#09-Formalization

August 17, 2025

➘ #09 Source Article

Symbolic Logic Reconstruction

$H_1$ = Hypothesis that the Holy Spirit indwells believers and actively influences cognition, conduct, and well-being.
Annotation: $H_1$ represents the supernatural hypothesis.

$H_0$ = Hypothesis that observed religious phenomena result solely from natural psychological and social processes.
Annotation: $H_0$ represents the naturalistic explanation.

$E$ = Body of evidence consisting of (i) persistent doctrinal diversity, (ii) mixed or null prosocial effects, (iii) context-dependent well-being, and (iv) absence of replicable miracles.
Annotation: $E$ is the collective empirical data under consideration.

Likelihood Framework

$L(E|H_1)$ = Likelihood of observing $E$ given $H_1$ .
Annotation: If the Holy Spirit exists and indwells believers, what is the probability of seeing the actual data?

$L(E|H_0)$ = Likelihood of observing $E$ given $H_0$ .
Annotation: If the phenomena are fully naturalistic, what is the probability of seeing the data?

$\Lambda = \frac{L(E|H_1)}{L(E|H_0)}$
Annotation: $\Lambda$ is the likelihood ratio, measuring evidential strength.

Domain-Specific Predictions

Wisdom
$H_1 \rightarrow \text{Doctrinal Convergence}$
$H_0 \rightarrow \text{Doctrinal Diversity}$
Observation: $\text{Doctrinal Diversity}$ .
Thus, $L(\text{Doctrinal Diversity}|H_0) > L(\text{Doctrinal Diversity}|H_1)$ .
Righteousness
$H_1 \rightarrow \text{Low Crime, High Prosociality}$
$H_0 \rightarrow \text{Mixed or Contextual Effects}$
Observation: $\text{Mixed/Contextual Effects}$ .
Thus, $L(\text{Mixed/Contextual Effects}|H_0) > L(\text{Mixed/Contextual Effects}|H_1)$ .
Happiness
$H_1 \rightarrow \text{Stable Elevated Well-Being}$
$H_0 \rightarrow \text{Context-Dependent Well-Being}$
Observation: $\text{Context-Dependent Well-Being}$ .
Thus, $L(\text{Context-Dependent Well-Being}|H_0) > L(\text{Context-Dependent Well-Being}|H_1)$ .
Miracles
$H_1 \rightarrow \text{Replicable Supernatural Events}$
$H_0 \rightarrow \text{Absence of Replicable Supernatural Events}$
Observation: $\text{Absence of Replicable Events}$ .
Thus, $L(\text{Absence of Replicable Events}|H_0) > L(\text{Absence of Replicable Events}|H_1)$ .

Aggregate Evidence

$E = {\text{Doctrinal Diversity}, \text{Mixed Prosociality}, \text{Context-Dependent Well-Being}, \text{No Replicable Miracles}}$

$\Lambda = \frac{L(E|H_1)}{L(E|H_0)} < 1$
Annotation: The cumulative evidence is more expected under $H_0$ than under $H_1$ .

Conclusion

$\therefore E \text{ favors } H_0 \text{ over } H_1$
Annotation: Therefore, the naturalistic hypothesis $H_0$ is better supported by the evidence than the supernatural hypothesis $H_1$ .

Fitch-Style Natural Deduction (Likelihoodist Core)

