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Encyclopedia > Fallacy of four terms

The fallacy of four terms (Latin: quaternio terminorum) is a logical fallacy that occurs when a three-part syllogism has four terms. Latin is the language originally spoken in the region around Rome called Latium. ... A logical fallacy is an error in logical argument which is independent of the truth of the premises. ... In traditional logic, a syllogism is an inference in which one proposition (the conclusion) follows of necessity from two others (known as premises). ...

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". The major premise in a categorical syllogism is the premise whose terms are the syllogisms major term and middle term. ... In a categorical syllogism, the minor premise is the premise whose terms are the syllogisms minor term and middle term. ...

Using four terms invalidates the syllogism. In logic, an argument is said to be valid if the truth of the conclusion follows from the truth of the premises. ...

Major premise: All fish have fins
Minor premise: All goldfish are fish
Conclusion: All humans have fins

In the above example, it should be clear that there are four terms ("fish", "fins", "All goldfish" and "All humans") 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. Non sequitur is Latin for it does not follow. ...

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: The fallacy of equivocation is committed when someone uses the same word in different meanings in an argument, implying that the word means the same each time round. ...

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). Syllogistic fallacies are logical fallacies that occur in syllogisms. ... A statistical syllogism is an inductive syllogism. ... In logic, a hypothetical syllogism is a valid argument of the following form: P → Q. Q → R. Therefore, P → R. In logical operator notation In other words, this kind of argument states that if one implies another, and that other implies a third, then the first implies the third. ... Wikipedia does not yet have an article with this exact name. ...

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