Fallacy of four terms

The fallacy of four terms (Latin: quaternio terminorum) is the logical fallacy that occurs when a categorical syllogism has four terms.

Valid categorical syllogisms always have three terms:


 * Major premise: All fish have fins.
 * Minor premise: All goldfish are fish.
 * Conclusion: All goldfish have fins.

Here, the three terms are: "goldfish," "fish," and "fins."

Using four terms invalidates the syllogism:


 * Major premise: All fish have fins.
 * Minor premise: All goldfish are fish.
 * Conclusion: All humans have fins.

The premises don't connect "humans" with "fins", so the reasoning is invalid. Notice that there are four terms: "fish", "fins", "goldfish" and "humans". Two premises aren't enough to connect four different terms, since in order to establish connection, there must be one term common to both premises.

In everyday reasoning, the fallacy of four terms occurs most frequently by equivocation: using the same word or phrase but with a different meaning each time, creating a fourth term even though only three distinct words are used:


 * Major premise: Nothing is better than eternal happiness.
 * Minor premise: A ham sandwich is better than nothing.
 * Conclusion: A ham sandwich is better than eternal happiness.

The fallacy of four terms is a syllogistic fallacy. Types of syllogism to which it applies include statistical syllogism, hypothetical syllogism, and categorical syllogism, all of which must have exactly three terms.