Distribution of terms

A categorical term is said to be distributed if all members of that category are included.

In a statement such as "all A are either B or C", the categorical term, A, is distributed, because all members of set A are included. The categorical terms, B and C, are not distributed because there may be Bs and Cs that are not A.

In a statement such as "some D are E", neither D nor E is distributed because nothing is said about either the Ds that are not E or the Es that are not D.

In a categorical syllogism, the distribution of terms depends on the quantifier:

Statement	Quantity	Subject (A)	Quality	Predicate (B)
All A are B.	universal	distributed	affirmative	undistributed
No A are B.	universal	distributed	negative	distributed
Some A are B.	particular	undistributed	affirmative	undistributed
Some A are not B.	particular	undistributed	negative	distributed

For the subject to be distributed, the statement must be universal (e.g., "all", "no"). For the predicate to be distributed, the statement must be negative (e.g., "no", "not").^[1]

Copi and Cohen state two rules about distribution of terms in valid syllogisms:^[2]

1. The middle term must be distributed in at least one premise.
2. If the major term or the minor term is distributed in the conclusion, then it must be distributed in the premises.

When these rules are not followed, a fallacy or sophism can ensue. Breaking the rules regarding distribution of the middle, major, and minor terms are respectively called the fallacy of the undistributed middle, the illicit major fallacy, and the illicit minor fallacy.

Peter Geach and others have criticized the use of distribution to determine the validity of an argument.^[3][4] It has been suggested that statements of the form "Some A are not B." would be less problematic if stated as "Not every A is B.",^[5] which is perhaps a closer translation to Aristotle's original form for this type of statement.^[6]

Notes

1. ^ Damer 2008, p. 82.
2. ^ Copi & Cohen 2009.
3. ^ Lagerlund, Henrik (2010-01-21). "Medieval Theories of the Syllogism". Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/medieval-syllogism/. Retrieved 2010-12-10. 
4. ^ Murphree, Wallace A. (Summer 1994). "The Irrelevance of Distribution for the Syllogism". Notre Dame Journal of Formal Logic 35 (3). http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdfview_1&handle=euclid.ndjfl/1040511349. 
5. ^ Geach 1980, pp. 62–64.
6. ^ Parsons, Terence (2006-10-01). "The Traditional Square of Opposition". Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/square/. Retrieved 2010-12-10. 

References

• Copi, Irving M.; Cohen, Carl (2009). Introduction to Logic. Prentice Hall. ISBN 9780131364196. 
• Damer, T. Edward (2008). Attacking Faulty Reasoning. Cengage Learning. ISBN 9780495095064. 
• Geach, Peter (1980). Logic Matters. University of California Press. ISBN 9780520038479. 

External links

• ChangingMinds.org: Categorical propositions