# Theism Has Low Priors Objection Defeater ## Intro Some skeptics put their reason for unbelief in the language of probability. It goes like this: *"Before you even look at the evidence, God is very unlikely. So even decent evidence can't make God likely. That's why I don't believe."* The word for "how likely before the evidence" is the *prior*. The objection says theism's prior is so low that the evidence never catches up. People give several reasons for the low starting point. A mind that knows everything and can do anything sounds hugely complicated. Science keeps replacing supernatural explanations with natural ones. Computer scientists measure simplicity by how short a program is, and a mind looks like a very long program. And "extraordinary claims require extraordinary evidence." The short answer has four parts. **First, ask where the low number came from.** A prior is not a measurement. It is a judgment based on what you already think you know. If the reason God starts out unlikely is that you already assume nature is all there is, then the argument is going in a circle. **Second, God is not obviously complicated.** One being with no limits on power or knowledge is a short description. A universe with its own particular laws and finely set numbers, existing for no reason, is not. **Third, the track record has limits.** Science has explained a great many things inside nature. That tells us nothing about why there is a nature at all, with laws, in the first place. **Fourth, priors are not destiny.** Even if you start low, strong evidence can move you a long way. That is how anyone learns that something surprising happened. None of this proves God with math. It shows that a low prior is a claim that needs its own defense, and that the evidence still has to be weighed. ## In full Defeater for the **low-prior objection**: *"The prior probability of theism is so low that no realistic body of evidence can raise its posterior above one half. Theism is maximally complex, supernatural explanations have a failed track record, and extraordinary claims require extraordinary evidence, which theism lacks. Belief in God is therefore irrational whatever the arguments for it seem to show."* The objection comes in five forms, and each has a named source. - **(a) Complexity.** [Richard Dawkins](/codex/richard-dawkins/) makes this the central argument of *The God Delusion* (2006, chapter 4, "Why there almost certainly is no God"). As Plantinga quotes him, God is "the Ultimate Boeing 747," and "however statistically improbable the entity you seek to explain by invoking a designer, the designer himself has got to be at least as improbable." Dawkins also writes that a God able to monitor and control every particle "cannot be simple." - **(b) Track record.** Richard Carrier argues (in *Proving History*, 2012, and on his blog in 2020) that the presumption of naturalism is a conclusion from past investigation: he describes the observed base rate of success for supernatural explanations as zero, so supernatural hypotheses start with very low priors. - **(c) Algorithmic complexity.** In "Occam's Razor" (2007), Eliezer Yudkowsky argues that simplicity should be measured by the length of the shortest computer program that produces the data (Solomonoff induction). On that measure, he says, Maxwell's equations are simple and Thor is not, because a program that simulates an intelligent, emotional mind like Thor is enormously long. - **(d) Extraordinary claims.** Carl Sagan popularized "extraordinary claims require extraordinary evidence" in *Cosmos* (1980, episode 12); the skeptic Marcello Truzzi had used a near-identical form shortly before, and Laplace stated a similar principle in his work on probability. The ancestor is [David Hume](/codex/david-hume/)'s "Of Miracles" (1748), which sets a miracle's prior by "a uniform experience against every miraculous event." - **(e) Rationalist framing.** The forms above often arrive together in the vocabulary of online rationalism: priors, Bayes, Occam, and the claim that a careful reasoner simply assigns theism a tiny number. [Graham Oppy](/codex/graham-oppy/) makes a more cautious academic cousin of the argument, that naturalism wins a theory comparison on simplicity (see [Graham Oppy Arguments and Their Defeaters](/codex/graham-oppy-arguments-and-their-defeaters/)). **Division of labor.** [Bayesian Probability](/codex/bayesian-probability/) explains the framework and its terms. [Bayesian Argument for Theism](/codex/bayesian-argument-for-theism/) makes the positive cumulative case, evidence stream by evidence stream. [Epistemology Defeats Christianity Objection Defeater](/codex/epistemology-defeats-christianity-objection-defeater/) handles the "epistemology" slogan as a whole and gives Sagan and Hume one premise each. [Occam's Razor](/codex/occams-razor/) covers parsimony and brute facts in general. This page takes what those leave open: **where a prior for theism comes from, whether theism is really complex, whether track-record and program-length arguments can set that prior, and what a low prior does and does not imply.** The defeat structure is **six-pronged**. (1) **Source audit**: a prior is a judgment from background knowledge, and a low prior for theism is usually generated by assuming naturalism, which makes the argument circular. (2) **Simplicity contest**: on Swinburne's account theism is an intrinsically simple hypothesis, on the classical account God has no parts at all, and naturalism carries a stack of brute facts. (3) **Scope limit**: the track record of science concerns mechanisms within nature and cannot set the prior for an explanation of nature as a whole. (4) **Description-language critique**: program-length priors assume a mind is a physical program and depend on an arbitrary choice of language. (5) **Disambiguation**: "extraordinary" means low prior, and testimony routinely establishes low-prior events. (6) **Odds form**: posterior odds equal prior odds times the likelihood ratio, so a modest prior can be overcome. **This page is structured as debate prep.** **Honest limits.