A Bayesian and Abductive Approach to Evil

The evidential argument from evil contends that the existence of evil (or at least certain kinds of evil) makes God's existence less likely than a godless universe. Using Bayesian probability, we can examine this claim more carefully. This approach lets us weigh competing explanations and see which better accounts for the data we observe.

Although these are not logical dichotomies, this post will discuss how we could use Bayesian and abductive reasoning to contrast whether perfect being theism (belief in the existence of an all-powerful and morally perfect God) or naturalism (belief that only natural forces exist) better explains the evidence of evil. While I'm a theist, I recognize the strength of the opposing view and aim to present both sides fairly.

The evidential argument from evil

Philosopher William Rowe put the evidential argument this way:¹

1. No good we know of justifies an omnipotent, omniscient, perfectly good being in permitting particular cases of horrendous suffering.

2. [Probably] No good at all justifies an omnipotent, omniscient, perfectly good being in permitting particular cases of horrendous suffering.

3. (Therefore) [Probably] There is no omnipotent, omniscient, perfectly good being. 

This reasoning seems sound at first glance. If a loving God would likely prevent pointless suffering, the fact that such seemingly pointless suffering exists suggests or makes it more likely that no such God exists.

But we need to look deeper at how well each worldview explains not just evil, but everything else we observe.

Bayesian reasoning

Bayesian reasoning helps us update our beliefs when we encounter new evidence. It uses a mathematical formula called Bayes' theorem:

P(H|E) = P(E|H) × P(H) / P(E)

This looks complex, but the idea is simple. We start with some initial belief about how likely something is (the "prior probability"). When we see new evidence, we adjust our belief to get a final assessment (the "posterior probability"). The term “hypothesis” is being used to mean any claim whose probability you’re trying to assess in light of evidence.

For the problem of evil:

• P(E|H) is the likelihood or probability P of observing the evidence E given that the hypothesis H (either theism or naturalism).

• P(H|E) is the likelihood or probability P of the hypothesis H after considering the evidence E.

• P(H) is the prior probability P of the hypothesis H. It’s how likely you think H is true before you look at the evidence E.

• P(E) is the probability P of the evidence E. It tells you how likely it is that E would happen at all, regardless of whether H is true.

From the perfect theism view: P(H), the prior probability of theism, is not low. P(E|H), the probability that a life-permitting universe would exist (given that God exists), is high. P(E), the probability that a life-permitting universe exists (regardless of whether God exists), is low.

In contrast, an atheist might have these credences for perfect being theism: P(H) is low, P(E|H) is uncertain or low, and P(E) is unknown or possibly not low.

Not all data is evidence

In the context of Bayesian reasoning and scientific inquiry, data and evidence are related but distinct concepts. Data is the raw observations or measurements collected from experiments or other sources. Data are objective facts or figures without interpretation or context. For example, the measured value of the cosmological constant or a list of fulfilled prophecies is data. Evidence is data that have been interpreted or evaluated in the context of a specific hypothesis or question. If data is deemed relevant to assessing the truthhood (or falsehood) or likelihood (or unlikelihood) of a hypothesis, then it is evidence (or disevidence). For example, the fact that the cosmological constant value supports a life-permitting universe is evidence for the fine-tuning argument. The existence of seemingly gratuitous evil is evidence supporting the absence of a loving God.

The atheistic evidential argument from evil says that suffering makes theism less likely than naturalism. But this depends on how well each view explains what we see.

In Bayesian reasoning, the posterior probability represents how likely a hypothesis is given the evidence. If theism and naturalism have equal posterior probabilities when evaluated against the evidence of evil, Bayesian analysis alone cannot favor one over the other. This occurs when the product of the likelihood and prior probability for each hypothesis equals out. For example, naturalism might have a higher prior probability due to its alignment with a scientific worldview, but theism could compensate with a higher likelihood through theodicies like free will or divine providence to govern the world in an orderly and rational manner, fulfilled prophecies, or cosmological arguments for a deity.

When the posterior probabilities for two hypotheses are equal, it means that both hypotheses are equally probable according to Bayes' theorem. To resolve this stalemate, theologians deploy abductive arguments, which make an inference to the best explanation, to examine if there is an explanation or hypothesis that better accommodates the data based on some relevant criteria.

Five common ways to judge a hypothesis

This stalemate situation can arise when a competing hypothesis, sometimes called a "stalking horse," is deliberately constructed to explain the same data equally well, matching the likelihood of another hypothesis despite different priors. This stalking horse approach is perfectly legitimate, because it can reveal the limitations of the hypothesis it's set against.

An example of a stalking horse explanation would be to propose that cookie-eating fairies are responsible for missing midnight snacks. A cookie-eating fairy hypothesis could be engineered just so to explain all of the same data (like the missing cookies and hallway light) as the hypothesis that someone in the household got a late-night snack. 

