#19-Formalization

August 24, 2025

➘ #19 Source Article

Symbolic Logic Formalization

$P_1$ If free will determines religious belief, then belief distributions should be independent of culture and geography.
Annotations: This states the expectation that if genuine free will were the driver, religious affiliations would not correlate strongly with cultural boundaries.

$P_2$ Empirical evidence shows that religious belief distributions correlate almost perfectly with cultural and geographical boundaries.
Annotations: Data demonstrates that most individuals adopt the religion of their upbringing or surrounding culture.

$P_3$ If religious belief were an outcome of divine fairness, then all individuals would have roughly equal access to knowledge of the true God.
Annotations: The fairness assumption implies that geography or culture would not determine eternal destiny.

$P_4$ Billions of sincere non-Christian believers experience no clear, universal revelation of the Christian God.
Annotations: The evidence of sincere devotion across diverse traditions suggests absence of universal divine revelation.

$P_5$ If eternal judgment is based on explicit belief, then individuals in regions with little or no exposure to Christianity are unfairly disadvantaged.
Annotations: Geographic inequality would make salvation dependent on cultural accident rather than genuine choice.

$P_6$ Religious diversity persists along predictable cultural lines, not random distributions expected from unconstrained free will.
Annotations: Religious pluralism is best explained by cultural transmission and cognitive predispositions rather than autonomous decision.

$C_1$ Therefore, religious belief is better explained by cultural conditioning, cognitive bias, and social reinforcement than by free will or divine fairness.
Annotations: This is the central inductive conclusion: naturalistic explanations are superior to theistic explanations of religious distribution.

$C_2$ If a just and omnipotent God exists, His presence is not reflected in global religious distribution, where it should be most visible.
Annotations: This secondary conclusion highlights the theological tension between claims of divine fairness and observed reality.

An expanded syllogistic chain version.

Domain and symbols

$\mathcal{P}=\text{the set of persons},\ \mathcal{R}=\text{the set of religions},\ \mathcal{C}=\text{the set of cultures},\ \mathcal{G}=\text{the set of geographic regions}$
Annotations: We quantify over persons, religions, cultures, and geographic regions.

$\forall x\in\mathcal{P}:\ R_x\in\mathcal{R},\ C_x\in\mathcal{C},\ G_x\in\mathcal{G}$
Annotations: For each person $x$ , let $R_x$ denote their religion, $C_x$ their culture, and $G_x$ their region.

$\text{Exp}(x) = \text{the effective exposure of person }x\text{ to the purportedly true religion}$

Annotations: $\text{Exp}(x)$ summarizes access, salience, and credible presentation of the “true” religion for person $x$ .

Competing explanatory hypotheses

$H_{\text{FW}}:\ \forall x\in\mathcal{P},\ \forall r\in\mathcal{R},\ \forall c\in\mathcal{C},g\in\mathcal{G},\ P(R_x=r\mid C_x=c,G_x=g)=P(R_x=r)$
Annotations: Under the free-will-driven hypothesis, a person’s religion is (approximately) independent of culture and geography.

$H_{\text{CC}}:\ \exists\delta>0,\ \exists r,c,g\ \text{s.t.}\ \big|P(R_x=r\mid C_x=c,G_x=g)-P(R_x=r)\big|\ge\delta$
Annotations: Under cultural conditioning, religion depends detectably on culture/region; distributions shift by at least $\delta$ .

$H_{\text{Fair}}:\ \forall x,y\in\mathcal{P},\ \text{Exp}(x)\approx\text{Exp}(y)$
Annotations: Divine fairness predicts roughly equal access to the “true” religion for all persons, regardless of birthplace or culture.

Observable regularities (empirical premises)

$E_1:\ \exists\delta^{*}!>!0,\ \exists r,c,g\ \text{s.t.}\ \big|P(R_x=r\mid C_x=c,G_x=g)-P(R_x=r)\big|\ge\delta^{*}$
Annotations: Measured belief distributions strongly track culture/region (clustering), contradicting independence.