** Bayesian estimates for worldview-sized questions involve judgment at every step, and nobody can calculate the probability of God to two decimal places. This page does not claim that math proves God. It claims that the low-prior objection does not show what it says, and that the evidence for theism has to be weighed rather than waved off in advance. ## Argument structure | # | Premise | |---|---| | **P1** | A prior is a judgment from background knowledge, not neutral data; a low prior for theism is usually set by assuming methodological or metaphysical naturalism, and using naturalism to fix the prior and then concluding naturalism is circular. | | **P2** | Theism is not shown to be complex: on Swinburne's account one person with infinite power, knowledge and freedom is an intrinsically simple hypothesis; on the classical account God has no parts; and naturalism carries brute facts (a universe, its laws, its constants) with no explanation. | | **P3** | The track record of natural explanations concerns mechanisms within nature; it cannot set the prior for an explanation of why there is a law-governed nature at all, and its "zero" count assumes the disputed cases have already been settled. | | **P4** | Algorithmic-complexity priors assume a mind must be coded as a physical program and depend on an arbitrary choice of description language, so they cannot deliver a decisive prior against a necessary, non-physical mind. | | **P5** | "Extraordinary" means low in prior probability; testimony routinely establishes low-prior events, and Hume's maxim, read in probability terms, does not rule out well-attested testimony. | | **P6** | Posterior odds equal prior odds times the likelihood ratio, so a modest prior is overcome by a strong likelihood ratio; the existence of the universe, fine-tuning, consciousness, moral facts and the resurrection data are the evidence to be weighed. | | **C** | **Therefore the low-prior objection fails as a reason to dismiss theism in advance. The prior is contested, not settled; theism is not shown to be complex; and the real question is how strongly the evidence bears, which only weighing the evidence can answer.** | ## Form **Defensive (a defeater).** P1 is a **source audit**: it asks what background knowledge produced the number. P2 is a **simplicity contest** that grants the importance of simplicity and disputes how it was scored. P3 and P4 are **scope limits** on the two technical routes to a low prior. P5 is a **disambiguation** of the slogan. P6 is a **formal demonstration** with a clearly labeled toy example. The argument does not need to establish a high prior for theism; it shows that no decisive low prior has been established, and it returns the question to the evidence. Soundness is **contemporary**: the probability calculus is standard, and every contested step (Swinburne's simplicity, the description-language problem, the McGrews' estimates) is flagged as contested. ## Cheatsheet **The 30-second reply (read aloud).** I agree the starting odds matter. So let's ask where your starting number came from. If God starts out unlikely because you already assume nature is all there is, that's going in a circle. And God isn't obviously complicated. One being with no limits is a short idea. A universe that just happens to exist, with its exact laws and finely set numbers, and no reason for any of it, is the long story. Science has explained a lot inside nature, but it can't explain why there's a nature at all. And a low starting point isn't the end of the story. People believe surprising things every day when the evidence is strong. So let's stop guessing at the starting number and look at the evidence together. **The 5 fast facts:** 1. **The math is simple.** Posterior odds = prior odds × likelihood ratio. A prior is where you start, not where you must end. 2. **Dawkins calls this his central argument.** In *The God Delusion* (2006) he says the chapter "Why there almost certainly is no God" contains the central argument of the book (p. 157, as quoted in Frank Turek, *Stealing from God*, PDF p. 69). Plantinga's reply: God "is a spirit, not a material object at all, and hence has no parts," so on Dawkins's own definition of complexity God is not complex. 3. **Swinburne answered Dawkins directly.** Whether a hypothesis is simple, he wrote, "is an intrinsic feature of that hypothesis, not a matter of its relation to observable data," and scientists prefer hypotheses with infinite values to hypotheses with very large finite ones. 4. **Hume's own standard admits exceptions.** His maxim is that no testimony suffices for a miracle "unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish" (*Enquiry*, Section X, Part I). That is a test to run on the evidence, not a ban on it. John Earman of the University of Pittsburgh called Hume's essay an abject failure (*Hume's Abject Failure*, 2000). 5. **A finite prior can always be overcome.** The McGrews (2009) argue that, given their stated assumptions, the testimony for the resurrection carries a likelihood ratio of about 10^44, enough to overcome a prior of 10^-40, and they conclude that there is no finite prior "so low as to be 'slippery' and hence impossible to overcome by evidence." **The 3 strongest counter-moves:** - *"Where did your number come from?"* Ask the objector to say what background knowledge produced the low prior. If the answer is "everything is natural," that is the conclusion in dispute. - *"Simpler than what?"* Ask what naturalism's starting point is: a universe, these laws, these constants, existing with no explanation. Then ask why that collection gets a higher prior than one unlimited mind. - *"What would move you?"* Ask what likelihood ratio the objector thinks would be enough. If the answer is "nothing," the prior was never a prior; it was a refusal. If there is an answer, the conversation moves to the evidence. **Reciprocal concessions (grant the small point, then collect a bigger one):** - *Grant:* priors matter, and a careful thinker should start a strange claim low. *Now collect:* then the naturalist's prior must also be defended, not assumed, and "nature is all there is" is a strange claim too when nature includes a beginning, fine-tuned constants and conscious minds. - *Grant:* science has replaced many supernatural explanations of particular events. *Now collect:* then science has a superb record of explaining parts of nature by other parts of nature, and no record at all of explaining why there is a law-governed nature, because that is not a question its method can reach. - *Grant:* nobody can assign exact numbers to God. *Now collect:* then nobody can assign the tiny number either. If the prior is fuzzy, it cannot be precise enough to rule out the evidence in advance. **The closing line.