9 Conclusion

This tripartite division exhausts the logical space of possibilities. Any given event either (a) follows necessarily from prior causes according to invariable laws, (b) occurs without any determining cause whatsoever, or (c) involves some mixture of determined and undetermined elements. There is no fourth option; any proposed alternative can be shown to reduce to one of these three cases. This is a logical truth, not an empirical claim: it follows from the law of excluded middle applied to the question of whether events have determining causes.↩︎

By “free will as traditionally conceived,” we mean libertarian free will: the capacity to have done otherwise under exactly identical circumstances, where this capacity is neither determined by prior causes nor random. This is the kind of free will presupposed by ordinary moral judgments, by religious doctrines of divine reward and punishment, and by retributive theories of justice. Compatibilist redefinitions of free will as “acting in accordance with one’s desires” or “absence of external constraint” may be coherent, but they do not capture what is at stake in theological and moral debates.↩︎

This definition captures Laplacean determinism: given complete knowledge of the present, the future is calculable in principle. The phrase “complete state” must be understood to include all physical variables relevant to the laws of nature—positions, momenta, field values, quantum states, or whatever the fundamental ontology requires.↩︎

This is objective or ontological randomness, to be distinguished from epistemic randomness (unpredictability due to ignorance). An event is epistemically random if we cannot predict it; it is ontologically random if nothing determines it. Quantum mechanics, on the standard interpretation, posits ontological randomness: the decay of a radioactive atom is not merely unpredictable but objectively undetermined.↩︎

This definition captures the intuitive notion that free actions must be “up to us” in a way that is neither the necessity of determinism nor the caprice of chance. The difficulty, as we shall see, is that conditions (a) and (b) exhaust the possibilities: an event is either determined or not determined, and if not determined, it is to that extent random. Condition (c) requires a tertium quid that does not exist.↩︎

Determinism, in its strongest form, holds that given the complete state of the universe at any time \(t\), together with the laws of nature, there is exactly one possible state at any subsequent time \(t + \Delta t\). This view traces at least to the ancient atomists Leucippus and Democritus, though its most famous articulation is Pierre-Simon Laplace’s thought experiment concerning an intelligence that could, given complete knowledge of the present, calculate all future states of the universe. See Laplace, A Philosophical Essay on Probabilities (1814).↩︎

The causal chain in a deterministic universe admits of no gaps or exceptions. When I deliberate and choose, that very deliberation is itself the product of antecedent causes. The feeling of freedom—the phenomenological sense that I could have done otherwise—is, on this view, an illusion generated by our ignorance of the determining factors. We feel free because we do not perceive the causes that determine our choices, just as a falling stone, if it were conscious, might feel that it “chose” to fall.↩︎

By “random” we mean genuinely indeterminate—events that are not merely unpredictable due to epistemic limitations but are objectively without determining cause. Quantum mechanics, on certain interpretations (particularly the Copenhagen interpretation), posits such fundamental indeterminacy at the subatomic level.↩︎

Randomness is the antithesis of control. If my choice to raise my arm rather than lower it was ultimately determined by an indeterministic quantum event in my neurons, then I no more controlled that decision than I control the decay of a radioactive atom. Randomness may liberate us from the iron grip of determinism, but it delivers us into the hands of chaos rather than freedom. As the philosopher Peter van Inwagen observes: “If what I do is not determined by my prior states and external circumstances, then what I do happens by chance. And if what I do happens by chance, then I am not in control of what I do.”↩︎

This is especially clear in entangled systems. If Alice and Bob share an entangled pair, a free choice by Alice about how to measure her particle instantly affects the probabilities for Bob’s measurements. If Alice’s choice is genuinely free—not determined by the prior wave function—then she is unilaterally altering the quantum state of Bob’s particle, potentially light-years away.↩︎

The axiomatic approach to quantum mechanics was developed by John von Neumann in his Mathematische Grundlagen der Quantenmechanik (1932), translated as Mathematical Foundations of Quantum Mechanics. The presentation here follows the standard Dirac-von Neumann formalism. For more rigorous treatments, see Reed & Simon, Methods of Modern Mathematical Physics, or Prugovečki, Quantum Mechanics in Hilbert Space.↩︎

