➘ #17 Source Article

Symbolic Logic Formalization

latex]H_1 :=[/latex] The Christian God exists and intervenes in the world in observable ways.
Annotation: Hypothesis affirms that God not only exists but also acts such that His influence should be detectable in measurable human outcomes.

The Christian God does not exist (or exists without producing observable effects).
Annotation: Hypothesis treats divine absence and divine irrelevance as empirically indistinguishable, since both yield no measurable effects.

No statistical differences in outcomes of intercessory prayer.
Annotation: Evidence refers to controlled studies (e.g., STEP trial) showing no measurable benefit from prayer.

No actuarial advantage in health, safety, or longevity among believers.
Annotation: Evidence denotes population-level data indicating that believers fare no better than non-believers.

Personal testimonies of divine action are common across religions.
Annotation: Evidence highlights that subjective claims are non-exclusive and cancel out probative force.

Cognitive science explains belief as projection and agency detection.
Annotation: Evidence reflects the psychological mechanisms that naturally generate religious experiences without external referents.

Emotional perception of God’s presence fails to track external truth.
Annotation: Evidence underlines that feelings may provide comfort but do not constitute reliable evidence.

---

Annotation: The joint probability of all five evidences under is far lower than under ; that is, these evidences are what we would expect if God does not intervene.

Annotation: The Bayes Factor strongly favors , since the observed evidence is far more probable if God does not exist (or is inactive).

Annotation: Therefore, hypothesis is epistemically preferred over .

The existence of the Christian God is empirically indistinguishable from His non-existence.
Annotation: The logical outcome is that the Christian God’s existence makes no measurable difference to the world, rendering Him empirically irrelevant.

---

Here’s the step-by-step syllogistic version of the core argument.

The Christian God exists and intervenes in observable ways.
Annotation: Under , scripture-backed claims entail measurable effects (e.g., prayer results, distinctive protection).

Either the Christian God does not exist, or exists without producing observable effects (empirically equivalent to non-existence).
Annotation: captures the paper’s indistinguishability thesis.

Intercessory prayer yields superior outcomes for targets of prayer (vs. controls).
Annotation: A predicted measurable effect if holds.

Believers show actuarial advantages in health/safety/longevity.
Annotation: Another predicted measurable effect under .

Testimonies would be distinctive to Christianity (not matched across rival religions).
Annotation: Distinctiveness would mark a unique divine source.

Religious experiences would resist full explanation by ordinary cognitive mechanisms.
Annotation: If , agency-projection accounts should be insufficient.

Emotional perception of “God’s presence” would track external truth in a testable, discriminating way.
Annotation: Feelings would correlate with verifiable outcomes if .

Annotation: abbreviates “at least one predicted measurable effect occurs.”

Premises and inferences

If , then .
Annotation: Classical Christian claims imply that at least one of the measurable markers should obtain.

Not : randomized studies (e.g., STEP) find no prayer advantage.

Not : actuarial/population data show no believer advantage once controls are applied.

Not : testimonies occur across religions, erasing distinctiveness.

Not : cognitive science (agency detection, projection) robustly accounts for experiences.

Not : emotional perception supplies meaning, not truth-tracking differentials.

Therefore, .
Annotation: From –, none of the predicted markers obtain.

If and , then .
Annotation: Modus tollens on and .

Annotation: The Christian-God-with-observable-effects hypothesis is rejected on the observed record.

By the two-hypothesis framing, .
Annotation: Given how is defined in the paper, denying commits us to in this partition.

Annotation: The world is empirically as we would expect if there were no such divine effects.

Annotation: Epistemic preference goes to over given the premises and observations.

◉ A plain English walkthrough of the symbolic logic above.

Hypotheses

• H₁ says: The Christian God exists and acts in the world in ways we could measure. If this were true, then things like answered prayer, special protection, or unique testimonies should show up in the data.
• H₂ says: Either the Christian God does not exist, or He exists but produces no measurable effects. In practice, both cases look the same, since either way we would observe nothing unusual.

Predicted Measurable Effects

If H₁ were true, we would expect at least one of these to occur:

1. M₁: Prayer would produce better outcomes than chance.
2. M₂: Believers would have measurable advantages in health, safety, or longevity.
3. M₃: Testimonies of divine action would be distinctive to Christianity, not found equally in other religions.
4. M₄: Cognitive science would fail to explain religious experiences fully by natural processes.
5. M₅: Emotional perceptions of God’s presence would correlate with actual truth-tracking outcomes, not just comfort.

Together, this bundle is abbreviated as M: “some measurable sign should exist.”

Premises

• P₁: If H₁ is true, then M must be true. (Christian doctrine itself promises measurable outcomes.)
• P₂a–e: In reality, none of the individual markers (M₁–M₅) hold up under scrutiny:
  • Controlled studies show no prayer effect (¬M₁).
  • Actuarial data show no believer advantage (¬M₂).
  • Testimonies occur in all religions (¬M₃).
  • Psychology explains experiences naturally (¬M₄).
  • Emotions provide comfort but not truth-tracking (¬M₅).
• P₂: Therefore, ¬M (no measurable effects exist).

Logical Inference

• P₃: If H₁ implies M, and yet M is false, then H₁ must also be false (modus tollens).
• C₁: Therefore, H₁ is false.
• P₄: If H₁ is false, then H₂ must be true (since those are the only two options defined).
• C₂: Therefore, H₂ is true — the world looks exactly as we would expect if there were no divine effects.
• C₃: Thus, H₂ is epistemically preferred over H₁ (∴ H₂ ≻ H₁).

Walkthrough Summary

The argument sets up a simple test: if the Christian God really acted in the world, we’d expect to see measurable signs. Careful investigation finds none of the signs that would be expected. By logical consequence, the “God-with-measurable-effects” hypothesis is ruled out, and the alternative — “no such effects exist” — becomes the better explanation.

◉ Flowing Narrative Summary

The argument begins by distinguishing two possibilities. On the one hand, if the Christian God exists and intervenes in the world, then His presence should be discernible in measurable ways: prayers should alter outcomes, believers should enjoy distinctive advantages, and testimonies of divine action should stand apart from those in rival religions. On the other hand, if there are no such measurable effects, then either the Christian God does not exist or He exists in a way that is empirically indistinguishable from non-existence.

From this starting point, the analysis surveys the evidence. Studies of intercessory prayer consistently fail to show benefits beyond chance. Actuarial data reveal no differences in health, safety, or longevity between believers and non-believers. Personal testimonies, though emotionally powerful, occur across all religions and therefore cancel out as evidence of any one faith. Cognitive science explains religious experiences in terms of agency detection, projection, and other psychological mechanisms. Emotional perceptions of God’s presence provide comfort but do not track external truth. Taken together, these findings demonstrate that none of the predicted signs of divine intervention are actually observed.

Given the absence of measurable effects, the logic proceeds by elimination. If God’s existence in the Christian sense implies that such effects should be present, and yet none are, then that hypothesis fails. What remains is the alternative: the world is exactly as we would expect if no such divine action occurs. In probabilistic terms, the data are far more likely under the non-existence or empirical irrelevance of God than under His promised activity.

The conclusion follows directly. The Christian God, as traditionally described, is empirically indistinguishable from a God who does not exist. The lack of any measurable difference tips the balance in favor of the hypothesis that divine influence is absent. In short, when tested against the observable world, the Christian God adds no explanatory power and is epistemically outweighed by naturalistic accounts.