Equivocation
Equivocation is the fallacy of using one word in two different senses within a single argument, so that the conclusion depends on a shift in meaning the sentence never announces. It is the best known of the fallacies of ambiguity, cataloged by Aristotle in the Sophistical Refutations under the heading of homonymy, and it is the one fallacy that survives translation badly, because the two senses that collide in one language rarely collide in the next.
Grain of Salt teaches the method rather than the verdict. Every argument quoted below is invented, and the interest is in the word that moves, not in the position it is used to defend.
What equivocation is
Equivocation runs a word through an argument twice and changes its meaning in between. The structure stays valid on the page, every individual sentence stays true, and the conclusion still fails, because the two premises are no longer about the same thing. That combination of a sound-looking form with a broken content is what makes it the most technically interesting entry in most lists of logical fallacies.
The classic schoolroom case has three lines: a feather is light, what is light cannot be dark, therefore a feather cannot be dark. The word light means low in weight in the first line and pale in color in the second. Nobody is fooled by that one. The same move, performed on the word significant or the word free, has fooled a great many people who were paying attention.
The fault in one sentence, and the two parts it always has
Every equivocation has two parts: a word that appears at least twice, and a conclusion that holds only if both appearances mean the same thing. Test the second part and the fallacy shows itself immediately, because the argument stops working the moment each sense is written out in full.
The best known example in English is the ham sandwich argument: nothing is better than eternal happiness, a ham sandwich is better than nothing, therefore a ham sandwich is better than eternal happiness. In the first premise, nothing means there is no thing that is better. In the second, it names an alternative, having no sandwich at all. Two senses, one word, and a conclusion that arrives with a straight face.
The four forms equivocation takes
Equivocation takes 4 forms, ordered here from the harmless to the expensive.
- The joke shift. A pun in argument's clothing, as in the feather example. Nobody is deceived and it is mainly used for teaching.
- The everyday to technical shift. A word that has a precise meaning in one field and a loose one outside it, moving from one to the other mid argument.
- The marketing shift. A term defined narrowly in the small print and read broadly in the headline.
- The moving definition. A word given a modest meaning when the claim is challenged and an extreme meaning when it is asserted, alternating as the conversation requires.
Form two supplies the vocabulary a skeptical reader most needs to watch, because these are the words that carry a license they did not earn.
| Word | Everyday sense | Technical sense | Where the shift bites |
|---|---|---|---|
| Significant | Large, important, worth acting on | Unlikely to have arisen by chance alone | A tiny effect is reported as an important one |
| Theory | A guess | An explanatory framework supported by evidence | A well tested account is dismissed as speculation |
| Average | Typical, ordinary | The mean, which may describe nobody | A skewed distribution is described by a value no member holds |
| Natural | Wholesome | Occurring without human manufacture | An origin is presented as a property |
| Free | At no cost and without conditions | At no additional charge, conditions applying | The conditions live in a footnote |
A worked example, and the repair
A worked example makes the repair obvious, because the shift is visible once both senses are written out. Here is the raw version, from a project meeting: "The new caching layer produced a statistically significant improvement in load time, so the improvement is significant and we should ship it." Both sentences use significant. The first is a claim about chance, that a difference this size is unlikely to be noise. The second is a claim about worth, that users will feel it. A difference of 11 milliseconds can satisfy the first and fail the second completely.
The repair is to write each sense out in full and never use the shared word again: "The improvement in load time is unlikely to be a fluke, and it is 11 milliseconds, which is below the threshold users can perceive. It is a real effect and not a useful one." The argument now says something, and what it says is more interesting than the version that equivocated. That is the usual outcome. Removing an equivocation rarely removes a claim; it exposes the claim that was hiding under two meanings.
What equivocation is confused with
4 faults sit close to equivocation, and separating them tells you which repair to reach for.
- Vagueness is a word with no sharp boundary, such as tall or crowded. It has one meaning that fades at the edges, where an ambiguous word has two meanings with a gap between them. Equivocation belongs to ambiguity, not to vagueness, though the two often travel together in advertising.
- Amphiboly is ambiguity in the grammar rather than the vocabulary: a sentence with two readings because of how it is built, not because of what a word means.
- Non sequitur is the general failure of a conclusion to follow. Equivocation is a particularly well disguised way of committing one.
- Ad hominem is its opposite in one useful respect. Ad hominem is a fault about the arguer, while equivocation is a fault entirely inside the words, and can be committed by someone arguing in perfect good faith with themselves.
When a double meaning is not a fault
A double meaning is not a fault in itself, and the same move that ruins one argument is most of what makes a language usable. Words with several senses are not a defect, they are the normal case, and using one is only a fallacy when an argument's validity depends on the senses being confused. Puns, jokes, headlines and poetry trade on ambiguity deliberately, and no conclusion is being drawn from them.
Two working conditions keep a multi-sense word honest in argument. Define it once, at first use, in the sense you intend, which is exactly why contracts open with a definitions clause and standards documents list their terms before their requirements. Then hold that sense for the whole document. A word that has been pinned down in writing can be used 40 times without risk, and a word that has not can betray an argument in 3 lines.
The test to run on the next argument you read
Ask 4 questions of any argument whose conclusion feels stronger than its premises.
- Find the word that appears in more than one premise, and ask whether it is carrying the weight of the conclusion.
- Replace each occurrence with a full definition rather than the word, and read the argument again to see if it still holds.
- Ask whether either sense is a technical one, and whether the speaker is entitled to the license that sense grants.
- Ask the speaker which sense they mean, and note whether the answer changes depending on which part of their claim is being challenged.
Equivocation in advertisements, and its association with vagueness
Advertisements are where equivocation is industrialized, because a headline and a footnote can hold different meanings of the same word without either being a lie. An unlimited data plan can mean no cap on volume while speed is reduced after a threshold. A free upgrade can mean no additional charge on a contract that has just been extended. A hand finished product can mean that 1 operation in 12 was done by a person. In each case the narrow sense is defensible in writing and the broad sense is what the reader takes away, which is the entire design.
People often say equivocation is a fallacy associated with vagueness, and the association is real even though the categories are distinct. Vague words make equivocation easier to perform and harder to prove, because a reader who challenges the shift can be told that the word simply covers a broad range. Confirmation bias completes the job from the reader's side, since a reader who already likes the claim will supply the generous sense without being asked to. The defense against all of it is the same and it is unglamorous: ask for the number, the threshold or the definition. A word that cannot be replaced by a specific value when asked was doing something other than describing.