The Four Term Fallacy
Subfallacy: Ambiguous Middle Term
Alias: Quaternio Terminorum
No Republicans are Democrats.
All conservatives are Republicans.
Therefore, no conservatives are democrats.
Syllogistic Rule Violated:
All categorical syllogisms have exactly three terms.
A valid categorical syllogism is an argument with three terms. A term is a word or phrase that refers to a class or category of thing, which is why such arguments are called "categorical". However, "term" is to be understood in a semantic sense, as opposed to the syntactic sense of "word" or "phrase"; in other words, a term is the meaning of a word or phrase. So, two different words with the same meaning are the same term, and the same word occurring twice with different meanings represents two distinct terms.
- A "categorical syllogism" is usually defined as a two-premissed argument made up of three categorical propositions containing exactly three terms. Thus, the syllogistic rule violated by an argument with four terms―see above―differs from the other rules for syllogisms in that it is a rule that partially defines what it is to be a categorical syllogism. Thus, an argument that commits the four term fallacy is not, in fact, a categorical syllogism. In contrast, the other rules all define what it is for a categorical syllogism to have a validating form.
Thus, the four term fallacy differs from the other fallacies of categorical syllogisms, each of which involves genuine categorical syllogisms which violate one or more of the rules for syllogisms. In contrast, the four term fallacy is committed by arguments which violate the definition of "categorical syllogism" by having too many terms.
- One might wonder why there is no "Five Term" fallacy, and a form which resembles a categorical syllogism can have as many as six terms in theory. However, an argument with so many terms would be unlikely to fool anyone into thinking that it was a categorical syllogism. Of course, this raises the question of how an argument with even one extra term could so confuse anyone.
The answer is that actual instances of the four term fallacy are usually polymorphously fallacious, that is, they are also instances of the fallacy of equivocation. So, the fact that the argument has four terms is concealed by an equivocation on two of the terms in the argument, when one word ambiguously means two terms. When the equivocation is on the middle term, the resulting subfallacy is called "ambiguous middle term"―see above.
- Irving Copi & Carl Cohen, Introduction to Logic (Tenth Edition) (Prentice Hall, 1998), pp. 274-5.
- A. R. Lacey, Dictionary of Philosophy (Third Revised Edition) (Barnes & Noble), 1996.
Acknowledgment: Thanks to Rob Thomas.
This example seems to have a validating syllogistic form, but it actually has four terms instead of three. The four terms are: conservatives, Republicans, Democrats, and democrats. The word "democrat" has two meanings when capitalized and uncapitalized:
- A member of the Democratic Party, as opposed to a member of the Republican Party. A party member may be called a "big-D" Democrat to distinguish them from the second sense:
- A supporter of democracy, as opposed to an anarchist, authoritarian, or totalitarian. These are referred to as "small-d" democrats, to distinguish them from the first sense.
In order for the example to be a genuine categorical syllogism, the two occurrences of "democrat" would have to be two occurrences of the same term, that is, they would have to have the same meaning. When two occurrences of the same word have different meanings they are two distinct terms. The Example commits the Four Term Fallacy if the major term of the conclusion is meant in sense 2―namely, that no conservatives are small-d democrats―which is not true.