This notation, introduced by Paul Dirac in his Principles of Quantum Mechanics (1930), elegantly captures the duality between vectors and linear functionals. The “bracket” \(\langle\phi|\psi\rangle\) splits into a “bra” \(\langle\phi|\) and a “ket” \(|\psi\rangle\).↩︎

A sequence \((|\psi_n\rangle)\) is Cauchy if for every \(\epsilon > 0\) there exists \(N\) such that \(\||\psi_m\rangle - |\psi_n\rangle\| < \epsilon\) whenever \(m, n > N\). Completeness ensures that such sequences have limits within the space, which is essential for the spectral theory of operators and for making sense of infinite-dimensional quantum systems.↩︎

The universal Hilbert space \(\mathcal{H}_{\text{universe}}\) is the tensor product of the Hilbert spaces for all subsystems: \(\mathcal{H}_{\text{universe}} = \bigotimes_i \mathcal{H}_i\), where the product runs over all fundamental constituents. The dimension of this space is unimaginably large—indeed, for infinitely many subsystems, it is infinite-dimensional in a very strong sense.↩︎

For bounded operators on all of \(\mathcal{H}\), the adjoint is uniquely defined on all of \(\mathcal{H}\). For unbounded operators (such as position and momentum), domain issues become important; see Reed & Simon for details.↩︎

For bounded operators on finite-dimensional spaces, Hermitian and self-adjoint are equivalent. For unbounded operators, self-adjointness is stronger and is required for the spectral theorem to hold in full generality. In physics, we often use “Hermitian” loosely to mean self-adjoint.↩︎

Equivalently, \(\hat{U}\) is unitary iff it preserves inner products: \(\langle \hat{U}\phi|\hat{U}\psi\rangle = \langle \phi|\psi\rangle\) for all \(|\phi\rangle, |\psi\rangle\). This means unitary operators preserve probabilities, which is essential for the consistency of quantum mechanics.↩︎

These postulates represent the standard Dirac-von Neumann formulation. Alternative formulations exist (path integrals, algebraic quantum mechanics, etc.) but are mathematically equivalent for the systems we consider.↩︎

More precisely, the physical state is a ray in Hilbert space: an equivalence class \(\{e^{i\theta}|\psi\rangle : \theta \in \mathbb{R}\}\). For most purposes, we can work with normalized representatives and remember that the overall phase is physically irrelevant.↩︎

For operators with continuous spectrum (like position), the “eigenvalues” become a continuum and the “eigenvectors” are generalized functions (distributions). The mathematical treatment requires more care but the physical interpretation remains the same.↩︎

The Born rule, proposed by Max Born in 1926, is the bridge between the mathematical formalism and experimental predictions. It is not derived from the other postulates but is an independent axiom. Born received the Nobel Prize in Physics in 1954 partly for this contribution.↩︎

This is sometimes called the “projection postulate” or “wave function collapse.” It is the most controversial postulate, as it introduces a discontinuous, non-unitary, and apparently random change to the state. The measurement problem—the question of how, when, and whether collapse actually occurs—remains one of the deepest unsolved problems in the foundations of quantum mechanics.↩︎

The Schrödinger equation was proposed by Erwin Schrödinger in 1926. It is a linear, first-order (in time) partial differential equation. Its linearity implies the superposition principle; its first-order nature implies time-reversibility and determinism at the level of the state vector.↩︎

This dichotomy is sometimes called the “measurement problem” when posed as a question about the transition between the two regimes. But for our purposes, the key point is that both regimes exclude free will: the first by determinism, the second by randomness.↩︎

The “interpretation” of quantum mechanics concerns the ontological status of the wave function, the nature of measurement, and the relationship between quantum and classical descriptions. All interpretations agree on the empirical predictions; they differ on what the theory says about reality.↩︎

Bohr emphasized the complementarity of wave and particle descriptions and the essential role of classical concepts in describing measurement apparatus. Heisenberg emphasized the epistemological limitations imposed by the uncertainty principle.↩︎

