Ambiguous Middle Term

Alias: Ambiguous Middle1

Taxonomy: Logical Fallacy > Informal Fallacy > Ambiguity > Equivocation > Ambiguous Middle Term2 < Four-Term Fallacy < Syllogistic Fallacy < Formal Fallacy < Logical Fallacy

Form:

Any validating form of categorical syllogism3 with an ambiguous middle term.

Example:

Only man is a rational animal.
No woman is a man.
Therefore, no woman is a rational animal.

Exposition:

A categorical syllogism is, by definition, an argument with three categorical terms occurring within it. Each such term occurs in two statements in the argument, and the middle term is the one that occurs in both premisses but not in the conclusion.

Since each term occurs twice in a syllogism, if any term is ambiguous it is possible that it occurs with two different meanings. In effect, such an argument has four terms, which violates the definition of "categorical syllogism", thus committing the Four Term fallacy. Moreover, if a word or phrase in such an argument ambiguously represents two terms, the argument commits the informal fallacy of Equivocation. Finally, if the argument equivocates on the middle term, it commits the fallacy of Ambiguous Middle.

The form of the Example argument appears to be that known as "Camestres"4, which is a validating argument form. Its three terms are "man", "woman", and "rational". "Man" is the middle term, because it occurs in both premisses. However, in order for the argument to be a genuine example of Camestres, each term must be used in the same sense in both of their occurrences. If any term is used equivocally in the argument, then it is not really an instance of Camestres.

In order for the first premiss to be true, "man" must there have the old-fashioned sense of "mankind", referring to humanity collectively. In contrast, for the second premiss to be true, "man" must mean "adult male human being". If "man" in the first premiss meant that then it would be false, since women are also rational animals. If "man" in the second premiss meant "mankind" then it too would be false, since women are part of mankind. Thus, for both premisses of the Example to be true, "man" must be ambiguous. For this reason, the Example is considered to really have four terms, not three. So, whether a word is a "term" for the purposes of categorical arguments is a matter of meaning. The Example argument is, in fact, not really a categorical syllogism, let alone an instance of Camestres, despite appearances.

Exposure:

Ambiguous Middle is an unusual fallacy that has both a formal and informal aspect that can be seen in the Taxonomy, above, which shows it as a type of both formal and informal fallacy. It is formal in that it is a subfallacy of the syllogistic fallacy of Four Terms, since an instance of Ambiguous Middle has two middle terms instead of one in the sense explained, above, in the Exposition. It is informal in that it is a subfallacy of Equivocation, since the fact that there are two middle terms is disguised by using a single word or phrase ambiguously. For this reason, to understand the fallacy it is necessary to understand both the formal fallacy of four terms and informal fallacies of ambiguity.

Notes:

  1. Simon Blackburn, Oxford Dictionary of Philosophy (1996).
  2. William L. Reese, Dictionary of Philosophy and Religion (Humanities Press, 1980), p. 169.
  3. For a short introduction to categorical syllogisms, see the entry for syllogistic fallacy.
  4. Camestres is the following form of categorical syllogism:

    All P is M.
    No S is M.
    Therefore, no S is P.

    Note that "Only S is P" is equivalent to "All P is S".