Fallacy of four terms
The fallacy of four terms, or quaternio terminorum, is a formal mistake in a syllogism when there are four or more terms instead of exactly three. A valid syllogism needs three terms because one term—the middle term—connects the two premises. When there are four terms, there isn’t a guaranteed middle term to link everything, so the argument is invalid.
In everyday reasoning this happens most often through equivocation: using the same word with two different meanings, which creates an apparent fourth term. For example, the word nothing can mean “no value” or “the absence of value.” If those readings get mixed, the argument looks like a valid three-term form but isn’t.
Sometimes what looks like a four-term problem can be rewritten as a proper three-term argument. For instance, a five-term setup with words like humans, immortal, Greeks, people, and mortal can be turned into a standard three-term form by replacing terms with synonyms and simplifying the statements.
The fallacy is a matter of form, not content, so it is classified as a formal fallacy. It can affect different kinds of syllogisms, including statistical, hypothetical, and categorical, all of which should have exactly three terms. Because the problem often comes from how the middle term is handled, the misstep is sometimes called the fallacy of the ambiguous middle. That particular issue sits at the border between formal and informal fallacies and is usually treated as informal because the fault lies in meaning rather than in form.
This page was last edited on 2 February 2026, at 21:42 (CET).