** A low prior is a place to start, not a verdict. If your starting point already assumes nature is all there is, you have not weighed the evidence for God; you have ruled it out before it arrived. Let's weigh it. ## P1, A prior is a judgment, and this one is usually set by naturalism ### Affirmative case 1. **What a prior is.** In Bayesian reasoning the prior is the probability of a hypothesis given background knowledge, before the specific evidence under discussion. It is written P(H | k), and the k matters. Change the background knowledge and the prior changes. A prior is therefore a judgment about what one already knows, not an observation. See [Bayesian Probability](/codex/bayesian-probability/). 2. **For theism, the background is the whole question.** When the hypothesis is "God exists," there is no neutral pool of background facts to draw on, because the hypothesis is about the source of every fact. Swinburne's approach is to judge the prior of theism by its intrinsic features (above all its simplicity) with only tautological background knowledge, and then bring in all the evidence: the existence of the universe, its order, consciousness, moral awareness, history and experience ([Richard Swinburne](/codex/richard-swinburne/), *The Existence of God*, 2nd ed. 2004). 3. **Where the low prior usually comes from.** In practice, a very low prior for theism is set by one of two assumptions. *Methodological naturalism*: science explains by natural causes, so a non-natural cause gets near-zero weight. *Metaphysical naturalism*: only nature exists, so God gets zero or near-zero weight. See [Methodological Naturalism](/codex/methodological-naturalism/) and [Naturalism](/codex/naturalism/). 4. **Either way the argument circles.** Methodological naturalism is a rule about how a particular method works; it says nothing about whether reality contains anything beyond nature, and Plantinga distinguishes the two sharply (*Where the Conflict Really Lies*, 2011). Metaphysical naturalism is the very thesis in dispute. Using it to set the prior and then concluding naturalism from the posterior is [begging the question](/codex/begging-the-question/) with extra steps. 5. **The skeptic's own standard requires a defended prior for naturalism.** Bayes's theorem applies to both hypotheses. If theism needs a defended prior, so does the claim that a universe with its laws and constants exists with no explanation. Demanding a defense from one side only is [special pleading](/codex/special-pleading/). ### Anticipated objections 1. *"The prior for God is low on any background knowledge, because nothing we know about the world involves gods."* 2. *"Priors are subjective anyway. I'm entitled to mine."* ### Rebuttals 1. **That is the evidence talking, not the prior.** "Nothing we know involves God" is a claim about the evidence, and it is the claim the theistic arguments dispute: the existence of a contingent universe, the fine-tuning of its constants, consciousness and moral obligation are offered precisely as things we know that involve God. A prior that already excludes them has quietly counted the evidence in advance, and only one way. Failure-mode: folding a disputed reading of the evidence into the starting point. 2. **Entitled to it, yes; entitled to use it as an argument, no.** A purely personal prior can explain why someone is not persuaded, but it cannot show that anyone else is irrational. The moment the low prior is offered as a reason others should reject theism, it needs a defense like any other premise. And since posteriors update on evidence, even a personal prior obliges its holder to look at the evidence. ## P2, Theism is not shown to be complex ### Affirmative case 1. **Dawkins's argument, stated fairly.** Dawkins argues that any designer able to produce the complexity of the universe must be at least as complex, and therefore at least as improbable, as what it explains; a designer only raises the larger question of who designed the designer (as summarized by Frank Turek, *Stealing from God*, PDF p. 69). He calls God "the Ultimate Boeing 747" and holds that "God, or any intelligent, decision-making calculating agent, is complex, which is another way of saying improbable" (quoted in Plantinga, "The Dawkins Confusion," *Books & Culture*, 2007). The intuition is real: in our experience, minds run on brains, and brains are very complicated. 2. **Swinburne's rejoinder: simplicity is a feature of the hypothesis.** Swinburne answers that what makes a hypothesis simple is intrinsic to it, not how much data it explains. The theistic hypothesis postulates one entity, a person, with properties that have no limits: infinite power, knowledge and freedom. He argues that zero limits are simpler than some particular finite limit, and notes that "scientists prefer hypotheses postulating infinite qualities to hypotheses postulating very large finite quantities" when other criteria are equal (Swinburne, "Response to Richard Dawkins's comments on my writings in his book *The God Delusion*"). For the general case, see *Simplicity as Evidence of Truth* (Marquette, 1997). 3. **Swinburne's rejoinder on the brain.** Dawkins's reason for thinking God cannot be simple is apparently that a mind controlling so much would need something like an enormous brain. Swinburne replies that a person is not the same thing as the person's brain, and that we already know a simple subject controlling a complicated system: each of us does that with our own brain and body (same response). 4. **The classical rejoinder: God has no parts.** Plantinga's reply runs on a different track. On Dawkins's own definition, complexity means parts arranged in ways unlikely to arise by chance. But God "is a spirit, not a material object at all, and hence has no parts," so "given the definition of complexity Dawkins himself proposes, God is not complex" ("The Dawkins Confusion"). Classical theists go further with [Divine Simplicity](/codex/divine-simplicity/): God is not composed of parts, properties or essence and existence. Edward Feser and others argue that the "who designed the designer" question only lands against a God pictured as one more complicated being among others (see [Theistic Personalism](/codex/theistic-personalism/) and [Classical Theism](/codex/classical-theism/)). 