Alias:

• Ambiguous Middle Term
• Four-Term Fallacy

Type:

• Equivocation
• Four-Term Fallacy

Form:

Any valid form of categorical syllogism with an ambiguous middle term.

Exposition:

A categorical syllogism is, by definition, an argument with three categorical terms occurring within it. "Term" is to be understood in a semantic sense, so that a single word may ambiguously stand for two terms. This leads to the possibility of ambiguous syllogisms in which one of the words equivocates on two terms. Such a syllogism may commit the fallacy of Equivocation. Thus, Ambiguous Middle is the fallacy of Equivocation when it occurs within the premisses of a categorical syllogism.

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:

• You seem to be under the misimpression that the argument in the Example is someone else's argument, but it is a cooked-up example, that is, it's my argument. However, it is based on some real-life arguments that I have studied, but cleaned-up and made more explicit. For instance, the argument used as an Example of Equivocation is essentially the same as the above Example. What I have done is to take the argument and turn it into a categorical syllogism in order to illustrate the syllogistic fallacy of Ambiguous Middle, which is an equivocation occurring in a syllogism. Unfortunately, arguments as they occur in the raw often don't make good examples. I use real examples whenever possible, but the point of the examples and counter-examples is to help people understand the nature of the fallacy, and real world arguments are often poor examples. For this reason, the examples that I use are often too obviously fallacious; they would never fool anyone.
• Arguments which commit a fallacy of ambiguity have two meanings. On one meaning, the argument is valid, but one of the premisses is false or controversial. On the other meaning, the premisses are uncontroversially true, but the argument is invalid. Here are the two meanings of the Example:
  1. All human fetuses are the fetuses of human beings.
     Any human being has the right to life.
     Therefore, all human fetuses have the right to life.

     The premisses of this argument are both uncontroversially true, but it is an invalid syllogism.

  2. All human fetuses are human beings.
     Any human being has the right to life.
     Therefore, all human fetuses have the right to life.

     This argument—which is the way in which you are interpreting the Example—is a perfectly valid syllogism of the form Barbara, but it has a controversial first premiss. No one who disagreed with the conclusion would be likely to agree with the first premiss. For this reason, despite the fact that the argument is valid, it commits a different fallacy, namely, Begging the Question, that is, it has a question-begging first premiss.

  The way in which ambiguous arguments are persuasive is by combining both these meanings into one, so that they seem to be both valid and to have uncontroversial premisses. But it is only by switching back and forth mentally between the two meanings of the ambiguous term that such an argument will seem to be sound.

  Thanks for raising a difficult issue, Jim, and I hope that this clarifies it at least a little.

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