#03-Formalization

Formalizations

August 12, 2025

➘ #03 Source Article

1) Language Domains — Symbols & Meanings

Hypothesis space

$H_1$ : Divine-authorship-with-clarity — the Bible was authored (or decisively inspired) by an omniscient, omnipotent agent intending sufficient clarity on core propositions to yield substantial convergence among sincere readers.
$H_2$ : Human-authorship — the Bible is a human cultural product subject to ordinary interpretive variability over time.

Evidence & states

$E$ : pervasive, persistent doctrinal diversity among sincere, informed readers on core issues (baptism, salvation, Eucharist, hell, women’s ordination, Sabbath, gifts, eschatology, creation views).
$U$ : substantial doctrinal unity (high convergence on essentials).

Predicates / functions

$\mathrm{Aim}(H_1,\mathrm{Clarity})$ : $H_1$ includes an explicit clarity-aim on essentials.
$\mathrm{Feat}(H_1)$ : texts engineered for clarity (redundancy, definitions, resolution of ambiguities, anticipation of pitfalls).
$\mathrm{Aux}_i$ : auxiliary modifiers to $H_1$ (e.g., narrowing “essentials”/perspicuity; relocating clarity to Magisterium; “journey/pedagogy” model).

Bayesian terms

$P(\cdot)$ : credence; $P(E\mid H)$ : likelihood; $\gg$ reads “much greater than”.

2) Core Axioms / Premises

P1 (Clarity-aim under $H_1$ ): $\mathrm{Aim}(H_1,\mathrm{Clarity}) \wedge \mathrm{Feat}(H_1) \Rightarrow P(U\mid H_1)$ is high and $P(E\mid H_1)$ is low, ceteris paribus.

P2 (Ordinary variability under $H_2$ ): Human, polyvocal, historically layered texts predict interpretive pluralism; thus $P(E\mid H_2)$ is high and $P(U\mid H_2)$ is low without coordination.

P3 (Observed state): $E$ obtains (extensive, persistent doctrinal diversity on core questions among sincere, informed readers).

P4 (Auxiliary flexibility): Introducing $\mathrm{Aux}_i$ to preserve $H_1$ (e.g., redefining “essentials,” relocating clarity to institution, or re-construing clarity as pedagogy) reduces $H_1$ ’s predictive specificity for $U$ vs. $E$ .

P5 (Likelihood asymmetry): If $P(E\mid H_1) \ll P(E\mid H_2)$ and $E$ obtains, then the likelihood ratio $\frac{P(E\mid H_1)}{P(E\mid H_2)}<1$ .

3) Immediate Derivations

D1 (Asymmetric prediction): From P1–P2, $P(E\mid H_1) < P(E\mid H_2)$ .

D2 (Empirical plug-in): From P3 and D1, $E$ favors $H_2$ over $H_1$ at the level of likelihoods.

D3 (Auxiliary penalty): From P4, conditioning $H_1$ on $\mathrm{Aux}_i$ weakens its prior constraint set, decreasing its explanatory sharpness relative to $H_2$ .

D4 (Bayes sketch): Given non-extreme priors,
$\frac{P(H_1\mid E)}{P(H_2\mid E)} = \frac{P(E\mid H_1)}{P(E\mid H_2)} \cdot \frac{P(H_1)}{P(H_2)} < \frac{P(H_1)}{P(H_2)}$ .
Thus $E$ shifts credence away from $H_1$ .

4) Fitch-Style Proof Goals

Goal A (Expectational contrast): Show $P(E\mid H_1) < P(E\mid H_2)$ .

Assume $H_1$ . By P1, $\mathrm{Aim}(H_1,\mathrm{Clarity}) \wedge \mathrm{Feat}(H_1) \Rightarrow P(U\mid H_1)$ high $\Rightarrow$ $P(E\mid H_1)$ low.
Assume $H_2$ . By P2, human textual properties $\Rightarrow P(E\mid H_2)$ high.
Therefore, $P(E\mid H_1) < P(E\mid H_2)$ . (D1)

Goal B (Evidential update): From $E$ , prefer $H_2$ over $H_1$ ceteris paribus.
4. From P3, observe $E$ .
5. From Goal A and Bayes (P5), $\frac{P(H_1\mid E)}{P(H_2\mid E)}<\frac{P(H_1)}{P(H_2)}$ . (D4)
6. Hence $E$ is evidence against $H_1$ relative to $H_2$ . (Goal B)

Goal C (Role of auxiliaries):
7. Suppose $H_1^\ast = H_1 \wedge \mathrm{Aux}_i$ (perspicuity-narrowing; magisterial relocation; journey-model).
8. By P4, $H_1^\ast$ fits $E$ better only by relaxing original clarity predictions, thereby losing predictive bite; comparative advantage remains with $H_2$ absent independent support for $\mathrm{Aux}_i$ . (D3)

5) Compact Sequent Summary

$\mathrm{Aim}(H_1,\mathrm{Clarity}) \Rightarrow P(E\mid H_1)$ low; human-authorship $\Rightarrow P(E\mid H_2)$ high. (P1–P2)
$E$ (pervasive diversity) obtains. (P3)
Therefore $P(E\mid H_1) < P(E\mid H_2)$ and $E$ favors $H_2$ over $H_1$ . (D1–D2, D4)
Adding $\mathrm{Aux}_i$ to $H_1$ preserves fit but weakens prediction, leaving $H_2$ comparatively stronger unless $\mathrm{Aux}_i$ gains independent warrant. (D3)

6) Objection Modules (as Auxiliary Schemas)

Module $\mathrm{Aux}_{\text{Persp}}$ (Perspicuity-narrowing):

Claim: “Only ‘essentials’ are clear; diversity is peripheral.”
Formal move: Replace $U$ with $U_{\text{min}}$ (a shrinking set).
Effect: Raises $P(E\mid H_1)$ by excluding much of $E$ from the target domain; but this redefinition is contested and reduces testability.

