Fallacy of Four Terms


Also called Ambiguous Middle Term, Quaternio Terminorum.

A standard form categorical syllogism contains four terms instead of three.


A standard categorical syllogism is made of three propositions (two premises and a conclusion) and uses three terms (minor, major and middle). For example:

Using a fourth term destroys the logical construct of the syllogism.

In many cases, the fallacy of four terms is a special case of equivocation. While the same word is used, the word has different meanings, and hence the word is treated as two different terms. Consider the following example: "Only man is born free, and no women are men, therefore, no women are born free." The four terms are: man (in the sense of 'humanity'), man (in the sense of 'male'), women and born free.


All dogs are animals, and all cats are mammals, so all dogs are mammals.
The four terms are: dogs, animals, cats and mammals.




Identify the four terms and where necessary state the meaning of each term.

Stick to the standard forms and rules of syllogistic logic.