Four-term fallacy

Cogito ergo sum Logic and rhetoric

Key articles

Logical fallacy Syllogism Argument

General logic

Appeal to mystery Appeal to the minority Nutpicking Friend argument Pathos gambit List of cognitive biases

Bad logic

Not as bad as Appeal to consequences Imprecision fallacy Definitional fallacies Argument de l'ami Not an argument 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.

C: W is Z.

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

P1: X is Y.

P2: Y is Z.

C: 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.

C: 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.

Often, however, the four term fallacy technically uses only three apparent terms, but the truth of either premise and the conclusion or both premises depends on the alternation of two meanings of one term:

P1: X (meaning 1) is Y.

P2: Y is Z.

C: X (meaning 2) is Z

Second, where the middle term alternates two meanings (ambiguous middle term proper):

P1: X is Y (meaning 1).

P2: Y (meaning 2) is Z.

C: X is Z.

Third, where the predicate alternates two meanings:

P1: X is Y.

P2: Y is Z (meaning 1).

C: X is Z (meaning 2).

Examples

Using the first form:

P1: All fish have fins.

P2: All humans have hair.

C: All fish have hair.

Using the second form:

P1: All fish have fins.

P2: All goldfish are fish.

C: 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.

C: 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