On this view, when a spin measurement has outcomes “up” and “down,” both occur—in different branches. The observer splits into two copies, each observing one outcome. The Born rule emerges as a measure of self-locating uncertainty: before the branching, I cannot know which branch I will find myself in.↩︎

One might think the branching introduces indeterminacy: “I” could end up in any branch. But this is self-locating uncertainty, not genuine indeterminacy in the physics. The wave function evolves deterministically; all branches exist with certainty; the only “uncertainty” is which branch the post-measurement copy of me will be in. This is analogous to not knowing which room I am in after being teleported while asleep—the physics is deterministic even if my self-location is uncertain.↩︎

The wave function evolves according to the Schrödinger equation as usual; the particle position evolves according to the guidance equation, which is also deterministic. The apparent randomness of quantum mechanics arises from our ignorance of the initial particle positions, which are assumed to be distributed according to \(|\Psi|^2\).↩︎

The apparent randomness in Bohmian mechanics is epistemic, not ontological—it reflects our ignorance of initial conditions, not genuine indeterminacy. But this does not help free will: if the initial conditions were fixed at the Big Bang, before any agent existed, then all agent “choices” are determined by those initial conditions.↩︎

Some exotic interpretations (e.g., objective collapse theories like GRW, consciousness-causes-collapse theories) might seem to offer alternatives, but on analysis they either introduce randomness (GRW) or require that consciousness influence quantum outcomes in ways that would themselves need to be determined or random.↩︎

This definition captures the common features of soul-concepts across religious and philosophical traditions: the Platonic immortal soul, the Cartesian res cogitans, the Christian soul subject to divine judgment, the Hindu ātman, etc. The key features are: (1) metaphysical independence from the body, (2) persistence through time, (3) unity (not a mere aggregate), (4) subjectivity (being a locus of experience), (5) agency (being a source of action), (6) free will, and (7) potential immortality.↩︎

The Milinda Pañha dates to approximately the 1st century BCE to 1st century CE. It is preserved in Pāli and is considered canonical in the Theravāda tradition of Southeast Asia. The dialogue format makes it an accessible introduction to Buddhist philosophy.↩︎

Adapted from Milinda Pañha, Book II, Chapter 1. The Pāli term translated as “person” is puggala, which corresponds roughly to the Western concept of a substantial self or soul.↩︎

Adapted from Milinda Pañha, Book II, Chapter 1.↩︎

The five khandhas (Sanskrit: skandhas) are the Buddhist analysis of what constitutes a sentient being: (1) rūpa (form/matter—the physical body), (2) vedanā (feeling/sensation), (3) saññā (perception/cognition), (4) saṅkhāra (mental formations/volitions), and (5) viññāṅa (consciousness). These are all impermanent and interdependent; none constitutes a self, and there is no self apart from them.↩︎

This two-levels-of-truth doctrine is central to Buddhist philosophy. Conventional truths are not false—it is true that there is a chariot, that Milinda arrived by it, etc.—but they do not describe ultimate reality. Confusing the two levels leads to philosophical error.↩︎

This formulation appears in the Visuddhimagga (Path of Purification) by Buddhaghosa (5th century CE), Chapter XIX. The teaching is attributed to the Buddha but the exact source in the early canon is debated. Similar statements appear in multiple places; see e.g. Saṁyutta Nikāya 12.17.↩︎

This is the doctrine of anattā (non-self) applied to consciousness itself. Even consciousness is not a self; it is a process, a flow, a series of momentary events. The illusion of a persistent witness arises from the continuity and self-referential character of the stream, but careful analysis reveals no fixed observer.↩︎

One cannot escape by positing a realm “without laws.” If events in such a realm have no determining causes and follow no patterns, they are random. Randomness, as shown, does not constitute free will.↩︎

This problem was famously pressed against Descartes by Princess Elisabeth of Bohemia in their correspondence of 1643. Descartes’s responses were unsatisfying, and the problem remains a fundamental objection to dualism.↩︎

Some have suggested that quantum indeterminacy provides a loophole: perhaps the soul influences which outcome occurs in a quantum measurement. But as shown in Chapter 2, such outcomes are random according to the Born rule; there is no evidence that anything beyond the wave function influences them. Moreover, such influence would itself need to be determined or random, not free.↩︎

