Ambiguous Middle

Alias:

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

Form:

Any validating form of categorical syllogism with an ambiguous middle term. For a short introduction to categorical syllogisms, see the entry for syllogistic fallacy.

Example Counter-Example
All human fetuses are human.
Any human is a being with a right to life.
Therefore, all human fetuses are beings with a right to life.
All dog fetuses are canine.
Any canine is an animal that must be on a leash.
Therefore, all dog fetuses are animals that must be on a leash.

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. If the syllogism would be otherwise valid, it is said to commit the syllogistic four-term fallacy―that is, a single word may ambiguously stand for two terms. In effect, such an argument has four terms, which violates the definition of "categorical syllogism". Moreover, if a word or phrase in such an argument ambiguously represents two terms, the argument commits the informal fallacy of Equivocation.

For instance, in the Example above, the three terms are "human fetus", "human", and "being that has a right to life". "Human" is the middle term, because it occurs in both premisses. In the first premiss, it is an adjective meaning "of or belonging to human beings", whereas in the second it is a noun meaning "human being". Thus, the Example really has four terms rather than three.

The Counter-Example is an argument of the same form that is obviously fallacious, thus showing that the Example also commits the fallacy. In the Counter-Example, "canine" is the middle term and it is clearly used in two different senses in the premisses: in the first premiss, it is an adjective meaning "of or belonging to a dog", while in the second it is a noun meaning "dog".

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 Ambiguous Middle really has two middle terms instead of one. 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.

Source: William L. Reese, Dictionary of Philosophy and Religion (Humanities Press, 1980), p. 169.

Reader Response:

Jim wrote in with a criticism of the Example used above―note that I subsequently changed the Counter-Example by replacing "organs" with "fetuses":

When someone says in an argument that "All human fetuses are human," I believe it is clear to most people that what they mean is "All human fetuses are humans," that is "are human beings," but have simply made a grammatical error that has become acceptable through common usage. To say that the term "human" in this statement is ambiguous is to be purposely obtuse. That you know that the word "human" in the first premise is meant to be taken as a noun and not as an adjective becomes clear in your counter example where you chose to substitute "dog organs" for "canine organs" to make the counter example clearer/more intelligible. The premise "All canine organs are canine" sounds silly whereas the premise "All human fetuses are human" does not. Your "counter example" becomes:
All dog organs are dogs.
Any dog must be on a leash.
Therefore, all dog organs must be on a leash.

and is wrong because the first premise is wrong, not because of equivocation.

A couple of points in reply:

Acknowledgment: Thanks to Elijah Smith for a criticism of the Counter-Example that led me to revise it.