The Four Term Fallacy

Alias: Quaternio Terminorum

Type: Syllogistic Fallacy

Form:

A two premiss argument containing four terms, which results from a validating syllogistic form by substituting two distinct terms for one variable.

Example:

No Republicans are Democrats.
All conservatives are Republicans.
Therefore, no conservatives are democrats.

Analysis

Syllogistic Rule Violated:

All valid categorical syllogisms have exactly three terms.

Exposition:

A categorical syllogism is, by definition, an argument with three categorical terms. "Term" is to be understood in a semantic sense, as opposed to the syntactic sense of "word" or "phrase". In other words, it is the meaning of the words that is important. So, two different words with the same meaning are the same term, and the same word occurring twice with different meanings is two distinct terms. An argument commits the Four Term Fallacy which appears to have the form of a validating categorical syllogism, but has four terms.

For this reason, the Four Term Fallacy differs from the other Syllogistic Fallacies, each of which involves genuine categorical syllogisms which violate one or more of the rules for syllogisms. The Four Term Fallacy, in contrast, involves arguments which fail to be categorical syllogisms because of too many terms.

Exposure:

One might wonder why there is no "Five Term" fallacy, and theoretically a form which resembles a categorical syllogism can have as many as six terms. 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 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 fallacy is Ambiguous Middle Term.

Subfallacy: Ambiguous Middle Term

Sources:

Acknowledgment: Thanks to Rob Thomas.


Analysis of the Example:

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:

  1. 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:
  2. 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.


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