William of Ockham, writing in the 1320s, kept insisting on a principle he never stated in the form now attached to his name. His version is plurality should not be posited without necessity, and the shaving metaphor was added centuries later.

He was not making a general remark about elegance. He was using it as a weapon, against a specific target.

What he was actually cutting

Scholastic metaphysics had accumulated an enormous population of real entities. Universals existed in some fashion, since otherwise it was unclear what two white things share. So did relations, considered as things distinct from their relata. So did the various formal distinctions Scotus had introduced to keep his account of God consistent.

Ockham's program was to show that none of these were needed. Two white things are simply both white; there is no third item, whiteness, existing somewhere and shared between them, and the word white is a sign that applies to each of them individually. That is nominalism, and the razor is its method.

The point is worth holding onto, because it shows what the principle is for. It is not advice to explain things briefly. It is a rule about what you are committed to existing, and it says that a commitment which does no explanatory work is not free.

The condition everyone drops

The principle applies to theories that account for the evidence equally well.

That clause is load-bearing and it is the first thing lost in ordinary use. A simpler theory that explains less is not preferred by Occam's razor; it is simply worse. The razor is a tie-breaker, and the tie has to be real.

So when someone invokes it to dismiss a complicated account of something, the first question is whether the simpler account actually handles all the same evidence. Usually it does not, and the razor was doing no work — it was a rhetorical gesture toward an argument nobody made.

Why it should work at all

This is the genuinely hard question, and it has no agreed answer.

It is not obvious that reality is parsimonious. The universe contains an unreasonable number of particle types, and biology is a monument to accumulated complication. So a preference for fewer entities cannot simply be a report on how things tend to be.

Three defenses are usually offered.

Practical. A theory with more moving parts has more ways to be wrong and more parameters to fit, and a sufficiently flexible theory can accommodate any data at all — which makes it unfalsifiable. Preferring the leaner theory is preferring the one that took a risk.

Statistical. This is the sharpest version. Added parameters let a model fit noise as well as signal, so an over-complicated model predicts new cases worse even though it fits the old ones better. That is overfitting, and it is exactly the shape of the problem of induction's grue case. Here the razor is not aesthetics — it is a theorem about generalization.

Semantic. On this reading the razor is not about the world at all. It concerns what you should say: posit as few entities as your account requires, and remain silent about the rest. This is closest to Ockham's own use, which was aimed at the vocabulary of theology rather than at nature.

Where it fails

It is worth knowing the cases where the principle misleads, because they are not rare.

Copernicus's system was not simpler than Ptolemy's when proposed — it needed epicycles too, and in the first version about as many. Special relativity abolished the ether, which is a clean cut, but general relativity replaced a straightforward force with a geometry of spacetime that no one would call parsimonious. Atomic theory multiplied entities enormously and was right to.

The pattern is that what counts as simple depends on how you are counting, and the theory usually decides that. Fewer kinds of thing, fewer laws, fewer free parameters and fewer brute coincidences are four different measures, and they do not agree. A theory that posits more entities to eliminate an unexplained coincidence is often the better one, which is why the razor is a tie-breaker and not a method.