Distributed and Undistributed Terms in 4 Types of Categorical Propositions (A, E, I & O)

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Distributed: Cats

Distributed: If the reference is to the whole of the class, then the class is said to be distributed. A term is distributed when it refers to all the members of the class (fully occupied) . Distribution can be designated by a stated or implied all.


Black Cat

Undistributed: If the reference is only to part of the class, then the class is said to be undistributed. A term is undistributed when it refers to less than all the members of its class (not fully occupied) .

Undistributed: Black Cat
  • Classes designated by the subject and predicate terms (roses, redness)
  • extent to which these classes are occupied or distributed (all or only part)
  • Classes: reference is made in all four types of categorical propositions to various classes designated by the two primary terms, the subject and the predicate

1. Universal subjects and negative predicates are distributed.

2. Particular subjects and affirmative predicates are undistributed.

Distributed and Undistributed


All horses are four-legged animals.

Distributed and Undistributed: Horses
  • All horses are four-legged animals
  • Type A propositions: All S is P (universal affirmative)
  • {S = Distributed, P = undistributed}
  • All horses are 4 legged – distributed
  • All 4 legged are not horses – undistributed


  • No Cats are Dogs
  • No Dogs are Cats
Distributed and Undistributed: Cats
  • No Cats are dogs
  • Type E propositions: No S is P (universal negative)
  • {S = distributed, P = distributed}
  • E propositions also state that not a single member of the S class is a member of the P class, and thus the reference is to the whole of the predicate class.
  • if the whole of the P (dogs) class were surveyed and no S (cats) were found.


Distributed and Undistributed: Men
Some Men Are Not Wealthy
  • Some men are wealthy (then women who are wealthy)
  • Type I propositions: Some S are P (particular affirmative)
  • {S = undistributed, P = undistributed}
  • I propositions, both the subject class and the predicate class are undistributed, and consequently such a proposition can be converted simply: β€œSome of the wealthy are men.”
Some Men Are Not Happy
  • Some men are not happy
  • Type O propositions: Some S is not P (particular negative)
  • {S = undistributed, P = distributed}
  • in type O propositions, the subject is always undistributed, and the predicate is always distributed
  • Some S are not P does not make a claim about every member of S, so S is undistributed
  • statement does assert that the entire P class is separated from this one member of S that is outside; that is, it does make a claim about every member of P
  • you have to know the sum total of happy people to assert that some men do not belong or are not found anywhere in the class of happy people.

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