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(Fallacy of the) Undistributed middle term

Describes an (invalid) syllogism, in which the middle term that is connecting the two premises is not used according to the rules of distributivity.

Example of a syllogism  with an undistributed middle:

Some animals are cats.
All dogs are animals.

All dogs are cats.

Other names

  • 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:

The middle term, which connects the two premises, must in at least one of the premises occur in a distributed position.

The following table gives an overview of the distributivity of the terms in the four categorical statement types:

Type Statement Subject Predicate
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 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.

See also

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