When two hypotheses have the same posterior probability, you need something else to choose between them. Bayesianism gives you degrees of belief, but not always a clear winner. So several criteria have been developed to reveal why a hypothesis with an equal posterior probability can still be preferred over another.² 

When scientists and philosophers compare competing theories, some of these criteria can be:

1. Explanatory scope: How much can the theory explain

2. Explanatory power: How well does it explain specific details

3. Plausibility: How believable is the theory given what we already know

4. Ad hoc-ness: If the theory relies on convenient assumptions made just to fit the data

5. Illumination: How well the theory helps us understand other things

Explanatory scope (what can it explain)

Explanatory scope asks how much territory does each theory cover.

Perfect being theism attempts to explain evil within a larger story about reality. It connects suffering to several other phenomena:

• Moral and natural evil: Free will explains why people choose evil, while natural disasters might serve purposes we don't fully grasp

• Cosmic purpose: Evil fits into a bigger narrative about human growth, divine justice, or life after death

• Fine-tuning: The precise conditions that allow life to exist is expected if God seeks to govern the world by rational and orderly natural laws that reflect God's rational and orderly nature.

• Moral awareness: Why humans have strong intuitions about right and wrong

• Religious experience: Why people across cultures report encounters with the divine

• Consciousness: The mystery of intentional conscious experience from indifferent unconscious matter.

The free will defense, for example, says God allows moral evil because eliminating it would require eliminating genuine choice. Without real freedom, love and moral responsibility become impossible. This connects the existence of evil to fundamental questions about human nature and relationships.

Naturalism explains evil as the inevitable result of natural processes folding into one another. Evolution produces creatures that can suffer because pain helps survival. Natural disasters occur because of physics and geology, not malice.

This explanation works for why suffering exists. But naturalism struggles with related questions:

• Why do humans see some suffering as gratuitous or wrong?

• How did moral consciousness emerge from mindless matter?

• Why does the early conditions and constants of the universe appear fine-tuned to be life permitting or determined by a necessary physical law if the early conditions and constants had to be what they were?

Naturalists can often answer the questions above, but only after bootstrapping additional constraints onto the naturalist theory. Each puzzle requires a separate naturalistic explanation. The theory fragments into multiple parts rather than forming a unified whole.

Perfect being theism offers a more unified framework. There exists at the foundation of reality a perfect being that aims to share Himself with others, which is a common expression of how rational agent's demonstrate they value something, by sharing what they value with others. It links evil to questions about purpose, morality, consciousness, and cosmic design. Naturalism explains evil well but leaves many related phenomena unexplained or requires additional theories to address them.

Explanatory power (how well do the details fit)

Explanatory power measures how well a theory accounts for specific features of what we observe.

Several theistic explanations make the existence of evil not just compatible with God's existence, but expected:

• Free will defense: God values genuine relationships, which require real choice. This makes moral evil likely in any world with free yet-to-be sanctified creatures.

• Nomological: Suffering (natural evil) arises as an unavoidable consequence or by-product of the physical laws designed to limit moral evil.

• Afterlife compensation: Present suffering might be balanced by future justice or reward.

Naturalism explains suffering as a byproduct of natural selection and physical laws. Pain motivates survival behaviors. Natural disasters result from geological processes. This broad explanation fits the evidence.

But naturalism struggles with why suffering feels gratuitous to us. If pain is just a survival mechanism, why do humans have such strong intuitions that some suffering is meaningless or unjust? Why did evolution give us moral sentiments that judge the very processes that created us? I'm not saying naturalists don't have answers here, but naturalism has to adopt evermore assumptions to maintain an expectation for these phenomena.

Both views can account for evil's existence, but perfect being theism better explains the specific ways humans experience and respond to suffering. The patterns of growth through adversity and moral outrage at injustice fit theistic predictions more harmoniously than naturalistic ones.

Plausibility (how believable are the basic assumptions)

Plausibility concerns how reasonable each theory seems given our background knowledge.

Perfect being theism's plausibility depends partly on other arguments for God's existence:

• Cosmological arguments answer why does anything exist rather than nothing.

• Fine-tuning arguments answer why are the physical constants precisely calibrated for a life-permitting universe.

• Moral arguments explain how objective moral truths fit in a purely physical universe.

• Ontological arguments reveal the divine and perfectly great nature of God.

If these arguments have force, they raise theism's likelihood of observing the evidence of evil. The existence of evil then becomes one piece of evidence to weigh against others, rather than a decisive refutation.

Naturalism appeals to many because it avoids supernatural entities and relies instead on observable natural phenomena. Naturalists argue that theism has a decreased likelihood because it posits both a natural and a speculative supernatural world.

Both worldviews face challenges to their basic plausibility. The question is which set of challenges is more manageable. This depends partly on your starting assumptions and which arguments you find compelling. Perfect being theism argues that theism doesn't add an extra layer of reality beyond the natural world, as naturalists might suggest. Instead, theism posits two types of entities: a necessary entity (God), which explains existence itself, and contingent entities (the natural world), which are explained by God. Naturalism, on the other hand, accepts contingent entities (the natural world) and either explainable or unexplained necessary entities, without requiring a divine explanation. So perfect being theism is committed to no more categories of entities and perhaps even one fewer than naturalism.

