Does J. Hare's program of "Bayesian Reasoning for Theistic Ethics" succeed in formulating probabilistic support for theism from the data of moral objectivity?

In his books "The Moral Gap" (Oxford UP, 1996) and "God's Command" (Oxford UP, 2015), John Hare—Professor of Philosophy at Yale and son of philosopher R.M. Hare—presents a distinctive systematic attempt: using Bayesian reasoning to assess how moral data supports the theistic hypothesis. This program represents an important technical development in the moral argument, moving it from traditional deductive formulations to a more precise probabilistic framework.

Inadequate Responses to Avoid

From some defenders: "Hare proved God's existence mathematically from ethics" is an exaggeration. Bayesian inference provides probabilistic support, not categorical proof. "Mathematics makes the argument certain" is a misunderstanding of the nature of Bayesian reasoning.

From some critics: "Using Bayesian methods in philosophy is mathematical sleight of hand" is an unjustified rejection. Bayesian methods are standard tools in contemporary epistemology. "Ethics is subjective so the argument is invalid from the start" ignores that Hare first discusses why moral objectivity is reasonable.

Hare's Bayesian Structure

First Premise: Formulating the Moral Data (E).

Hare precisely defines the moral data:
- E₁: Existence of objective moral facts (innocent killing is objectively wrong)
- E₂: Moral knowledge availability (we know some moral facts)
- E₃: Moral obligation (we are morally obligated)
- E₄: Expected congruence between happiness and virtue (Kant's highest good)

Second Premise: Identifying Competing Hypotheses.

- T: Theism (personal God who is creator and moral)
- N: Naturalism (no God, reality is only material/natural)

Third Premise: Applying Bayes' Theorem.

P(T|E) = P(E|T) × P(T) / P(E)
P(N|E) = P(E|N) × P(N) / P(E)

Bayesian ratio: P(T|E)/P(N|E) = [P(E|T)/P(E|N)] × [P(T)/P(N)]

If P(E|T) > P(E|N), then moral data supports T over N.

Central Argument: P(E|T) >> P(E|N)

Hare argues that the probability of moral data on theism is much higher than its probability on naturalism:

Regarding E₁ (Objectivity):
- On T: A moral God grounds objective moral facts. P(E₁|T) ≈ 0.9
- On N: Naturalism faces difficulty grounding objectivity. P(E₁|N) ≈ 0.1-0.3

Regarding E₂ (Knowledge):
- On T: God designed humans to know moral facts. P(E₂|T) ≈ 0.8
- On N: Evolutionary accident that we reach moral facts. P(E₂|N) ≈ 0.05

Regarding E₃ (Obligation):
- On T: God is the source of moral obligation. P(E₃|T) ≈ 0.95
- On N: Obligation without an obligator is problematic. P(E₃|N) ≈ 0.2

Regarding E₄ (Expected Congruence):
- On T: God guarantees ultimate cosmic justice. P(E₄|T) ≈ 0.9
- On N: No guarantee of congruence between virtue and happiness. P(E₄|N) ≈ 0.1

Cumulative result: P(E|T)/P(E|N) ≈ 100-1000

Critique of the Bayesian Program

First Critique: Problem of Determining Prior Probabilities.

Alan Hájek and Graham Oppy argue that the numbers Hare assigns (0.9, 0.1, etc.) are arbitrary. There's no objective way to determine P(E₁|N) = 0.1 rather than 0.5.

Hare's response: Precise numbers aren't necessary. What matters is the relative ordering: P(E|T) > P(E|N). Even if we differ on degree, the direction is clear.

Second Critique: Problem of Alternative Hypotheses.

Paul Draper argues that options aren't limited to T and N. There are other hypotheses: impersonal divinity, polytheism, expanded naturalism that includes objective values.

Hare's response: Hypotheses can be added, but most face similar difficulties to naturalism in explaining E. The analysis can be expanded to include multiple hypotheses.

Third Critique: Robust Moral Naturalism.

Erik Wielenberg argues that Hare underestimates naturalism's capacity. Robust moral realism makes P(E₁|N) much higher than Hare assumes.

Hare's response: Even if we accept Wielenberg on E₁, E₂, E₃, and E₄ remain problematic for naturalism. The cumulative analysis still favors theism.

Fourth Critique: The Reverse Problem of Evil.

If we use Bayesian methods on evil: P(evil|T) < P(evil|N), then evil supports N over T. Does the overall balance still favor T?

Hare's response: Yes, evil counts against T, but must be balanced against all data. In "God and Evil" (2021), Hare develops comprehensive Bayesian analysis that includes evil.

Program Developments (2015-2026)

The Technical Development Stream includes Hare's students (Justin Mooney, Chris Toner). They develop:
- Multi-level Bayesian models
- Integration of data from cognitive science of morals
- Sensitivity analysis for prior assumptions

The Bayesian Critique Stream includes Hájek, Oppy, Draper. They develop:
- Deeper critique of probability assignments
- Alternative Bayesian models reaching different conclusions
- Problems in applying Bayesian methods to metaphysics

The Integration Stream includes Swinburne, Brower. They integrate:
- Bayesian moral arguments with other arguments (cosmological, fine-tuning)
- Comprehensive cumulative Bayesian analysis for theism

The Deeper Philosophical Point

The Bayesian program reveals a fundamental tension: Can probabilities be applied to major metaphysical questions?

Supporters: Bayesian methods are our best tool for rational thinking under uncertainty. Even if not perfect, they help structure thinking.

Opponents: Metaphysical questions transcend the scope of probabilities. Attempting to quantify them distorts their nature.

Middle position: Bayesian methods are useful as an organizational framework, not as a calculating machine. They help clarify relationships between data and hypotheses without claiming numerical precision.

Assessment from the Perspective of Rational Preference (rajḥān ʿaqlī)

Hare's Bayesian program makes a valuable contribution:

Strengths:
- Structures the moral argument precisely
- Avoids claims of categorical certainty
- Allows integration of multiple data points
- Aligns with cumulative preference methodology

Weaknesses:
- Difficulty determining prior probabilities
- Sensitivity to assumptions
- Doesn't definitively settle the debate

Evaluative Conclusion

The program succeeds in showing that moral data probabilistically supports theism over naturalism, but doesn't provide categorical "proof." This is consistent with the rational preference methodology: multiple data points accumulate to form a cumulative case for theism, without claiming certainty.

The program's basic value: transforming the debate from "Does morality prove God?" to "How much do moral considerations support the probability of theism?"—and this is an important methodological advance.

Where We Stand Today

Bayesian methods in philosophy of religion are experiencing growth. Hare's moral program is part of a broader movement (Swinburne for cosmology, Collins for fine-tuning). Technical debate is developing, with attempts to overcome initial problems.

The project isn't settled, but it has shown the value of probabilistic tools in organizing philosophical discussion about God. Even critics accept that the Bayesian framework clarifies points of disagreement.

For Reading

- John E. Hare, God's Command (Oxford UP, 2015) Chapters 8-10
- John E. Hare, "Kant and Divine Command Theory" (Oxford Studies, 2020)
- C.S. Evans & J. Hare, "Moral Arguments: Bayesian Approach" (Blackwell Companion, 2019)
- Graham Oppy, "On Hare's Bayesian Moral Argument" (Sophia, 2018)
- Paul Draper, "Moral Arguments and Probabilistic Problems" (Oxford Studies, 2017)
- "Formulation: Bayesian Moral Argument" page on the website
- "Method: Bayesian Analysis" page on the website