====== Fallacies of distribution ======

If the [[glossary:distributivity|distributivity]] of the terms is not taken into account in a logical conclusion, this can lead to an invalid conclusion.

For example, in the following syllogism <span noprint>[[app>#AA2A|Show in Syllogism-Finder App]]</span>:

> All <var>rectangles</var> are <var><u questionable "Undistributed term">polygons</u></var>.
> All <var>hexagons</var> are <var><u questionable "Undistributed term">polygons</u></var>.
> <span conclusio><s invalid>All <var>rectangles</var> are <var>hexagons</var></s>.</span>

In both premises, the term "polygons" is in an //undistributed// position, i.e. it is used in a way that refers only to a subset of all polygons (namely those that are //rectangles// or //hexagons//, respectively). For this reason, the terms refer to different extensions and thus cannot connect the two premises. A conclusion based on such premisses can not be valid.

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

The term distribution or [[glossary:distributivity|distributivity]] describes if a term is used refers to a subset of the objects it designates or to all objects.

In the example above, a statement such as "all rectangles are polygons" describes //all rectangles//, but only a //part// of the polygons - in particular those that are also //rectangles//. Thus, the term "rectangles" is //distributed//, while "polygons" is //undistributed//. 

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 |

Specifically for [[glossary:syllogism|syllogisms]], the following rules apply:

  * The //middle term//, which connects the two //premises//, must in at least one of the premises occur in a distributed position. A syllogism where the middle term is undistributed in both premises commits the fallacy of the [[logic:formal_fallacies:fallacies_of_distribution:undistributed_middle|undistributed middle]].

  * If a term appears in the conclusion statement in a distributed position, it must also be distributed in the premise in which it appears. Traditionally, there a distinction between fallacies of undistributed //major// and //minor// term is often made, but for simplicity, these both are treated here as [[logic:formal_fallacies:fallacies_of_distribution:illicit_process|illicit process]].
===== See also =====

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

== Subpages ==

  * [[logic:formal_fallacies:fallacies_of_distribution:undistributed_middle|Undistributed middle]]
  * [[logic:formal_fallacies:fallacies_of_distribution:illicit_process|Illicit process]]

==== Other syllogistic fallacies ====

  * [[logic:formal_fallacies:affirmative_conclusion_from_negative_premise|Affirmative conclusion from a negative premise]]
  * [[logic:formal_fallacies:exclusive_premises|Fallacy of exclusive premises ]]
  * [[logic:formal_fallacies:negative_conclusion_from_affirmative_premises|Negative conclusion from affirmative premises]]