(Fallacy of the) Undistributed middle term
Example of a syllogismwith an undistributed middle:
Some animals are cats.
All dogs are animals.
Therefore, all dogs are cats.
- Non distributio medii
- Non distributivi sed collectivi medii
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:
Remember: The middle term, which connects the two premises, must occur in a distributed position in at least one of the premises.
The following table gives an overview of the distributivity of the terms in the four categorical statement types:
All S are P
No S is P
Some S are P
|not distributed||not distributed|
Some S are not P
With regards to the example above, the premises therein are of the types I and A; The middle term (“animals”) appears in both cases in undistributed positions, therefore this form of a syllogism is not valid.