How is divine hiddenness formulated in contemporary Bayesian terms (Charity Anderson, Sanford Russell), and does this formulation succeed in overcoming skeptical theist responses?

This issue lies at the heart of contemporary analytic philosophy of religion, where Bayesian probabilistic tools are used to formulate the problem of divine hiddenness with mathematical precision. This methodological development is important because it moves the discussion from the rhetorical level to the precise analytical level.

Inadequate Responses to Avoid

From some defenders of theism:

"Bayesian formulation is merely mathematical complexity that adds nothing." This is a reductive oversimplification. Bayesian formulation reveals the logical structure of the argument and precisely identifies points of disagreement. Rejecting it merely for being "complex" misses its analytical value.

"God cannot be tested by probabilities." This confuses levels of analysis. Probabilities here are tools for analyzing the reasonableness of beliefs, not "testing" God. Even classical theism used logical tools to analyze arguments.

"Believers find God, so there is no hiddenness." This ignores the core of the problem. The question is not about the existence of believers, but about the existence of sincere nonbelievers who seek but do not find.

From some critics:

"Bayesian formulation proves the impossibility of a loving God." This is an unjustified leap. Bayesian formulation provides a probabilistic argument, not a definitive proof. Confusing "reduces probability" with "proves impossibility" is a logical error.

"Anyone who doesn't believe is a sincere seeker who is hidden from." This is an unsupported generalization. The existence of some sincere seekers who are hidden from does not mean that every nonbeliever is such.

"Skeptical theism is merely a maneuver to avoid the problem." This is reductive. Skeptical theism is a philosophical position with deep historical roots, not merely a defensive response.

Why These Responses Are Inadequate

They share a failure to engage with the technical complexity of Bayesian formulation and what it reveals about precise logical structure. Serious discussion requires understanding Bayesian tools and how they apply to philosophical questions.

Bayesian Formulation of Hiddenness

Basic Structure According to Charity Anderson:

Anderson in "Divine Hiddenness: Defeated Evidence" (Royal Institute of Philosophy Supplement, 2017) formulates the problem as follows:

Let:
- H = hypothesis of a perfectly loving God's existence
- E = existence of nonresistant nonbelief
- K = our background knowledge

The Bayesian argument:
P(H|E&K) < P(H|K)

That is: the probability of a loving God's existence after knowing about nonresistant nonbelief is less than the probability of his existence before this knowledge.

The central question: How much is this decrease? Is it large enough to make belief unreasonable?

Sanford Russell's Development:

Russell in "The Persistent Problem of Divine Hiddenness" (Faith and Philosophy, 2019) develops the formulation:

He distinguishes between:
1. Total hiddenness: no evidence for God whatsoever
2. Partial hiddenness: evidence exists but is insufficient for some
3. Differential hiddenness: varying evidence across persons

The developed Bayesian formulation:
P(H|E₁&E₂&E₃&K) << P(H|K)

Where:
- E₁ = existence of partial hiddenness
- E₂ = existence of differential hiddenness
- E₃ = persistence of hiddenness despite sincere seeking

Analytical Power of Bayesian Formulation

First: Precisely Identifying Points of Disagreement

Bayesian formulation reveals that disagreement centers on:
1. Prior probability P(H|K): What is the probability of a loving God before considering hiddenness?
2. Conditional probability P(E|H&K): If a loving God exists, what is the probability of allowing nonresistant nonbelief?
3. Alternative probability P(E|~H&K): If a loving God doesn't exist, what is the probability of nonresistant nonbelief?

Second: Revealing Implicit Assumptions

- Assumption that divine love entails seeking relationship with everyone
- Assumption that relationship requires clear knowledge
- Assumption that sincere seeking is sufficient for finding

Third: Allowing Quantitative Analysis

Probabilistic values can be estimated and discussed, rather than open-ended qualitative debate.

Skeptical Theist Responses

First Response: Skepticism About Knowledge of Divine Motives

Skeptical theism (Dostoevsky, Kierkegaard, Mitchell) argues: we cannot know P(E|H&K) precisely because we don't know all God's possible reasons for hiddenness.

In Bayesian terms: P(E|H&K) is indeterminate because H involves a God who transcends our understanding.

Strength of this response: Avoids specific commitments about God's behavior. Maintains epistemic humility.

Its weakness: May lead to general skepticism that prevents any inference about God's attributes.

Second Response: Reversing the Probabilistic Burden

Some defenders (Moriston, later Swinburne) argue that P(E|~H&K) is also very low. If God doesn't exist, why would sincere seekers after ultimate meaning exist at all?

Third Response: Distinguishing Types of Knowledge

Polkinghorne and others distinguish between:
- Propositional knowledge: "that God exists"
- Experiential knowledge: "knowing God personally"

Hiddenness may be only in the latter type, changing Bayesian calculations.

Counter-criticism of Bayesian Formulation

Oppy's criticism: Bayesian formulation assumes we have reliable intuitions about metaphysical probabilities. But where do we get these intuitions?

Draper's criticism: Even if we accept the Bayesian framework, determining probabilistic values remains largely subjective.

Kaplan's criticism: Bayesian formulation assumes God acts according to human decision logic, which is a questionable assumption.

Recent Developments (2020-2024)

Charity Anderson develops the "defeated evidence" model: perhaps God provides sufficient evidence, but psychological or social factors "defeat" it for some people.

Sanford Russell explores the "gradualist model": God reveals himself gradually through history, and hiddenness is a temporary phase.

Kirk Lougheed develops the "cumulative hiddenness argument": not just the existence of nonresistant nonbelievers, but patterns of hiddenness across cultures and times.

Current Sites of Debate

Discussion centers on:
1. Criteria for "sincere seeking": What makes someone a "sincere seeker"?
2. Role of psychological and social factors: Do they excuse hiddenness?
3. Religious diversity: How does it affect hiddenness calculations?

The Deeper Philosophical Point

Bayesian formulation reveals a fundamental tension: how do we apply human cognitive tools (probabilities) to a subject claimed to transcend human understanding (God)? This tension reflects a deeper problem in philosophy of religion about the limits of human reason in knowing the divine.

From the Perspective of Rational Preference (rajḥān ʿaqlī)

Bayesian formulation aligns perfectly with the method of rational preference:
- Claims no definitive certainty but probabilistic preference
- Allows for accumulation of evidence and counter-evidence
- Accepts varying degrees of argumentative strength

Skeptical theism, in turn, represents an epistemically humble position that acknowledges limits of our knowledge about divine motives.

Where We Stand in This Debate Today

Bayesian formulation has enriched but not settled the debate. It has succeeded in:
- Precisely determining the problem's structure
- Revealing essential points of disagreement
- Providing a shared framework for discussion

But it has not succeeded in:
- Settling disagreement about probabilistic values
- Definitively overcoming skeptical theism
- Convincing all parties of the validity of the Bayesian framework itself

The debate continues and evolves, with attempts to develop more sophisticated models that account for the complexities of human religious experience.

For Reading

- Charity Anderson, "Divine Hiddenness: Defeated Evidence" (Royal Institute of Philosophy Supplement, 2017)
- J. L. Schellenberg, Divine Hiddenness and Human Reason (Cornell UP, 2nd ed. 2015)
- Sanford Goldberg & Nathan Ballantyne, "The Persistent Problem of Divine Hiddenness" (Faith and Philosophy, 2019)
- Michael Rea, The Hiddenness of God (Oxford UP, 2018)
- Kirk Lougheed, The Axiological Status of Theism and Other Worldviews (Palgrave, 2020)
- "Formulation: Divine Hiddenness and Skeptical Theism" page on the website