A logical fallacy that occurs when a categorical syllogism has four terms.
A valid syllogism has 3 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." The object being described, fish, occures in both premises and therefore logically links both premises.
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.
Dealt with by showing the formal logical flaw as demonstrated in the example.