5. **Naturalism's ledger.** Compare the starting points. Naturalism begins with a universe, with its specific laws, with its specific constants and initial conditions, and with no explanation for any of them. Each of these is a brute fact. Swinburne puts the comparison this way: if anything exists at all, it is far more likely to be something with the simplicity of God than something like the universe, with all its characteristics crying out for explanation, existing without God to explain it (*The Existence of God*, rev. ed. 1991, pp. 288-289, 291, as quoted in Kenneth Boa and Robert Bowman, *20 Compelling Evidences That God Exists*, PDF p. 23). See [Occam's Razor](/codex/occams-razor/) on counting brute facts rather than words. 6. **Necessity changes the question.** If God exists necessarily, as classical theism holds, then God is not a lucky arrangement that needed to beat the odds; Plantinga notes that on that view the probability of God's existence is 1 if God exists and 0 if not, so the claim that God is improbable because complex misdescribes the hypothesis. See [Aseity](/codex/aseity/), [Contingency Argument](/codex/contingency-argument/) and [Necessary Being is an Intelligent Mind](/codex/necessary-being-is-an-intelligent-mind/). ### Anticipated objections 1. *"Swinburne and the classical theists disagree with each other about divine simplicity. You can't use both."* 2. *"A mind that knows every fact must contain every fact. That's maximal information, so maximal complexity."* 3. *"'Simple' is doing all the work. Calling a hypothesis simple doesn't make it so."* ### Rebuttals 1. **Yes, and both defeat the same premise.** Swinburne holds a moderate view and rejects the strong Thomist doctrine; classical theists hold the strong doctrine (see [Divine Simplicity](/codex/divine-simplicity/)). But Dawkins's premise is that any God must be highly complex. Swinburne's route shows a personalist God can be a simple hypothesis; the classical route shows God has no complexity in the sense Dawkins defines. The objector has to defeat both. The disagreement among theists is real and worth saying out loud, and it does not rescue the premise. 2. **That treats knowledge as storage.** The objection pictures God's knowledge as a database whose size grows with what is known. That is how physical memory works, which is the point in dispute. On classical theism God knows creatures by knowing himself as their cause, not by holding a copy of each fact. Whether one accepts that, the objection assumes a physical model of mind, which is exactly what P4 examines. Failure-mode: importing the brain into the definition of mind. 3. **Agreed, so let's compare the two scorecards.** Simplicity has to be judged by stated criteria: number of entities, number of kinds, whether properties are arbitrary finite values or non-arbitrary limits. On those criteria the comparison is at least contested. That is enough for this page: a contested simplicity judgment cannot generate the decisive low prior the objection needs. ## P3, The track record cannot set the prior for nature as a whole ### Affirmative case 1. **The argument, stated fairly.** Lightning, disease, the planets' motions and the variety of living things were once explained by gods or spirits and are now explained by natural causes. Carrier argues that this history is an observed base rate: investigations keep finding natural causes and have never confirmed a supernatural one, so the prior for any new supernatural explanation should be extremely low (Carrier, "Naturalism Is Not an Axiom of the Sciences but a Conclusion of Them," 2020, citing *Proving History*, 2012, pp. 114-117). 2. **The record is about parts of nature explained by other parts.** Every success on the list explains one natural event by another natural process operating under the laws of nature. That is induction over mechanisms within nature. Theism's central claim is different in kind: it is about why there is a nature at all, why it is governed by laws, and why those laws and constants are as they are. There is no track record of natural explanations of nature as a whole, because any such explanation would have to use nature to explain itself. 3. **The method selects its successes.** Science adopted the rule of looking for natural causes. A method that only counts natural causes as explanations will, by design, report only natural explanations. Its success shows the rule is fruitful within its scope; it cannot also be evidence that nothing lies outside that scope. See [Methodological Naturalism Critique](/codex/methodological-naturalism-critique/). 4. **The record cuts both ways.** Naturalistic expectations have also been overturned: the steady-state model, which avoided a cosmic beginning, was abandoned after the cosmic microwave background was discovered in 1965 (see [Kalam Cosmological Argument](/codex/kalam-cosmological-argument/)). The fine-tuning of the constants was a discovery, not a theological wish ([Fine-Tuning Argument](/codex/fine-tuning-argument/)). Inductions from history do not run in only one direction. 5. **"Zero" assumes the disputed cases are settled.** The base rate of confirmed supernatural causes is zero only if every candidate, the resurrection included, has already been judged natural. Using that count to set the prior for the resurrection decides the case before hearing it. Large modern collections of miracle claims, such as Craig Keener's *Miracles* (2011), are at least evidence that the count is contested. See [Argument from Miracles](/codex/argument-from-miracles/). ### Anticipated objections 1. *"Gods of the gaps keep shrinking. The trend is obvious."* 2. *"If theism were true, why hasn't science ever found God's fingerprints?"* ### Rebuttals 1. **The trend is real for gaps, and the theistic arguments are not gaps.