$E_2:\ \text{For most }x,\ R_x\ \text{matches the dominant tradition of }(C_x,G_x)\$ $\text{with high probability}$
Annotations: Most individuals adopt the locally dominant religion; parental/community tradition is highly predictive.

$E_3:\ \text{Large populations of sincere non-Christians report no clear, }$ $\text{universal revelation uniquely selecting Christianity}$
Annotations: Across cultures, sincere adherents do not receive unambiguous, convergent signals to the same “true” religion.

$E_4:\ \text{Exposure is uneven: }\exists x,y\ \text{s.t.}\ \text{Exp}(x)\ \ll\ \text{Exp}(y)\ \text{due to }(C_x,G_x)\ \text{vs. }(C_y,G_y)$
Annotations: Access to the “true” religion systematically varies with culture/geography.

Immediate logical consequences

$E_1\Rightarrow \neg H_{\text{FW}}$
Annotations: If observed distributions depend on culture/region, the free-will independence claim is false (or at least not the primary driver).

$E_1\land E_2\Rightarrow H_{\text{CC}}\ \text{is strongly confirmed relative to }H_{\text{FW}}$
Annotations: Cultural conditioning explains clustering parsimoniously; free-will independence does not.

$E_3\land E_4\Rightarrow \neg(H_{\text{Fair}}\ \text{as stated})$
Annotations: If fairness entailed equal access yet exposure and “revelation” vary by culture/region, then fairness (as an empirical claim) fails.

Formal fairness–exposure tension

$H_{\mathrm{Fair}} \Rightarrow \forall x,y:\ P(\mathrm{Awareness_True}(x)) \approx P(\mathrm{Awareness_True}(y))$

Annotations: Fairness implies near-equal probability of adequate awareness of the true religion for any two persons.

$E_4 \Rightarrow \exists x,y:\ P(\mathrm{Awareness_True}(x)) \ll P(\mathrm{Awareness_True}(y))$

Annotations: Unequal exposure entails unequal awareness probabilities across persons in different cultures/regions.

$\big(H_{\mathrm{Fair}} \Rightarrow \forall x,y:\ P(\mathrm{Awareness_True}(x)) \approx P(\mathrm{Awareness_True}(y))\big)\ \land\ \big(\exists x,y:\ P(\mathrm{Awareness_True}(x)) \ll P(\mathrm{Awareness_True}(y))\big)\ \Rightarrow \neg H_{\mathrm{Fair}}$

Annotations: Direct contradiction: predicted equal awareness vs. observed unequal awareness.

Consequences for belief-based verdicts (conditional)

$S:\ \text{Salvation requires explicit assent to a particular doctrine (belief-criterion)}$
Annotations: Define $S$ as the exclusivist condition tying outcomes to explicit belief.

$S\land E_4\Rightarrow \exists x:\ \text{Outcome}(x)\ \text{is strongly driven by }(C_x,G_x)\ \text{via exposure, }$ $\text{not autonomous appraisal}$
Annotations: If explicit belief is required while exposure is uneven, outcomes track cultural accident rather than independent choice.

$S\land \neg H_{\text{Fair}}\Rightarrow \text{Outcome variation reflects exposure disparity, not uniform opportunity}$
Annotations: Under $S$ , unequal access yields unequal outcomes that are incongruent with fairness.

Likelihood comparison (inference to best explanation)

$\mathcal{L}(E_1\land E_2\land E_3\land E_4\mid H_{\text{CC}})\ \gg\ \mathcal{L}(E_1\land E_2\land E_3\land E_4\mid H_{\text{FW}}\lor H_{\text{Fair}})$
Annotations: The total evidence is far more likely if cultural conditioning is true than if free-will independence or fairness holds.

$\mathrm{BF} {\mathrm{CC},\mathrm{FW}\lor \mathrm{Fair}}=$ $\dfrac{\mathcal{L}(E_1\land E_2\land E_3\land E_4\mid H {\mathrm{CC}})}{\alpha,\mathcal{L}(E_1\land E_2\land E_3\land E_4\mid H_{\mathrm{FW}})+(1-\alpha),\mathcal{L}(E_1\land E_2\land E_3\land E_4\mid H_{\mathrm{Fair}})}\$ $\gg\ 1$

Annotations: A Bayes factor greatly favoring cultural conditioning over the alternatives formalizes the evidential tilt.

