Argument from Silence in Bayesian Historiography

Argument from silence infers hypotheses from absent expected evidence, formalized Bayesially as low posterior when P(E|H) high but E unobserved. In historiography, it counters binary fallacies by quantifying silence strength.

Definition

If P(E|H) ≈1 (evidence expected if true) and E absent, then P(H|E) ↓ via likelihood ratio L = P(E|H)/P(E|¬H) <<1. Silence valid when source comprehensive and unbiased.

Priors: Baseline mention rates from cohorts (e.g., 0.7 for Quaker arrests in Great Book of Sufferings).

Workflow

Establish P(E|H): From source scope (e.g., Penn diaries exhaustive for Keithians). Compute L; update posterior. Adjust for biases (e.g., destruction multiplier). Threshold: L<0.1 demotes to uncertain.

Applications

Debunk myths (e.g., no Eastern van Helmont mentions in Sendivogius parallels → P<0.2). Correlate with EMS for evasion. Historiographic audits: Silence in Hartlib → probable Italy 1650s.

Example: Van Helmont

Quaker crackdowns 1680s: High P(mention|H) in Sufferings if London-resident; absence → mobility/immunity, P(static London) from 0.7 to 0.4.

Related Concepts

Methodological Foundations for Probabilistic Geo-Temporal Timelines, Network Gravity in Intellectual History, Peripatetic Esotericism.