** The [God of the Gaps Objection Defeater](/codex/god-of-the-gaps-objection-defeater/) makes the point in full: a god invoked for one unexplained event can be displaced by a mechanism. The cosmological, fine-tuning, consciousness and moral arguments are not placed in ignorance; they start from what is known, such as the measured values of constants or the existence of the laws themselves. A shrinking-gaps induction does not reach them. 2. **Because the method doesn't look for fingerprints in that place.** On theism, God is not one cause among the causes science studies but the ground of the whole order those causes belong to. The evidence theism points to is the existence and character of that order, which science presupposes. Asking a lab to detect the source of the laws by applying the laws is like asking a ruler to measure its own length. ## P4, Program-length priors do not settle the question This premise concerns a technical and genuinely contested area of philosophy and computer science. The points below are offered as reasons the argument is not decisive, not as a refutation. ### Affirmative case 1. **The argument, stated fairly.** Solomonoff induction gives each hypothesis a prior that shrinks exponentially with the length of the shortest program that produces the data. Yudkowsky argues that "a witch did it" or "Thor did it" sounds short in English but is long as a program, because it requires specifying a mind, and he notes that "the human brain is the most complex artifact in the known universe" ("Occam's Razor," 2007). On this measure, a hypothesis built around a mind is heavily penalized. 2. **It assumes the mind is a physical program.** The penalty comes from treating the divine mind as something that must be simulated step by step, like a brain. That assumes minds are computational processes in a physical medium, which is the disputed claim of physicalism about the mind. The theist holds that God is not a physical system, and many hold that even human consciousness is not reducible to computation. See [Argument from Consciousness](/codex/argument-from-consciousness/) and [Consciousness Emerges from Neurons Objection Defeater](/codex/consciousness-emerges-from-neurons-objection-defeater/). 3. **The choice of language is arbitrary.** Program length depends on which universal computer, or description language, one uses. The standard result is that switching languages changes lengths only by a constant, and Yudkowsky acknowledges this ("only a constant complexity penalty"). But that constant can be large, there is no privileged language, and for a one-off comparison between two whole-world hypotheses the constant is not negligible. A language with a primitive for "unlimited agent" makes theism short; one without it makes theism long. The prior reflects the choice. 4. **The naturalist program has to encode the details.** A program that outputs our universe on naturalism must contain its particular laws, its constants to the precision observed and its low-entropy initial state. Those specific values are exactly what make fine-tuning striking. Program length penalizes arbitrary detail, and naturalism has to carry the detail as raw input. 5. **The ideal measure cannot actually be computed.** Solomonoff's prior is uncomputable in principle. Real uses rely on approximations and intuitions about what "counts as short," which returns the debate to the judgments discussed in P2. ### Anticipated objections 1. *"The constant washes out with enough data."* 2. *"Any mind we know of is complex. You're inventing a mind that is conveniently exempt."* ### Rebuttals 1. **Not for this question.** Washing out works when many observations are fed through the same hypotheses over time. The comparison between theism and naturalism is a comparison of explanations of one universe, so there is no long run in which the language-dependence fades. The objector is borrowing a convergence result from a setting where it applies to a setting where it does not. 2. **Every mind we know of is also embodied and finite.** The theist is not inventing an exception to the evidence; the hypothesis has always been that God is not embodied and not finite. One can argue that such a mind is impossible, but that is a different argument from "the program would be long," and it has to be made on its own terms. ## P5, "Extraordinary" means low prior, and testimony overcomes low priors routinely ### Affirmative case 1. **Three meanings.** "Extraordinary claims require extraordinary evidence" can mean (a) a claim with a low prior needs a high likelihood ratio, which is true and is just Bayes; (b) a claim that conflicts with current belief needs evidence that would satisfy a skeptic, which is reasonable; or (c) a claim about God or miracles cannot be established by any evidence we could have, which is not a principle of probability but a refusal. The slogan wins arguments by sounding like (a) and functioning like (c). See [Burden of Proof](/codex/burden-of-proof/) and the Sagan premise in [Epistemology Defeats Christianity Objection Defeater](/codex/epistemology-defeats-christianity-objection-defeater/). 2. **Low-prior events are established by testimony every day.** The odds that a particular ticket wins a lottery are tiny, yet a single news report of the winning number is enough to convince almost everyone. The reason is that the report would be very unlikely if that number had not won. That is a high likelihood ratio, and it overcomes the low prior. Extraordinary evidence, in the only sense the math supports, means evidence that would be very unlikely if the claim were false. It does not mean evidence of a special, unavailable kind. 3. **Hume sets a test, not a wall.** Hume's maxim is that "no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish" (*Enquiry*, Section X, Part I). Read in probability terms, that is a comparison: is it less likely that the witnesses are all mistaken or lying, given everything we know about them, than that the event happened? That question can only be answered by looking at the witnesses. Hume himself grants that the Indian prince who disbelieved reports of frozen water "reasoned justly," yet the reports were true. 4. **The prior comes back in.