Main conclusions

$C_1:\ \neg H_{\text{FW}}\ \land\ H_{\text{CC}}\ \text{(best explanation of the observed distributions)}$
Annotations: Free-will independence does not explain the data; cultural conditioning does.

$C_2:\ \neg H_{\text{Fair}}\ \text{(as an empirical claim about equal access), given }E_3,E_4$
Annotations: The fairness hypothesis fails against observed exposure and revelation patterns.

$C_3:\ \text{If }S\ \text{(belief-criterion) holds, then outcomes systematically track exposure, }$ $\text{not uniform opportunity}$
Annotations: Under an exclusivist belief requirement, culturally driven exposure disparities dominate outcomes, contradicting fairness.

$C_4:\ \text{Therefore, global religious distribution is better explained by cultural }$ $\text{conditioning, cognitive predispositions, and social reinforcement than by free will }$ $\text{or divine fairness}$
Annotations: The overall abductive verdict: naturalistic mechanisms outperform free-will independence and fairness in explaining the observed pattern.

◉ A plain English walkthrough of the symbolic logic above.

The formula is a Bayes factor — a way of comparing how well two competing hypotheses explain the same body of evidence.

The hypotheses being compared
- $H_{\mathrm{CC}}$ : Religion is primarily explained by cultural conditioning (environment and upbringing).
- $H_{\mathrm{FW}}$ or $H_{\mathrm{Fair}}$ : Religion is explained instead by either free will independence or divine fairness (everyone supposedly has equal access to God).
The evidence being evaluated
The evidence set includes four key empirical findings:
- $E_1$ : Belief distributions strongly track culture and geography.
- $E_2$ : Most people adopt their parents’ or community’s religion.
- $E_3$ : Large populations of sincere non-Christians never experience a clear revelation pointing uniquely to Christianity.
- $E_4$ : Exposure to any one religion is highly unequal across the globe.
What the Bayes factor means
- The numerator is the probability of seeing that whole package of evidence if cultural conditioning ( $H_{\mathrm{CC}}$ ) is true.
- The denominator is the probability of seeing that same evidence if either free will or divine fairness is true. Because those are two separate hypotheses, the denominator is written as a weighted average (with weights $\alpha$ and $1-\alpha$ ) to represent how much credence you give each.
The inequality $\gg 1$
The expression says the Bayes factor is much greater than 1. That means the observed evidence is far more likely under cultural conditioning than under free will or divine fairness.

Summary in plain words:
If people’s religions were truly the result of free choice or equal divine access, we wouldn’t expect beliefs to line up almost perfectly with geography and upbringing. But they do. That evidence makes much more sense if religion is mainly the product of cultural inheritance. The Bayes factor quantifies this: the data are vastly more probable given cultural conditioning than given free will or divine fairness.

◉ Narrative Analogy

Analogy: Languages vs. Free Choice

Imagine you’re trying to figure out why people speak the languages they do. Two explanations are on the table:

Free Choice Hypothesis: People independently choose their language, so we should expect languages to be scattered around randomly — Japanese in Brazil, Spanish in rural China, Hindi in Canada.
Cultural Conditioning Hypothesis: People mostly inherit the language of their parents and community, so we should expect strong clusters — Japanese in Japan, Spanish in Latin America, Hindi in India.

Now, look at the world: languages are clustered by geography, not randomly scattered. That’s the “evidence.”

The Bayes factor is like asking: Which explanation makes the evidence more probable? Clearly, the clustering of language is many, many times more likely under cultural inheritance than under pure free choice.

Applying this to religion:

If religious belief were driven by free will or equal divine access, we’d expect a scattered pattern — people all over the world converging on the same “true” religion.
Instead, we see the same thing we see with language: tight clusters determined by where and into what culture someone is born.

So the Bayes factor comes out heavily tilted: the “language-style” explanation (cultural conditioning) makes the actual evidence thousands of times more likely than the “free choice/divine fairness” explanation.

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