The Four Term Fallacy

Taxonomy: Logical Fallacy > Formal Fallacy > Syllogistic Fallacy > The Four Term Fallacy

Subfallacy: Ambiguous Middle Term

Alias: Quaternio Terminorum

Form:

An argument similar in form to a categorical syllogism, but with four terms instead of three.

Example:

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

Analysis

Syllogistic Rule Violated:

All categorical syllogisms have exactly three terms.

Exposition:

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.

Exposure:

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.