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

Valid syllogisms always take the form:

Major premise (connects the minor premise and the conclusion): All fish have fins

Minor premise: That thing is a fish

Conclusion: That thing has fins

The three terms are: "That thing", "fish", and "fins".

Using four terms invalidates the syllogism.

Major premise: All fish have fins

Minor premise: President Bush is a fish

Conclusion: Al Gore has fins

In the above example, it should be clear that there are four terms ("fish", "fins", "Al Gore" and "President Bush") and therefore the major premise does not actually connect the minor premise and the conclusion. When premises are not connected to the conclusion it is called a non-sequitur.

Such examples may seem ludicrous, but the nature of human language makes it possible to hide offensive premises, and the exact number of terms may not always be clear in casual writing and speech. Equivocation is a common subfallacy where two terms use the same word or phrase but with different definitions giving a false appearance of a valid syllogism:

Major premise: Nothing is better than complete happiness.

Minor premise: A ham sandwich is better than nothing.

Conclusion: A ham sandwich is better than complete 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).

External links

• Stephen's guide: Fallacy of four terms
• Fallacy files: Fallacy of four terms
• Atheismweb: Fallacy of four terms