Undistributed middle
(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 distribution.
Example of a syllogism with an undistributed middle:
Some animals are cats.
All dogs are animals.
Therefore, all dogs are cats.
Other names
- Non distributivi [sed collectivi ] medii
Rules of distribution
The distribution rules for syllogisms are summarized in the article on distribution. The specific rule that is violated by this fallacy can be formulated as follows:
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 distribution of the terms in the four categorical statement types:
| 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
Weitere Informationen
- Fallacy of the undistributed middle on Wikipedia
- Fallacy of (the) Undistributed Middle on Logically Fallacious
- Undistributed Middle Term on Fallacy Files