The principle that moral responsibility requires the ability to do otherwise (the “principle of alternate possibilities”) has been challenged by Harry Frankfurt and others with ingenious thought experiments. But even on Frankfurt-style alternatives, responsibility requires that the agent be the source of the action, which is incompatible with both determinism (action sourced in prior causes) and randomness (action sourced in nothing).↩︎

One could stipulate a definition of “soul” that does not require free will, but such a soul would be a soul in name only—it would lack all the features that make the soul-concept important in religious and philosophical thought.↩︎

This broad definition encompasses many specific conceptions: the Christian heaven and hell, the Islamic jannah and jahannam, the Jewish olam ha-ba, the Greek Hades, the Norse Valhalla, various conceptions of purgatory, limbo, and intermediate states, as well as secular conceptions of digital immortality or survival as patterns of information.↩︎

Conceptions vary: Hindu traditions speak of the ātman passing through many bodies until achieving moksha; Buddhist traditions, while denying an eternal ātman, posit continuity of karmic imprints or consciousness; Jain traditions speak of the jīva; etc.↩︎

This is the doctrine of dependent origination (paṫicca-samuppāda): the next life arises dependent on conditions from this life (including karmic imprints), but there is no substantial self that passes from one to the other. It is like a flame passing from one candle to another: there is causal continuity but no “fire-stuff” that transmigrates.↩︎

This argument assumes that moral responsibility attaches to numerically identical persons, not to causal descendants. This assumption is widely shared and underlies our intuitions about justice: we do not imprison someone’s innocent relatives for their crimes, even if the relatives are causally connected.↩︎

This is not atheism—it does not deny God’s existence. It is something stranger: an acknowledgment that the existence question is practically irrelevant. A God who cannot justly reward or punish, and to whom we cannot meaningfully relate as free agents, is functionally equivalent to no God at all.↩︎

This independence is philosophically important. Even a libertarian about free will should find these arguments compelling. The case against the Biblical God does not rest solely on our conclusions about determinism.↩︎

J.L. Mackie, “Evil and Omnipotence,” Mind 64 (1955): 200–212. Mackie argues that the existence of evil is logically incompatible with the existence of the traditional God.↩︎

This premise is uncontroversial. The existence of suffering—from childhood cancer to the Holocaust to natural disasters killing innocents—is an empirical fact.↩︎

This is the “Free Will Defense,” developed most fully by Alvin Plantinga in God, Freedom, and Evil (1974). Plantinga argues that a world with free creatures who sometimes choose evil may be more valuable than a world of automata who always do good.↩︎

The evidential argument, distinct from the logical argument, was developed by William Rowe in “The Problem of Evil and Some Varieties of Atheism,” American Philosophical Quarterly 16 (1979): 335–341.↩︎

This example is from Rowe’s original paper. The key features are: (1) the suffering is intense, (2) no human free will is involved (it’s a natural evil), and (3) no apparent greater good results.↩︎

This is based on an actual case cited by Rowe. Such cases are tragically common.↩︎

Natural disasters provide particularly clear cases of apparently gratuitous evil, since no human free will causes them, and the suffering of children cannot be justified as punishment for sin.↩︎

This is an inference to the best explanation. The theist must claim that every instance of apparently pointless suffering actually serves some greater good that we cannot fathom. This “skeptical theism” makes God’s goodness unfalsifiable and unknowable.↩︎

This argument was developed systematically by J.L. Schellenberg in Divine Hiddenness and Human Reason (1993).↩︎

This premise captures the intuition that love involves openness to relationship. A perfectly loving being would not remain hidden from those who genuinely seek relationship with that being.↩︎

The existence of such people is empirically evident. Former believers who honestly sought God and lost their faith, indigenous peoples who lived and died without exposure to Biblical revelation, philosophers who have spent careers examining the evidence—all testify to the reality of nonresistant nonbelief.↩︎

This is the problem with “skeptical theism”: if we cannot trust our moral intuitions when evaluating God’s behavior, we have no basis for calling God “good” in the first place. The word loses all meaning.↩︎