$H_1$
Annotation: $H_1$ is the hypothesis that a supernaturally indwelling Holy Spirit actively shapes believers’ cognition, conduct, and well-being.
$H_0$
Annotation: $H_0$ is the hypothesis that observed religious outcomes arise from ordinary psychological, social, and institutional processes.
$E \equiv E_w \wedge E_r \wedge E_h \wedge E_m$
Annotation: The total evidence $E$ is conjoined from domain components: wisdom $E_w$ , righteousness/prosociality $E_r$ , happiness/well-being $E_h$ , and miracles $E_m$ .
$E_w$
Annotation: Observation: persistent doctrinal diversity and no systematic decision-quality advantage constitute $E_w$ .
$E_r$
Annotation: Observation: mixed or context-sensitive prosocial deltas (attenuating under controls) constitute $E_r$ .
$E_h$
Annotation: Observation: context-dependent well-being largely mediated by community/support constitutes $E_h$ .
$E_m$
Annotation: Observation: non-replication of specific, testable miracle claims constitutes $E_m$ .
$\text{Def: } L(X|Y)$
Annotation: $L(X|Y)$ denotes the likelihood of evidence $X$ if hypothesis $Y$ were true.
$\text{Def: } \Lambda(E) \equiv \frac{L(E|H_1)}{L(E|H_0)}$
Annotation: The likelihood ratio $\Lambda(E)$ measures whether $E$ is more expected on $H_1$ or on $H_0$ .
$H_1 \rightarrow \text{Doctrinal Convergence}$
Annotation: If $H_1$ were true, stable doctrinal alignment across believers would be expected.
$H_0 \rightarrow \text{Doctrinal Diversity}$
Annotation: If $H_0$ were true, enduring doctrinal diversity is expected from ordinary hermeneutical variation and cognition.
From 4, 10–11: $L(E_w|H_0) > L(E_w|H_1)$
Annotation: Given observed diversity $E_w$ , it is more expected under $H_0$ than under $H_1$ .
$H_1 \rightarrow \text{Low Crime \& Robust Prosociality (net controls)}$
Annotation: On $H_1$ , sanctification predicts clear population-level signals after covariate control.
$H_0 \rightarrow \text{Mixed/Contextual Prosocial Effects}$
Annotation: On $H_0$ , heterogeneous social/institutional influences yield mixed effects.
From 5, 13–14: $L(E_r|H_0) > L(E_r|H_1)$
Annotation: The prosocial data $E_r$ are better predicted by $H_0$ .
$H_1 \rightarrow \text{Stably Elevated Well-Being}$
Annotation: A reliably imparted “joy/peace” would produce broadly elevated and stable well-being on $H_1$ .
$H_0 \rightarrow \text{Context-Dependent Well-Being}$
Annotation: On $H_0$ , well-being tracks secular supports and context.
From 6, 16–17: $L(E_h|H_0) > L(E_h|H_1)$
Annotation: The well-being pattern $E_h$ is more expected under $H_0$ .
$H_1 \rightarrow \text{Replicable Supernatural Events}$
Annotation: On $H_1$ , we should observe replicable healings/signs with adequate controls.
$H_0 \rightarrow \neg \text{Replicable Supernatural Events}$
Annotation: On $H_0$ , such events should not replicate beyond placebo/expectancy/noise.
From 7, 19–20: $L(E_m|H_0) > L(E_m|H_1)[$
Annotation: The miracle record $E_m$ is more expected under $H_0$ .
$\text{Lemma}:\ \Big(\forall i\in{w,r,h,m}\Big)\ L(E_i|H_0)\ge L(E_i|H_1)\ \Rightarrow\ L(E|H_0)\ge L(E|H_1)$
Annotation: If each domain component $E_i$ is at least as likely on $H_0$ as on $H_1$ , then their conjunction $E$ is at least as likely on $H_0$ (mild dependence assumptions; standard evidential aggregation).
From 12, 15, 18, 21, 22: $L(E|H_0) > L(E|H_1)$
Annotation: Aggregating the domain inequalities yields a strict advantage for $H_0$ over $H_1$ on the total evidence $E$ .
From 9, 23: $\Lambda(E)=\frac{L(E|H_1)}{L(E|H_0)} < 1$
Annotation: Since $L(E|H_1) < L(E|H_0)$ , the likelihood ratio $\Lambda(E)$ is less than $1$ .
$\text{Likelihoodist Principle}:\ \Lambda(E) < 1 \ \Rightarrow\ E \text{ favors } H_0 \text{ over } H_1$
Annotation: In likelihoodist terms, $\Lambda(E)<1$ is precisely the condition for $E$ to count as evidence for $H_0$ over $H_1$ .
From 24, 25: $E \text{ favors } H_0 \text{ over } H_1$
Annotation: Therefore, the observed world $E$ evidentially supports the naturalistic hypothesis $H_0$ against the indwelling-Spirit hypothesis $H_1$ .

◉ A plain English walkthrough of the symbolic logic above.

We begin with two competing hypotheses. The first, $H_1$ , says that the Holy Spirit actually dwells in Christians and should reliably shape their thinking, their social behavior, their happiness, and even bring about miracles. The second, $H_0$ , says that everything we see can be explained by normal human psychology, culture, and institutions, without any supernatural intervention.
The evidence to be tested covers four main areas: wisdom (do Christians agree more and make better decisions?), righteousness (are Christians distinctly less criminal and more prosocial?), happiness (do Christians enjoy unusually high well-being?), and miracles (do Christians produce replicable supernatural outcomes?). The combination of these four categories forms the total body of evidence, $E$ .
Under $H_1$ , we should expect to see doctrinal unity, superior decision-making, clearly lower crime and higher prosociality, reliably higher well-being across contexts, and actual verifiable miracles. Under $H_0$ , we should expect doctrinal diversity, mixed or context-bound prosocial results, well-being that depends on environment and community, and an absence of replicable miracles.
When we look at the actual world, what we find matches the expectations of and not .
- Wisdom: Christians remain divided on doctrines and do not systematically outperform in forecasting or decision-making.
- Righteousness: The data on crime and prosocial behavior is inconsistent, small, or context-dependent once controls are applied.
- Happiness: Religious people may report higher well-being in some settings, but these effects disappear or reverse in secure societies, showing that social context—not supernatural joy—is the driver.
- Miracles: Rigorous studies fail to confirm healing or supernatural signs beyond placebo, expectancy, or reporting bias.
Each category of evidence therefore fits the naturalistic hypothesis $H_0$ better than the supernatural hypothesis $H_1$ . Put differently, the probability of seeing doctrinal diversity, context-bound prosocial effects, socially mediated well-being, and non-replicable miracles is much higher if no Holy Spirit is active.
The likelihoodist method says that when the evidence is more probable under one hypothesis than another, that evidence counts in favor of the better-predicting hypothesis. Since in each domain the evidence favors $H_0$ , the combined body of evidence overwhelmingly favors $H_0$ .
The final conclusion is straightforward: the world we observe looks like one without a supernaturally indwelling Spirit. It does not look like the world we would expect if Christians were uniquely guided by an omniscient and omnipotent agent. Therefore, the total evidence provides support for $H_0$ over $H_1$ .

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