◄ UD0   ← Llull   LOGIKĒ · the medieval root
LOGIKĒ · the medieval root · c. 1320

William of Ockham

c. 1287 – 1347 · Ockham, Surrey & Oxford & Munich · Franciscan friar · the greatest logician of the Middle Ages
Between [[ramon-llull]]'s combinatorial wheel and [[leibniz]]'s dream of calculation, logic did not sleep — it was refined, hard, in the medieval universities, and its sharpest mind was a Franciscan friar from Surrey. Ockham built a deep theory of how words refer (supposition theory), stated the rules we now credit to [[augustus-de-morgan]] five centuries early, and argued that universals — "redness," "humanity" — are not things in the world but names in the mind (nominalism). But he is famous for a principle of method so durable it outlived the entire scholastic project: do not multiply entities beyond necessity. Given two explanations that fit the facts equally, prefer the simpler. Ockham's Razor — and it turns out to be the founding intuition of modern model selection.
✓ STRONG

A real logician, a lasting principle. Ockham's supposition theory and his statement of the De Morgan rules are genuine medieval logic of high order; and the razor — prefer the simpler adequate explanation — is sound methodological guidance that science still runs on.

◐ A HEURISTIC, NOT A LAW

Simpler ≠ true. The razor is a tie-breaker, not a theorem: when two theories fit equally, bet on the simpler — but reality is sometimes complicated, and the razor can cut the right answer. It guides; it does not prove.

◔ THE WORDING IS LATER

He didn't quite say it. "Entities must not be multiplied beyond necessity" (entia non sunt multiplicanda…) is a 17th-century paraphrase. Ockham used the idea repeatedly, in other words; the famous Latin slogan was put in his mouth afterward.

I · The razor, as the machine sees it — overfitting

Ockham's razor has a precise modern face: the problem of overfitting. Here are noisy data points that really come from a simple line. Slide up the model's complexity — let it use a higher-degree curve — and watch it bend to pass through every point, error on the data dropping to zero. But look what it does between the points: it wiggles wildly, fitting the noise, not the signal. The simplest model that explains the data is the one that will be right about the next point. Razor: don't multiply curves beyond necessity.

model complexity (degree)
degree 1 fit error on the data wiggle (between points)
Crank the degree and the fit error falls toward zero while the wiggle explodes — the model is memorising noise, not learning the line. ⚑ This is Ockham's razor made quantitative: it is the bias-variance tradeoff, the principle behind regularisation, the Minimum Description Length, and the "Bayesian Occam factor" that penalises complex models automatically. Seven centuries before machine learning had a name, a friar wrote down its first commandment — prefer the simpler adequate hypothesis — and it is still the line between learning and overfitting.
"It is futile to do with more what can be done with fewer." — William of Ockham (Summa Logicae, paraphrased)

II · The logician behind the razor

SUPPOSITION THEORY & THE DE MORGAN RULES

A rigorous medieval account of how a term refers in a sentence, and an explicit statement that negating "A and B" gives "not-A or not-B" — [[augustus-de-morgan]]'s laws, five centuries before De Morgan.

NOMINALISM

Universals like "redness" are not real things floating in a Platonic heaven — they are names, mental signs that stand for many particulars. Reality is individuals; generality lives in language. A razor applied to metaphysics itself.

The razor is not a stray maxim — it is the method of a thinker who used it on everything. Ockham's nominalism is the razor turned on metaphysics: don't posit a whole realm of universal Forms when names in the mind will do the job. His logic of supposition is the razor turned on language: pin down exactly what a word stands for, and the pseudo-problems dissolve. He was a working logician of the first rank — the medieval period this lineage had skipped was not a gap in reasoning but a forge of it, and Ockham was its sharpest edge. That his rules for negation, his theory of reference, and his principle of parsimony all resurfaced — in [[augustus-de-morgan]], in modern semantics, in machine learning — is the measure of how far ahead he was working. ⚑ The friar who told the future to keep it simple.

III · The razor's edge, and the heretic who held it

Gate kept on. Two honesties, on the principle and the man. On the principle: the razor is real and useful but it is a heuristic, not a law — it says that when two explanations fit the evidence equally, you should bet on the simpler, because it is less likely to be fitting noise and more likely to generalise (which the overfitting demo makes precise). It does not say the simpler theory is true — reality is sometimes genuinely complicated, and a too-eager razor can shave off the correct answer; its modern formalisations (regularisation, MDL, Bayesian model comparison) make the tradeoff exact rather than mystical. And the famous Latin slogan, entia non sunt multiplicanda praeter necessitatem, is a 17th-century formulation — Ockham expressed the idea many times, but not in those words. On the man: William of Ockham was a brilliant and combative Franciscan who was summoned to Avignon on suspicion of heresy, took the Pope's side then broke with him violently over the doctrine of apostolic poverty, fled to the protection of the Holy Roman Emperor, was excommunicated, and died — probably of the Black Death — still in exile. A friar who sharpened the tools of reason, applied them without mercy to the Church's own metaphysics, and paid for it. ⚑ The medieval root of the lineage, restored. [[ramon-llull]] ← · the lineage runs on to [[leibniz]] and the modern age.