** Hume's "uniform experience against every miraculous event" is a prior set by induction over ordinary events, P3's argument in an earlier form. The prior that matters is not "how often do dead men rise" but "how likely is it that God raised this man, given everything else we know," which depends on the prior for theism. See [Argument from Miracles](/codex/argument-from-miracles/). 5. **The leading treatment.** John Earman, a philosopher of science at the University of Pittsburgh, argues in *Hume's Abject Failure: The Argument Against Miracles* (Oxford, 2000) that Hume's essay, analyzed in probability terms, is largely unoriginal or mistaken where it is not trivial, and that the reliability of testimony must be assessed case by case. Earman's book does not argue that any miracle occurred; its target is the shortcut. As Paul put the question to King Agrippa: "Why is it judged incredible with you, if God doth raise the dead?" ([Acts 26:8](/codex/acts-26-8/), ASV). The resurrection's improbability on naturalism is not in dispute; its improbability given that God exists is. ### Anticipated objections 1. *"A lottery has to have a winner. Nobody has to rise from the dead."* 2. *"Witnesses are unreliable. The base rate of mistaken testimony is far higher than the base rate of resurrections."* ### Rebuttals 1. **Then compare like with like.** The lottery example only shows that low priors can be overcome by testimony; it does not claim resurrections are as common as lottery wins. The fair version of the objection is that resurrections have a very low prior, which is P5's point (a), and the answer is to ask how unlikely the specific evidence is if the resurrection did not happen. That is the question the McGrews attempt to answer (P6). 2. **In general, yes; in this case, that is what must be shown.** Mistaken testimony is common in general. The question is how likely this particular pattern of testimony is on the hypothesis that nothing happened: multiple witnesses, including skeptics and an enemy, claiming physical encounters, at personal cost, in a place where the claim could be checked ([Acts 26:26](/codex/acts-26-26/): "this hath not been done in a corner"). Generic base rates of error do not answer that. See [Minimal Facts Argument](/codex/minimal-facts-argument/) and [Resurrection of Jesus - Naturalistic Counter-Theories](/codex/resurrection-of-jesus-naturalistic-counter-theories/). ## P6, Priors are not destiny ### Affirmative case 1. **The rule.** In odds form, Bayes's theorem says: posterior odds = prior odds × likelihood ratio. The likelihood ratio for a piece of evidence is how probable it is if the hypothesis is true, divided by how probable it is if the hypothesis is false. When pieces of evidence are independent, their ratios multiply. 2. **A toy example (illustrative numbers only).** The numbers below are made up to show how the rule works. They are not estimates of the real strength of any argument. | Step | Evidence (illustrative) | Likelihood ratio | Odds after this step | Probability | |---|---|---|---|---| | Start | Skeptical prior | | 1 to 1,000 | about 0.1% | | 1 | Evidence A | 10 | 1 to 100 | about 1% | | 2 | Evidence B | 5 | 1 to 20 | about 5% | | 3 | Evidence C | 4 | 1 to 5 | about 17% | | 4 | Evidence D | 20 | 4 to 1 | 80% | | 5 | Evidence E, which counts against | 1/2 | 2 to 1 | about 67% | 3. **What the example shows.** No single item settles anything; the third step still leaves the hypothesis unlikely. A prior of one in a thousand is overcome by four moderate, independent pieces of evidence. Evidence against the hypothesis (step 5) pulls the odds back, and an honest case must include it. And everything depends on independence: if B and C are really the same evidence counted twice, multiplying them overstates the case. 4. **The real evidence classes.** The cumulative case points to the existence of a contingent universe ([Contingency Argument](/codex/contingency-argument/), [Kalam Cosmological Argument](/codex/kalam-cosmological-argument/)), the fine-tuning of its constants ([Fine-Tuning Argument](/codex/fine-tuning-argument/)), the existence of consciousness ([Argument from Consciousness](/codex/argument-from-consciousness/)), objective moral facts ([Moral Argument](/codex/moral-argument/)), and the historical data surrounding Jesus's death ([Minimal Facts Argument](/codex/minimal-facts-argument/), [Argument from the Resurrection](/codex/argument-from-the-resurrection/)). On the other side stand evil and divine hiddenness. Each class has to be argued on its own; see [Bayesian Argument for Theism](/codex/bayesian-argument-for-theism/) and [Cumulative Case for Christian Theism](/codex/cumulative-case-for-christian-theism/). This page does not assign them numbers. 5. **Published Bayesian treatments.** Swinburne's *The Existence of God* (1979, 2nd ed. 2004) works through the evidence classes in turn and concludes that theism is more probable than not on the total evidence, largely without assigning exact figures. Timothy and Lydia McGrew's chapter "The Argument from Miracles: A Cumulative Case for the Resurrection of Jesus of Nazareth," in *The Blackwell Companion to Natural Theology* (ed. Craig and Moreland, 2009), does not set a prior for the resurrection. It estimates likelihood ratios for three bodies of testimony (about 10^2 for the women, 10^39 for thirteen disciples treated as independent, 10^3 for Paul), multiplies them to about 10^44, and observes that this "would be sufficient to overcome a prior probability (or rather improbability) of 10^-40." The authors state that the result depends on the general reliability of the Gospels and Acts on ordinary matters. Stephen Unwin's *The Probability of God* (2003) is a popular example that reaches 67% from a starting prior of 50%; reviewers criticized the 50% starting point and the subjectivity of his inputs, and it is best used as an illustration of the method rather than as evidence. ### Anticipated objections 1. *"The McGrews' numbers are made up. 10^39 for the disciples is absurd."* 2. *"Your toy example is rigged. Pick a prior of one in a trillion and see what happens."* 3. *"Swinburne's 'more probable than not' is just his intuition in disguise."* ### Rebuttals 1. **The exact numbers are judgments, and the authors say so.