which that claim was first stated. Cause followed by effect is the natural language of an agent embedded in time, but it need not be the grammar of the most fundamental description. Variational principles, constrained quantum states, and other global formulations suggest a different possibility: what appears locally as causal evolution may, more fundamentally, be part of an atemporal relational structure. Agency then need not be a primitive causal exception; it can be a higher-level pattern instantiated in that structure.

Only then did the question of god become precise. In causal language, an external chooser that changes physical outcomes must couple to the physical world; if it does not, it cannot explain why one physical history rather than another occurs. In an atemporal language the same question becomes more general: does adding god change the observable relational structure of the theory? If it does, the difference belongs to the empirical description. If it does not, the posit adds no distinguishable physical content.

The more unusual turn comes with duality. A primitive may appear indispensable in one representation and disappear entirely in another that is exactly physically equivalent. Gravity already teaches us to take that possibility seriously. Applied to god, it shifts the question from whether a particular representation contains such an entity to what, if anything, survives the change of representation. Representation-invariant structure is then a stronger candidate for physical reality than representation-dependent furniture; the latter may be emergent, conventional, or in some cases not even well defined as an invariant claim.

The final restraint concerns the word why. Causes, grounds, derivations, constitutive explanations, and purposes are not the same relation. A demand for explanation that is perfectly meaningful inside the world need not remain meaningful when applied to the totality of the structure itself. Before asking for the purpose of the universe—or for a cause outside it—we must first establish that the requested explanatory relation is well defined.

The resulting picture contains no need for a breach in physical law through which agency enters, and no automatic vacancy for an external chooser once that breach is removed. We choose as organized parts of the world. At a deeper level, even the causal language in which that statement is made may give way to structure. And at that level, the sharpest ontological question is no longer which primitives a particular description names, but what remains invariant when the description changes.

References