The Sense

A dictionary entry for a common English word lists its senses in order, and for the commonest words — set, run, take — the list runs to hundreds. What the order means varies. Historical dictionaries arrange senses by first attestation, so the sequence is a chronology and says nothing about use. Corpus-based learner dictionaries arrange them by frequency, so the sequence does carry information — but the frequency is measured over the general corpus the lexicographers assembled, which is not the text in front of the reader. Either way, the entry catalogues what the word is capable of meaning, and the question a reader of any particular passage actually has is which of those is operating here. Word-sense disambiguation, the computational form of that question, found early that the crudest baseline is the hardest to beat: ignore context entirely and always guess whichever sense is commonest in the training data. The baseline is strong because sense distributions are violently skewed. A word with a dozen catalogued senses will, within one body of text, use one of them nearly always. The catalogue describes a space of possibilities; the corpus is a distribution over that space; and the two are not the same object.

Failure mode and effects analysis enumerates the ways a component can fail — a valve can stick open, stick closed, leak internally, leak externally, respond slowly, respond erratically — and the enumeration is exhaustive by design, because an unlisted failure mode is one nobody has provisioned for. It does attach numbers: each mode receives an occurrence rating, which multiplies with severity and detectability into a risk priority number. But those ratings are ordinal, and they are very often carried in from generic reliability handbooks or supplied by engineering judgement rather than measured on the installation being analysed. Two identical valves in different plants, on different duty cycles and different fluids, produce genuinely different failure distributions over the same enumerated set, and the analysis will frequently give them the same scores. The enumeration is a claim about the possible. The maintenance log is a claim about the actual. When the score is borrowed, the document has quietly substituted the first for the second while still presenting a number.

Allergen labelling has the same structure and is more honest about it. May contain nuts asserts possibility and declines to quantify. The manufacturer knows a shared production line makes contamination conceivable and does not know whether it occurs in one packet per thousand or one per million. The label is scrupulous precisely in refusing to convert a possibility into a rate. Every reader supplies a rate anyway, from somewhere other than the label.

The error these share is not that possibility lists are wrong; each is correct about what it covers. The error is in the direction of inference. A catalogue of what can happen is assembled from the union of many contexts, which makes it an upper bound on any single context, often a very loose one. Reasoning from catalogue to particular case runs the derivation backwards, and the backwards step carries no warrant. The dictionary was built from many corpora; no corpus contains the dictionary. Whether a given ambiguity is live in a given body of text is a fact about that text, and there is no route to it except looking.

What makes this durable rather than obvious is that the catalogue is cheap to consult and the corpus is usually cheap to measure, and the second gets skipped anyway. The catalogue is already written, general, authoritative, and available before the question is asked; the measurement is specific, must be constructed, and yields a number good for one corpus only. So the general artifact stands in for the particular one, and the substitution is hard to see, because the catalogue is not wrong. It is answering a question about the language, or the component class, or the production line, while the reader needs an answer about this text, this valve, this packet. A possibility is not a rate, and nothing converts one into the other except counting.