Ad hoc-ness (are the explanations convenient or principled)

Ad hoc explanations are suspiciously tailored to fit problematic evidence. Principled explanations flow naturally from the theory's basic prior commitments.

Major theistic responses to evil build on core theological concepts that exist independently:

• Free will is central to most theistic traditions because personal relationship with God requires genuine choice

• Soul-making connects to theological views about human purpose and spiritual development

• Afterlife is a standard component of most theistic religions, not invented to solve the problem of evil

• Divine mystery follows from the belief that God's understanding exceeds human comprehension

These are natural extensions of theistic belief in a perfect being.

Naturalism's basic explanation of evil isn't ad hoc. Suffering naturally results from physical processes. But explaining related phenomena sometimes requires additional assumptions:

• Why did evolution produce moral consciousness that judges in-group favoritism as unjust?

• How could evolution allow us to desire for non-existent transcendent meaning?

Some naturalistic answers to these questions feel more forced than theistic ones. However, an atheistic naturalist likely has the opposite intuition or seeming.

Both views can explain evil without obviously ad hoc moves. But theism's broader explanations seem to flow more naturally from its core commitments.

Illumination (what new insights does each view provide)

Illumination measures how much a theory helps us understand other areas of knowledge.

Perfect being theism links the problem of evil to many other domains:

• Philosophy: What gives life meaning and purpose?

• Ethics: What grounds moral values and duties?

• Psychology: Why do humans search for transcendence and hope?

• Anthropology: Why do almost all cultures develop religious beliefs?

The problem of evil becomes part of a larger conversation about human nature, purpose, and ultimate reality.

Naturalism explains evil mechanistically without need for an unseen agent but offers fewer connections to broader questions. Physical processes account for suffering, but this doesn't illuminate questions about meaning, purpose, or value that suffering raises for humans.

Naturalistic explanations of related phenomena (consciousness, morality, religious experience) often require separate theoretical frameworks that don't obviously connect to each other or to the explanation of evil.

Theism provides a more illuminating framework by connecting evil to fundamental questions about existence, purpose, and value. Naturalism's explanations are more isolated and mechanistic.

Putting it together

Recalling the two hypothesis for the missing late-night snacks, the household snack hypothesis is more fitting based on the criteria discussed.

• Explanatory scope: The household member hypothesis explains the missing cookies and the hallway light, but the fairy hypothesis only explains the cookies.

• Explanatory power: Household members eating at night fits known behavior, but but eating cookies is not a common trait associated with fairies.

• Plausibility: People getting snacks is common, but fairies are not known to exist.

• Ad hoc-ness: The household explanation uses ordinary assumptions, but the fairy hypothesis adds an unseen agent just to explain this case.

• Illumination: The household view fits with how people act and may suggest a pattern, but the fairy view adds nothing useful beyond this event.

The evidential argument from evil claims that gratuitous suffering makes God's existence less likely. I would argue that this focus misses the bigger picture. When we evaluate perfect being theism and naturalism across multiple criteria, the god-hypothesis often performs better.

This doesn't prove theism is true. Both worldviews face serious challenges, and reasonable people disagree about which set of problems is more manageable.

I should acknowledge several limitations in my analysis:

• Some suffering seems truly pointless and excessive.

• Hidden purpose explanations can become unfalsifiable.

• Different religions offer conflicting accounts of evil.

• No single theodicy accounts for the moral permissibility of all evils.

Naturalism's strengths avoids the complexity of theological explanations, deploys a scientific understanding of suffering that continues to advance, and doesn't require defending problematic religious doctrines or truth-claims.

I don't claim to have solved it or proven beyond all doubt that theism is more probable than naturalism. The evidence is complex, and our reasoning is fallible.

But I do think the evidential argument from evil is weaker than it initially appears. When we look beyond the narrow question of whether God would allow suffering, theism offers a richer, more unified explanation of human experience, at least by my lights.

The existence of evil is compatible with God's existence when we consider the broader context of human freedom and moral development, both of which lead to our final cosmic purpose. These explanations may not satisfy everyone, but they're more substantial than critics sometimes acknowledge.

At the same time, naturalism deserves respect as a coherent worldview that explains much about our universe. The most candid conclusion is that both worldviews face puzzles, and neither provides easy answers to life's deepest questions. The problem of evil challenges theists to think carefully about God's nature and purposes.

What matters most may not be which view wins in some abstract sense, but how these questions shape the way we live. Both theists and naturalists can find resources in their worldviews for responding compassionately to suffering and working to reduce it where possible.

Image credit

1. J.L. Fisher, “Realism and the Absence of Value,” PhilArchive, https://philpapers.org/archive/OPPREA.pdf.

2. William Lane Craig and J.P. Moreland, Philosophical Foundations for a Christian Worldview (Downers Grove, IL: InterVarsity Press, 2003), 111, https://archive.org/details/wlc-and-jp-moreland-philosophical-foundations-for-a-christian-worldview/page/n111/mode/2up.