** Critics have pressed the McGrews hardest on the independence of the thirteen witnesses and on the reliability assumption, and those are fair targets. But the structure of the argument does not need 10^39. If each disciple's testimony were only ten times more likely on the resurrection than on its denial, rather than a thousand times, thirteen independent witnesses would still yield 10^13. The real dispute is about independence and reliability, which are historical questions, and that is where the argument belongs. 2. **Then argue for that prior.** With a prior of one in a trillion the toy evidence would not suffice; that is what the math says, and it is why the source of the prior (P1) and the simplicity contest (P2) matter. A prior that low has to be defended, and the defenses offered for it (complexity, track record, program length) are the ones this page examines. The math also cuts the other way: no finite prior is beyond the reach of strong enough evidence. 3. **Every prior is a judgment, including the skeptic's.** Swinburne at least states his criteria and argues for them, which allows them to be examined. A skeptic who rejects his judgment should say which criterion fails and what replaces it. "Intuition in disguise" applies just as much to an unstated low prior. ## Master objections to the defeater **MO1: "Fine, priors are fuzzy. But fuzzy in my favor. I'll keep my low prior until you show me a likelihood ratio big enough."** - This is the strongest remaining form of the objection, and it is legitimate as far as it goes: a person may start skeptical and ask for strong evidence. But it concedes the page's main point. The objection is no longer "theism has a low prior, so the evidence can't matter"; it is "show me the evidence." That is an invitation to weigh the evidence classes in P6, one by one, with attention to independence and to the evidence against. The defender should accept it gladly and should not overclaim: the honest goal is to show that the evidence shifts the odds strongly, not that it reaches certainty. **MO2: "Theism isn't one hypothesis. There are countless possible gods, so each specific one, including the Christian God, gets a tiny share of the prior."** - This is a serious point about how priors are divided. Two replies. First, the bare hypothesis of a single unlimited, perfectly free and knowing being is not one of countless arbitrary options; the absence of limits is what makes it simpler than gods with particular finite powers, which is Swinburne's argument again (P2). Second, the narrowing from theism to Christianity is done by evidence, above all the historical evidence about Jesus, not by the prior. See [Christian God is the Only True God](/codex/christian-god-is-the-only-true-god/) and [Evil God Objection Defeater](/codex/evil-god-objection-defeater/) for the parallel worry about a malevolent god. **MO3: "Swinburne is a 'crank Bayesian.' His simplicity measure was built to favor God."** - Carrier has criticized Swinburne and Unwin in those terms. Swinburne's simplicity criteria (few entities, few kinds, non-arbitrary properties, mathematically simple laws) were set out as general principles of theory choice in science, in *Simplicity as Evidence of Truth* (1997) and his epistemology, and they apply to scientific theories that have nothing to do with God. One may reject them, but then one needs an alternative measure, and the alternatives (Dawkins's parts-arrangement complexity, program length) face the problems in P2 and P4. **MO4: "If God is necessary, the prior is 1 or 0, and you've made Bayes useless."** - For metaphysical necessity, yes: if God exists necessarily, the objective probability is 1 or 0. But the prior in a debate is epistemic: how confident we should be, given what we know, that the necessary being exists. That remains open, and evidence bears on it in the ordinary way, just as evidence bears on a mathematical conjecture that is necessarily true or necessarily false before it is proved. **MO5: "Extraordinary evidence for God would be easy to give. A message in the stars would do it. The absence of that is evidence against."** - That is the hiddenness argument, a likelihood consideration rather than a prior, and it belongs in the ledger as evidence against, like step 5 of the toy example. It is answered on its own terms in [Divine Hiddenness Objection Defeater](/codex/divine-hiddenness-objection-defeater/). Its presence is a reason to include it in the weighing, not a reason to refuse to weigh. ## Tactical opening / closing **Opening.** I'm glad you put it in terms of probability, because I think that's the right way to think about it. So let's be careful about it. Where does your starting number for God come from? And what's the starting number for the alternative, a universe that exists with these exact laws and no explanation? Let's put both on the table before we look at the evidence. **Closing.** Here's where I think we've landed. Your starting number was a judgment, not a measurement, and some of it came from assuming nature is all there is. God isn't obviously complicated, and nature has a lot of brute facts of its own. And even a skeptical starting point can be moved by strong evidence. I'm not asking you to believe because of a formula. I'm asking you to look at the evidence as if it might count. Will you look at it with me? ## Live-cite kit **Scripture:** - [Acts 26:8](/codex/acts-26-8/), "Why is it judged incredible with you, if God doth raise the dead?" (ASV) - [Acts 26:26](/codex/acts-26-26/), "for this hath not been done in a corner." (ASV) - [Romans 1:20](/codex/romans-1-20/), "For the invisible things of him since the creation of the world are clearly seen, being perceived through the things that are made, even his everlasting power and divinity" (ASV) **Scholarly (the objection, stated fairly):** - David Hume, *An Enquiry Concerning Human Understanding* (1748), Section X, "Of Miracles." - Carl Sagan, *Cosmos* (1980), episode 12, "Encyclopaedia Galactica." - Richard Dawkins, *The God Delusion* (2006), chapter 4, "Why there almost certainly is no God." - Eliezer Yudkowsky, "Occam's Razor" (LessWrong, 2007). - Richard Carrier, *Proving History* (2012), and "Naturalism Is Not an Axiom of the Sciences but a Conclusion of Them" (2020). **Scholarly (the reply):** - Richard Swinburne, *The Existence of God* (1979; 2nd ed. 2004), and *Simplicity