====== (Fallacy of the) Undistributed middle term ======

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

Example of a syllogism <span noprint>[[app>#IA1A|Show in Syllogism-Finder App]]</span> with an //undistributed middle//:

> Some <var><u questionable "Undistributed middle term">animals</u></var> are <var>cats</var>.
> All <var>dogs</var> are <var><u questionable "Undistributed middle term">animals</u></var>.
> <span conclusio><s invalid "Invalid because of undistributed middle term">Therefore, all <var>dogs</var> are <var>cats</var>.</s></span>

===== Other names =====

  * <i :la>Non distributio medii</i>
  * <i :la>Non distributivi sed collectivi medii</i>

===== Rules of distributivity =====

The distribution rules for syllogisms are summarized in the article on [[glossary:distributivity|distributivity]]. The specific rule that is violated by this fallacy can be formulated as follows:

<div important>
**Remember:** The //middle term//, which connects the two premises, must occur in a distributed position in //at least one// of the premises.
</div>

The following table gives an overview of the distributivity of the terms in the four [[glossary:categorical_statement|categorical statement types]]:

^  <span noprint>Type</span>  ^ Statement ^ Subject ^ Predicate ^
^  A  | <q>All <abbr "Subject">S</abbr> are <abbr "Predicate">P</abbr></q> | distributed | not distributed | 
^  E  | <q>No <abbr "Subject">S</abbr> is <abbr "Predicate">P</abbr></q> | distributed | distributed | 
^  I  | <q>Some <abbr "Subject">S</abbr> are <abbr "Predicate">P</abbr></q> | not distributed | not distributed | 
^  O  | <q>Some <abbr "Subject">S</abbr> are not <abbr "Predicate">P</abbr></q> | 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 =====

  * [[glossary:distributivity|Distributivity]]
  * [[glossary:syllogism|Syllogism]]

===== Weitere Informationen =====

  * [[wp>Fallacy of the undistributed middle]] on //Wikipedia//
  * [[https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/87/Fallacy-of-the-Undistributed-Middle|Fallacy of (the) Undistributed Middle]] on //Logically Fallacious//
  * [[http://www.fallacyfiles.org/undismid.html|Undistributed Middle Term]] on //Fallacy Files//