Occam's razor

Occam's razor

novacula Occami

The likeness, such as it is: a marginal sketch in a 1341 manuscript of the Summa Logicae, captioned frater Occham iste, "this brother Ockham". A reader drew the author beside the text and labelled him the way one labels a face in a margin, and it is the best portrait there is.

Field	Logic; methodology
Usually quoted as	Entia non sunt multiplicanda praeter necessitatem
Written by Ockham	No[1]
Written by	John Punch, 1639[2]
Originated by Ockham	No[3]
Named by	Libert Froidmont, 1649[4]
Named while describing	One of Ockham's critics
Actually Ockham's	The surname
Adjudicates between	Accounts making the same predictions
Adjudicates between different predictions	No; that is what measurement is for

Occam's razor is the methodological principle that, among competing explanations, the one requiring the fewest assumptions is to be preferred. It is named for William of Ockham (c. 1287–1347), an English Franciscan and one of the sharpest logicians of the fourteenth century, and it is the most frequently cited rule in the whole of philosophy.

Almost every part of that attribution is wrong, and the parts are worth separating, because the article's subject turns out to be a well-founded principle with a badly kept provenance and a wildly overstated range.

What Ockham wrote

He did state the principle, repeatedly and in his own words. The clearest is Numquam ponenda est pluralitas sine necessitate: plurality must never be posited without necessity, from his commentary on the Sentences of Peter Lombard. Elsewhere: it is futile to do with more what can be done with fewer.^[1]

These are good formulations and nobody quotes them. What is quoted is Entia non sunt multiplicanda praeter necessitatem, and that sentence is not in his works.

Where the famous words come from

They were written by John Punch, an Irish Franciscan, in 1639, in a commentary on the works of Duns Scotus.^[2]

That is two hundred and ninety-two years after Ockham's death, by a different man, in a book about a different philosopher. It is nonetheless the version on every mug.

Who named it, and after whom

The phrase novacula Occami is later still. It was claimed by Libert Froidmont, in his Philosophia Christiana de Anima of 1649, and Froidmont coined it in the course of describing Gregory of Rimini – who was not a follower of Ockham but one of his critics.^[4]

So the razor is named for a man who did not phrase it, by a writer who was talking about somebody else, and that somebody else disagreed with him. This is the ordinary condition of a scientific name rather than an accident of this one: see Stigler's law of eponymy.

Nor did he originate it

The principle was ordinary scholastic furniture long before Ockham picked it up. Aristotle has it in the Posterior Analytics: the demonstration deriving from fewer postulates is, other things equal, the better. Grosseteste has it around 1220, Aquinas has it in the Summa Theologica, Duns Scotus and Maimonides have versions, and phrases to the effect that a plurality is not to be posited without necessity were commonplace in thirteenth-century writing.^[3]

Ptolemy has it too, which this encyclopedia records with some pleasure: we consider it a good principle to explain the phenomena by the simplest hypothesis possible. The man whose cosmos is the standing example of a system saved by adding wheels stated the rule against adding them.

Ockham's association with the razor is real but is a matter of use rather than authorship. He wielded it harder and more often than his contemporaries, chiefly against entities he thought the schoolmen had invented, and the reputation followed the habit.

What the razor is for

The operation the razor names, which is counting. Every entity an account requires is set down; those not required are struck out; what stands at the foot is the explanation, shorter than the list it came from. The instrument does no work until the list has been written.

Here is the part that matters, and it is a restriction rather than a licence.

The razor operates between accounts that make the same predictions. Given two explanations that fit the evidence equally well and disagree about nothing observable, prefer the one carrying fewer assumptions. That is its whole scope. It is a rule for choosing between empirically equivalent hypotheses, and it is not a rule for choosing between hypotheses that differ about what will be observed.^[5]

Where predictions differ, you do not need a razor. You need a measurement, and the measurement decides.

This encyclopedia contains a clean instance of the razor working properly. Lorentz's ether theory and special relativity predict the same number for every experiment ever performed. No measurement separates them, and none can. That is precisely the situation the razor was made for, and it is why the profession went with the account that carries no undetectable ether: not because Lorentz was refuted, but because he was carrying something for nothing.^[6]

The use made of it

The razor is invoked constantly, in the quarters this encyclopedia documents, in the form: the simplest explanation is that the Earth is flat, and the globe requires an enormous conspiracy.

Two things have gone wrong, and only one of them is arithmetic.

The first is that the two accounts do not make the same predictions, so the razor has no jurisdiction. They disagree about stellar parallax, about aberration, about the dipole, about the plane of a swinging pendulum, about the fringe in a rotating interferometer, and about whether the sun sets in Antarctica in December. Each of those has been measured. A principle for breaking ties is being applied to a contest that was not tied.

The second is the count. Simplicity in the razor's sense is counted in entities and assumptions, not in how easy a thing is to picture. Set out what the flat account has to carry: a sun of a few thousand miles' altitude on a bespoke circuit, a mechanism keeping it circling rather than falling, a separate reason it appears to set, a dome, an account of the southern stars, a suppression of the sine law, a suppression of the fringe, and the coordinated silence of every navy, airline and observatory on Earth.

Set out what the round account has to carry: a ball, and gravitation.

The flat account is not the parsimonious one. It only feels parsimonious because its entities are not enumerated, and the razor's entire operation consists of enumerating them.^[7]

See also

• Grimble's razor – the inverse instrument, which cuts the consequence and keeps the premise
• Stigler's law of eponymy – the general rule this razor's name is a case of
• Hendrik Lorentz – whose theory is the corpus's clean case of the razor applying
• Special relativity – the account it was applied in favour of, and why
• Ptolemy – who stated the principle, and whose cosmos is the standing example against it
• Kinematic and dynamic equivalence – where empirical equivalence is claimed and does not hold

References

1. ^ Numquam ponenda est pluralitas sine necessitate, in the commentary on the Sentences of Peter Lombard. He also has frustra fit per plura quod potest fieri per pauciora. Both are his, both are clear, and neither is on anything.
2. ^ John Punch (Johannes Poncius), 1639, in a commentary on Duns Scotus. The form he gives is non sunt multiplicanda entia sine necessitate; the word order that became famous is later still.
3. ^ Aristotle, Posterior Analytics; Grosseteste, c. 1217–1220; Aquinas, Summa Theologica; and a general scholastic commonplace besides. Ockham inherited the principle in the ordinary way, which is how principles are usually come by.
4. ^ L. Froidmont, Philosophia Christiana de Anima, 1649, who claimed the coinage. That he was describing Gregory of Rimini at the time is the sort of detail that gets lost in three hundred years of citation, and is the reason this article exists in the form it does.
5. ^ This restriction is not a modern hedge. It is what the principle says: other things being equal is doing the work in every formulation from Aristotle onward, and other things are equal only when the accounts predict the same observations.
6. ^ See special relativity, where the point is made at length and in Lorentz's favour. A person may hold the Lorentzian view and be committed to no error whatever; the razor is a preference, not a refutation, and it has never pretended otherwise.
7. ^ Which is the quiet joke in the whole business. The razor is invoked by people who have not performed the operation it names, and the operation is counting.

External links

• William of Ockham – Stanford Encyclopedia of Philosophy – the standing scholarly account
• The sketch labelled frater Occham iste, 1341 – Wikimedia Commons
• Occam's razor – general reference