This argument appears in various forms throughout the history of religious criticism. A sophisticated modern version is developed in John Hick’s An Interpretation of Religion (1989).↩︎

The theist might claim that their revelation is correct and all others are human inventions or demonic deceptions. But adherents of other religions make the same claim with equal conviction. Without an independent criterion for identifying the “true” revelation, this response is question-begging.↩︎

A child born in Saudi Arabia is overwhelmingly likely to become Muslim; a child born in Mississippi is overwhelmingly likely to become Christian; a child born in Thailand is overwhelmingly likely to become Buddhist. This “accident of birth” determining eternal destiny is incompatible with a just God who wants all to be saved.↩︎

“Whoever believes in him is not condemned, but whoever does not believe stands condemned already because they have not believed in the name of God’s one and only Son” (John 3:18). See also Mark 16:16: “Whoever believes and is baptized will be saved, but whoever does not believe will be condemned.”↩︎

The evidence includes: the fossil record showing gradual transitions between species; comparative anatomy revealing homologous structures (e.g., the same bone structure in human hands, whale flippers, and bat wings); molecular biology demonstrating shared DNA sequences across species, with similarity proportional to evolutionary relatedness; directly observed speciation events; biogeographical distribution patterns explicable only by common descent; vestigial organs (e.g., the human appendix, whale pelvis bones); and embryological similarities. Every major scientific organization in the world affirms evolutionary theory. The evidence is as strong as for any scientific theory.↩︎

Genesis 1:26–27, 2:7. The text describes God forming Adam from dust and Eve from Adam’s rib—not humans evolving from earlier primates over millions of years.↩︎

These ages are determined by multiple independent methods that converge on the same answers: cosmic microwave background radiation analysis, measurements of the universe’s expansion rate, radiometric dating using multiple isotope systems (uranium-lead, potassium-argon, rubidium-strontium), analysis of meteorites, stellar evolution models, and many others. The convergence of independent methods makes these estimates extraordinarily robust.↩︎

Archbishop James Ussher famously calculated creation as occurring on October 23, 4004 BC, based on the genealogies in Genesis 5 and 11. While some modern interpreters allow for gaps in the genealogies, even the most generous interpretations cannot reconcile Scripture with a universe billions of years old. The Bible describes a young Earth created in six days, with humans present from the beginning—not appearing billions of years after the universe began.↩︎

Examples include: two contradictory creation accounts in Genesis 1 and Genesis 2 (different order of creation, different names for God); contradictory genealogies of Jesus in Matthew 1 and Luke 3; contradictory accounts of Judas’s death (hanging in Matthew 27:5 versus falling and bursting open in Acts 1:18); contradictory numbers in parallel passages (e.g., 2 Samuel 24:9 vs. 1 Chronicles 21:5 on the census of Israel); contradictory accounts of the resurrection appearances; and many others. Entire books have been written cataloging these contradictions.↩︎

Ezekiel 26:3–14 prophesies that Nebuchadnezzar would destroy Tyre completely and it would never be rebuilt—yet Nebuchadnezzar’s siege failed to take the island city, and Tyre exists to this day. Jesus prophesied his return within the lifetime of his listeners (Matthew 16:28, 24:34)—nearly two thousand years ago. The Book of Daniel contains historical errors about Babylonian and Persian kings. The Exodus as described—involving millions of Israelites wandering the Sinai for forty years—leaves no archaeological trace whatsoever, despite extensive excavation.↩︎

The traditional doctrine of hell involves conscious, eternal suffering. See Matthew 25:46 (“eternal punishment”), Mark 9:43–48 (“unquenchable fire”), Revelation 14:11 (“the smoke of their torment rises forever and ever”), and Revelation 20:10 (tormented “day and night forever and ever”).↩︎

Try to believe, right now, that the Earth is flat. You cannot do it by an act of will. Belief is a response to evidence and argument, not a choice. Punishing someone for a belief is therefore punishing them for something outside their control.↩︎

No finite crime can merit infinite punishment. A human life lasts at most about 100 years; eternal punishment means suffering for billions upon billions of years, and then having not even begun. This violates any conceivable principle of proportional justice.↩︎