Module $\mathrm{Aux}_{\text{Mag}}$ (Magisterial relocation):

Claim: Clarity resides in an authoritative interpreter rather than in the text.
Formal move: Condition $U$ on an institution $M$ : $U \equiv U(M)$ .
Effect: Shifts burden from text to institution; mitigates $E$ internally but alters the content of $H_1$ .

Module $\mathrm{Aux}_{\text{Ped}}$ (Pedagogical journey):

Claim: Diversity is intended for growth; propositional convergence is not the aim.
Formal move: Replace $\mathrm{Aim}(H_1,\mathrm{Clarity})$ with $\mathrm{Aim}(H_1,\mathrm{Formation})$ .
Effect: Explains $E$ but abandons original clarity-prediction; trade-off in explanatory focus.

7) Plain-English Gloss (One sentence)
Given that deep, long-running doctrinal disagreement on core issues is far more expected on a human-authorship model than on a divine-authorship-with-clarity model, the observed diversity is evidentially weighty against $H_1$ and in favor of $H_2$ , unless one weakens $H_1$ ’s clarity aim via auxiliaries that themselves require independent support.

Here’s a set of technical explanations and reader-friendly notes for the symbolic logic in the content above, allowing a non-specialist to follow the reasoning without losing the rigor. We’ll move section by section, unpacking the notation and argument flow.

Layer 1: Technical Explanations (for those comfortable with logic and probability)

H₁ and H₂ (Hypotheses)

$H_1$ is the “God of clarity” hypothesis: if God authored the Bible with the intent of making core teachings clear, then we should expect strong convergence among sincere readers.
$H_2$ is the human-authorship hypothesis: if humans wrote the Bible without divine clarity-engineering, the normal messiness of interpretation will persist.

Evidence variables ( $E$ and $U$ )

$E$ = evidence of large, long-term doctrinal disagreements even among informed, sincere believers.
$U$ = evidence of substantial agreement on key doctrines.
These are mutually exclusive in the simplified formalization.

Predicates ( $\mathrm{Aim}$ , $\mathrm{Feat}$ , $\mathrm{Aux}_i$ )

$\mathrm{Aim}(H_1,\mathrm{Clarity})$ says that $H_1$ involves the explicit goal of clarity in essentials.
$\mathrm{Feat}(H_1)$ means the text would contain built-in design elements to secure that clarity (redundancy, clear definitions, explicit conflict resolution).
$\mathrm{Aux}_i$ are “auxiliary hypotheses” — ad hoc adjustments used to explain away conflicting evidence (e.g., saying God only made some doctrines clear, or that clarity comes through an institution instead of the text).

Probabilities and likelihoods

$P(E\mid H)$ = the probability of seeing the kind of diversity we have, if hypothesis $H$ is true.
$P(U\mid H)$ = the probability of seeing unity under $H$ .
The reasoning compares $P(E\mid H_1)$ to $P(E\mid H_2)$ .

Premises

P1–P2: Under $H_1$ , clarity-aim + design features predict unity and make diversity unlikely; under $H_2$ , ordinary textual processes predict diversity.
P3: The world we see is full of persistent doctrinal diversity ( $E$ ).
P4: Adding auxiliaries makes $H_1$ flexible but less testable.
P5: If $P(E\mid H_1) \ll P(E\mid H_2)$ and $E$ is observed, Bayes’ theorem says our credence in $H_1$ should drop.

Derivations

D1–D2: The observed diversity fits $H_2$ better than $H_1$ .
D3: Auxiliaries rescue $H_1$ from immediate falsification but at the cost of predictive sharpness.
D4: Bayes’ theorem explicitly shows that the ratio of posterior credences decreases for $H_1$ when $E$ is observed.

Fitch-style goals

Goal A: Show that the diversity we see is less probable under $H_1$ than $H_2$ .
Goal B: Show that $E$ is evidence against $H_1$ relative to $H_2$ .
Goal C: Show that auxiliary explanations preserve compatibility but erode the original hypothesis’s precision.

Layer 2: Reader-Friendly Notes (for non-specialists)

Two competing ideas

If God really wrote or guided the Bible to make its key teachings clear, then believers who sincerely try to understand it should end up agreeing on those key teachings.
If the Bible was written entirely by humans without divine clarity, then disagreements about meaning are exactly what we’d expect.

What we actually see
Across history and today, sincere and well-informed believers disagree about major doctrines — baptism, salvation, communion, hell, Sabbath, women’s ordination, spiritual gifts, the end times, and creation. This isn’t just small details; it’s about the big questions.

Why this matters
If the “God of clarity” idea were right, such persistent disagreements should be rare. If the “human authorship” idea is right, they should be common. Since they are common, that’s a better fit for the human-authorship view.

What about excuses for the disagreements?
Supporters of the “God of clarity” idea sometimes say:

God only made some things clear.
You need a special Church authority to interpret the Bible.
God deliberately left disagreements so believers would “grow” through the process.
These explanations keep the God-of-clarity idea alive, but they make it vague and less testable — meaning it no longer clearly predicts unity over disagreement.

The bottom line
When we compare the two ideas, the pattern of disagreement fits the “human authorship” explanation much better than the “God of clarity” one. Unless there’s strong independent proof for those extra excuses, the simpler and better-fitting explanation is that the Bible is a human work.

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