Four-term fallacy

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.

Cogito ergo sum
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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*

gollark: I can't.
gollark: Sorry for the horrible formatting but I can't do much better.
gollark: <@293066066605768714> As detailed in infocontext.txt palaiologos also wants acknowledgement that you got this.
gollark: Hello! As you may know, I am (barely) staff in old esolangs. For transparency purposes I also share some of the staff discussion which goes on there. They recently complained about this; palaiologos apparently wants me to post *full* context for staff discussions instead of my somewhat small screenshots, including retroactively in the case of the rules change discussion since apparently people have been led to believe that the staff weren't mostly in favour of this. Thusly, here you go.
gollark: And also the permissions system, via [REDACTED] beeonic incursions.

See also
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