This is analogous to a parent who hides all evidence of their existence from their children, then punishes those children eternally for not believing the parent exists. Such a parent would be considered not loving but sadistic.↩︎

The theist might abandon either the doctrine of hell or the doctrine of Biblical inerrancy to escape this conclusion. But doing so abandons traditional Biblical Christianity. The God who remains after such revisions is not the God of the Bible.↩︎

This argument was made forcefully by Thomas Paine in The Age of Reason (1794) and has been developed by many subsequent critics.↩︎

The command explicitly includes infants. No theory of divine justice can render the execution of babies morally acceptable.↩︎

Punishing children for the sins of rulers they could not influence violates basic principles of justice.↩︎

A being who would command child sacrifice—even as a “test”—is not a being of perfect goodness. What kind of “test” is it to command murder?↩︎

Infinite punishment for finite crimes violates any reasonable principle of proportionality. Even the worst human criminal does not deserve infinite suffering.↩︎

Punishing people for actions committed by ancestors before they were born is the paradigm case of injustice.↩︎

Power does not confer moral authority. A powerful being who commits atrocities is not thereby justified; the being is merely a powerful perpetrator of atrocities.↩︎

This trilemma has no satisfactory resolution for the traditional theist. Each horn leads to the abandonment of some central tenet of Biblical Christianity.↩︎

This argument has been developed in various forms by many authors, including Carl Sagan and more recently by Michael Martin.↩︎

These figures are from current cosmological observations and represent lower bounds; the universe may be much larger.↩︎

The theist might respond that God’s purposes are inscrutable. But this, again, makes theism unfalsifiable. If any observation is compatible with theism, then no observation can confirm it.↩︎

For the Problem of Evil: suffering is expected in a godless universe, surprising if an omnibenevolent God exists. For divine hiddenness: nonbelief is expected if there’s nothing to believe in, surprising if a loving God wants relationship. And so on for each phenomenon.↩︎

Even if the theist could explain away one or two of these phenomena, explaining all five becomes increasingly implausible. At some point, the accumulation of “explanations” becomes more convoluted than simply accepting that the hypothesis is false.↩︎

This conclusion does not entail that no god exists—perhaps some deistic or non-interventionist deity created the universe. But it does entail that the specific God of the Bible—omnipotent, omniscient, omnibenevolent, who desires relationship with humans and rewards or punishes them based on their choices—does not exist.↩︎

This is not mere wordplay. The concept of “my death” presupposes a unified, enduring “me” that comes to an end. If the self is a conventional fiction, then “my death” is the end of a fiction, not the end of a real entity. This does not mean nothing happens when the body ceases to function—clearly something happens—but it does mean that what happens is not accurately described as “the death of a self.”↩︎

This is complete annihilation of the pattern that constituted the conventional self. There is no remainder, no ghost, no surviving essence. The atoms that composed the body will persist and enter into new combinations, but the organization that made them “me” is gone forever. This is not transformation into something else; it is the end of the something that was there.↩︎

The argument can be reconstructed formally: (1) Something is bad for me only if I experience it as bad. (2) After death, I experience nothing. (3) Therefore, death cannot be bad for me. Premise (1) is sometimes called the “experience requirement” and has been challenged by deprivationists who argue that losing goods is bad even if one does not experience the loss. However, our analysis does not depend on the experience requirement alone.↩︎

See Lucretius, De Rerum Natura, Book III.↩︎

The universality and intensity of death-fear is remarkable given its apparent irrationality. Surveys consistently show that death is among the most common fears, and observations of human behavior in life-threatening situations reveal the extraordinary lengths to which people will go to preserve their lives. This fear persists even in those who intellectually accept Epicurean arguments.↩︎

Or so we may hope—though if the foregoing arguments are correct, we are not in any business at all. We do not pursue truth; the causal processes that constitute us unfold in patterns that sometimes resemble the pursuit of truth. Even this book, with its pretensions to rational argument, is nothing more than the determined or random product of physical processes no more capable of “seeking truth” than a river is capable of seeking the sea.↩︎