Four-term fallacy

Part of the series on Logic and rhetoric

Key articles

Logical fallacy Syllogism Argument

General logic

Argument from marginal cases Argument from omniscience Fallacy of accent Gish Gallop Motte and bailey Type theory

Bad logic

Anonymous authority Appeal to novelty Appeal to shame Danth's Law Good old days Moving the goalposts v - t - e

A four-term fallacy (also quaternio terminorum, fallacy of four terms, and if using equivocation, ambiguous middle term) occurs when a syllogism uses four or more terms instead of the required three.

The fallacy is a formal fallacy, because the conclusion does not follow even if the premises are correct.

Form

A four term fallacy uses (at least) four terms, represented here as letters W, X, Y, and Z. The fallacy (when limited to 4 terms) takes two forms. First, where the premises contain 4 terms:

P1: W is X.
P2: Y is Z.

C1: W is Z.

Second, where a new term is introduced in the conclusion:

P1: X is Y.

P2: Y is Z.

C1: W is X.

In both cases, the conclusion does not follow, because all of the terms used in the conclusion are not used in the premises. Compare this to a proper syllogism:

P1: X is Y.

P2: Y is Z.

C1: X is Z.

Here, only three terms (X, Y, and Z) are used, and both terms used in the conclusion are used in the premises.

Examples

Using the first form:

P1 : All fish have fins.

P2 : All humans have hair.

C1 : All fish have hair.

Using the second form:

P1: All fish have fins.
P2: All goldfish are fish.
C1: All humans have fins.

Many first-cause arguments are based on a four-term fallacy:

P1: All events have a cause.
P2: Causal chains have to start somewhere.
C1: God is the cause!

Wow, that God really came out of nowhere! *ba-dum-tss*

See also

Equivocation, one of the most common four-term fallacies

External links

• See the Wikipedia article on Fallacy of four terms.

• FALLACY OF FOUR TERMS, Logically Fallacious