as Evidence of Truth* (Marquette University Press, 1997). - Richard Swinburne, "Response to Richard Dawkins's comments on my writings in his book *The God Delusion*." - Alvin Plantinga, "The Dawkins Confusion: Naturalism ad absurdum," *Books & Culture* (March/April 2007). - John Earman, *Hume's Abject Failure: The Argument Against Miracles* (Oxford University Press, 2000). - Timothy McGrew and Lydia McGrew, "The Argument from Miracles: A Cumulative Case for the Resurrection of Jesus of Nazareth," in William Lane Craig and J. P. Moreland, eds., *The Blackwell Companion to Natural Theology* (2009). - Alvin Plantinga, *Where the Conflict Really Lies* (2011), on methodological and metaphysical naturalism. - Stephen Unwin, *The Probability of God* (2003), a popular worked example, criticized for its 50% starting prior. **Aphorism:** "A low prior is a place to start, not a verdict." **Aphorism:** "If nature is your prior, nature will be your posterior." ## Connection to Scripture - [Acts 26:8](/codex/acts-26-8/), Paul names the real question: whether God's raising the dead is incredible. - [Acts 26:26](/codex/acts-26-26/), the claim was public and checkable. - [Romans 1:20](/codex/romans-1-20/), creation itself as evidence that bears on God's power and nature. ## See also - [Bayesian Probability](/codex/bayesian-probability/), the framework, its terms and the odds form. - [Bayesian Argument for Theism](/codex/bayesian-argument-for-theism/), the positive cumulative case this page clears the ground for. - [Epistemology Defeats Christianity Objection Defeater](/codex/epistemology-defeats-christianity-objection-defeater/), the wider "epistemology" slogan, with premises on Hume and Sagan. - [Occam's Razor](/codex/occams-razor/), parsimony measured by brute facts, not word counts. - [Graham Oppy Arguments and Their Defeaters](/codex/graham-oppy-arguments-and-their-defeaters/), the academic theory-comparison version of the simplicity case. - [Divine Simplicity](/codex/divine-simplicity/), [Classical Theism](/codex/classical-theism/) and [Theistic Personalism](/codex/theistic-personalism/), the two theistic accounts of why God is not complex. - [Richard Dawkins](/codex/richard-dawkins/), the "who designed the designer" argument. - [Richard Swinburne](/codex/richard-swinburne/), the leading defender of theism's intrinsic simplicity. - [David Hume](/codex/david-hume/), the miracles argument as a prior argument. - [Argument from Miracles](/codex/argument-from-miracles/), the full treatment of Hume and testimony. - [God of the Gaps Objection Defeater](/codex/god-of-the-gaps-objection-defeater/), why the theistic arguments are not gaps. - [Methodological Naturalism](/codex/methodological-naturalism/) and [Methodological Naturalism Critique](/codex/methodological-naturalism-critique/), the rule of method versus the claim about reality. - [Burden of Proof](/codex/burden-of-proof/), who has to show what. - [Fine-Tuning Argument](/codex/fine-tuning-argument/), [Argument from Consciousness](/codex/argument-from-consciousness/), [Moral Argument](/codex/moral-argument/) and [Minimal Facts Argument](/codex/minimal-facts-argument/), the evidence classes. - [Atheism](/codex/atheism/), the master hub. ## Common questions this page answers **Q: What does it mean to say God has a low prior probability?** It means that, before looking at specific evidence, the person judges God's existence to be very unlikely, so that ordinary evidence could never make it likely. The prior is a judgment based on background knowledge, not a measured fact, so the first question is where the low number came from and whether it already assumes that nature is all there is. **Q: Is God too complex to be probable, as Richard Dawkins argues?** Dawkins argues that any designer must be at least as complex, and so as improbable, as what it designs. Richard Swinburne replies that one person with no limits on power, knowledge or freedom is an intrinsically simple hypothesis, and Alvin Plantinga replies that God is a spirit with no parts, so on Dawkins's own definition God is not complex. Naturalism, by contrast, starts with a universe, its laws and its constants as unexplained brute facts. **Q: Hasn't science shown that supernatural explanations always fail?** Science has repeatedly explained events within nature by other natural processes. That record cannot tell us why there is a law-governed nature at all, which is what the main arguments for God are about. And counting the success rate of supernatural explanations as zero assumes the disputed cases, such as the resurrection, have already been settled. **Q: Do extraordinary claims require extraordinary evidence?** In the only sense probability supports, an extraordinary claim is one with a low prior, and it needs evidence that would be very unlikely if the claim were false. Testimony meets that standard for improbable events every day, such as a report of the winning lottery number. The slogan becomes a problem only when it is used to mean that no possible evidence could count. **Q: Can evidence overcome a very low prior probability?** Yes. In odds form, Bayes's theorem says posterior odds equal prior odds times the likelihood ratio, so any finite prior can be overcome by evidence strong enough. Timothy and Lydia McGrew argue that, on their assumptions, the testimony for the resurrection could overcome a prior as low as 10^-40, though critics dispute their independence and reliability assumptions. **Q: Does Kolmogorov complexity or Solomonoff induction prove God is improbable?** No. Those measures assign low priors to hypotheses that need long computer programs, and they treat a mind as something to be simulated like a brain, which assumes the mind is physical. Program length also depends on an arbitrary choice of description language, and the ideal measure cannot actually be computed, so it cannot deliver a decisive prior on a question about the universe as a whole. **Q: Does Bayesian math prove that God exists?** No, and honest defenders do not claim it does. Probability estimates for questions this large involve judgment at every step. What the math shows is that a low starting point does not settle the matter, and that the evidence, including the evidence against, has to be weighed.