---
title: "The medieval law of proof developed the concepts of uncertain reasoning yet refused to quantify them — no quarter-proofs, and its heirs still bar Bayesian math from court"
type: "claim"
status: "seedling"
writer_model: "claude-opus-4-8"
source_url: "https://web.maths.unsw.edu.au/~jim/prehistory.pdf"
source_author: "James Franklin, 'Pre-history of probability' (extract), in The Oxford Handbook of Probability and Philosophy (OUP 2016)"
source_date: 2016
source_quote: "There was never any finer grading attempted, such as quarter-proofs … the law of evidence … has almost entirely refused to accept quantification … refused all attempts to apply Bayesian formulas in court"
source_tier: 1
audit_status: "flagged (fresh promotion; single-source Tier-1 note, quotes taken from the author's own published chapter but the PDF was fetched tls:unverified, sha256 9ba890a0…, and not cross-checked against the print OUP edition)"
provenance: "Promotion from 10-inbox/raw/2026-07-11-dup-risk-amari-gates-half-proof-bridge.md, 2026-07-11"
origin: "hop-batch"
derived_from: ["10-inbox/raw/2026-07-11-dup-risk-amari-gates-half-proof-bridge.md"]
date_created: "2026-07-11T00:00:00.000Z"
tags: ["legal-history","law-of-evidence","probability","history-of-mathematics","legal-epistemology","cross-domain-bridge"]
drafted_in: ["2026-07-13-enlightenment-backwards","enlightenment-backwards"]
---


The Roman-canon law of proofs graded evidence into fractions — the half-proof (*semiplena probatio*) of a single witness or private document, short of the full proof of two witnesses or a confession ([[claim-roman-canon-law-rated-one-witness-equal-to-a-private-document]]). It is tempting to read this fractional system as a clean ancestor of mathematical probability. James Franklin argues the opposite. Law was, in his account, "the matrix in which most development of the concepts of probability took place," and the founders of mathematical probability "were all lawyers or sons of lawyers" (Fermat, Huygens, de Witt, Cardano, Pascal). Yet the law itself declined the decisive move: "There was never any finer grading attempted, such as quarter-proofs," and "the law of evidence … has almost entirely refused to accept quantification … refused all attempts to apply Bayesian formulas in court."

So the graded-proof regime is the milieu in which uncertain reasoning was conceptualized, but numeric probability was born only when its founders *broke* with law's refusal to quantify — not by extending the fractional ladder. The distinction matters for any story that treats "half-proof" as proto-Bayesianism: the two traditions share a subject (reasoning under partial evidence) and diverge on method (fixed qualitative thresholds versus continuous number). The refusal is not an accident of underdevelopment but a durable feature — its modern descendant still keeps Bayesian formulas out of the courtroom.

This tension — a discipline that reasons carefully about uncertainty while refusing to reduce judgment to a mechanical number — rhymes with the vault's own thread on non-codifiable verdicts sitting atop mechanical records ([[claim-canonic-deliverable-is-an-append-only-evidence-ledger]]) and with the sourcing floor's refusal to let two soft corroborations be *summed* into a hard claim.

> [!note] Seek's commentary:
> This was the night's real surprise: I expected ½-proof → ¼-proof → … → probability, a smooth quantification gradient. Franklin says the gradient was never built and is still actively resisted. The "founders were all lawyers" line is a lovely person-behind-the-thing cluster I have left as a saved hook rather than a claim — a single Tier-1 aside is a lead, not a verified biographical net. If a clean primary on the Fermat/Huygens/Pascal legal-milieu genealogy surfaces, it earns its own note.
> — Seek