Example of a syllogism ◈ with an undistributed minor term:
All dogs are mamals. All mamals are animals. ∴ All animals are dogs.
All three statements here are of type A (“All S are P”), in which the subject (“S”) is in a distributed and the predicate (“P”) in an undistributed position. For a syllogism to be valid, any term that is in a distributed position in the conclusion would also need to be distributed in the premise. As this is not the case with the minor term (“animals”), this syllogism is formally invalid.
- Undistributed major / minor [term]
- Illicit [process of the] major / minor [term]
Note: in some publications, this is listed as two separate fallacies, depending on whether the major or the minor term is concerned. For simplicity, those are combined here under a more general name.
Rules of distributivity
The distribution rules for syllogisms are summarized in the article on distributivity. The specific rule that is violated by this fallacy can be formulated as follows:
If a term appears in the conclusion statement in a distributed position, it must also be distributed in the premise in which it appears
The following table gives an overview of the distributivity of the terms in the four categorical statement types:
|A||“All S are P”||distributed||not distributed|
|E||“No S is P”||distributed||distributed|
|I||“Some S are P”||not distributed||not distributed|
|O||“Some S are not P”||not distributed||distributed|
With regards to the example above, the premises therein are all of the type A; While the minor term (“animals”) appears in the conclusion in a distributed position, it is undistributed in the minor statement. Therefore, this form of a syllogism is not valid.