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[[Image:Square of opposition.svg|right|352px|The traditional square of opposition]]

[[Image:Square101-74.JPG|right|352px|The traditional square of opposition]]

In the system of [[Term Logic|Aristotelian logic]] , the '''square of opposition''' is a diagram representing the different ways in which each of the four [[propositions]] of the system are logically related ('opposed') to each of the others. The system is also useful in the analysis of [[Syllogism|Syllogistic Logic]], serving to identify the allowed logical conversions from one type to another.

In the system of [[Term Logic|Aristotelian logic]] , the '''square of opposition''' is a diagram representing the different ways in which each of the four [[propositions]] of the system are logically related ('opposed') to each of the others.  

== Summary ==

== Summary ==

{| border="1"

{| border="1"

|+ The Four Aristotelian Propositions

|+ The Four Aristotelian Propositions

! Name !! Symbol !! Latin !! English !! SSF{{what}}

! Name !! Symbol !! Latin !! English  

|-

|-

| Universal affirmative || A || Omne S est P || Every S is P || All S is P

| Universal affirmative || A || Omne S est P || Every S is P  

|-

|-

| Universal negative || E || Nullum S est P || No S is P || All S is not P

| Universal negative || E || Nullum S est P || No S is P  

|-

|-

| Particular affirmative || I || Quoddam S est P || Some S is P || Some S is P

| Particular affirmative || I || Quoddam S est P || Some S is P  

|-

|-

| Particular negative || O || Quoddam S non est P || Some S is not P || Some S is not P

| Particular negative || O || Quoddam S non est P || Some S is not P  

|}

|}

Aristotle states (in chapters six and seven of the ''Perihermaneias'' (Latin ''De Interpretatione'', English 'On Exposition'), that there are certain logical relationships between these four kinds of proposition. He says that to every affirmation there corresponds exactly one negation, and that every affirmation and its negation are 'opposed' such that always one of them must be true, and the other false. A pair of affirmative and negative statements he calls a 'contradiction' (in medieval Latin, ''contradictio''). Examples of contradictories are 'every man is white' and 'not every man is white', 'no man is white' and 'some man is white'.

Aristotle states (in chapters six and seven of the ''[[On Interpretation|Perihermenias]]'' (Latin ''De Interpretatione'', English 'On Exposition'), that there are certain logical relationships between these four kinds of proposition. He says that to every affirmation there corresponds exactly one negation, and that every affirmation and its negation are 'opposed' such that always one of them must be true, and the other false. A pair of affirmative and negative statements he calls a 'contradiction' (in medieval Latin, ''contradictio''). Examples of contradictories are 'every man is white' and 'not every man is white', 'no man is white' and 'some man is white'.

'Contrary' (medieval: ''contrariae'') statements, are such that both cannot at the same time be true. Examples of these are the universal affirmative 'every man is white', and the universal negative 'no man is white'. These cannot be true at the same time. However, these are not contradictories because both of them may be false. For example, it is false that every man is honest, since some men are not honest. Yet it is also false that no man is honest, since there are some honest men.

'Contrary' (medieval: ''contrariae'') statements, are such that both cannot at the same time be true. Examples of these are the universal affirmative 'every man is white', and the universal negative 'no man is white'. These cannot be true at the same time. However, these are not contradictories because both of them may be false. For example, it is false that every man is honest, since some men are not honest. Yet it is also false that no man is honest, since there are some honest men.

== See also ==

== See also ==

==References==

==References==

==External links==

==External links==

 

* [http://plato.stanford.edu/entries/square/ Stanford Encyclopedia of Philosophy article]

* [http://plato.stanford.edu/entries/square/ Stanford Encyclopedia of Philosophy article]

* [http://www.square-of-opposition.org/ International Congress on the Square of Opposition]

* [http://www.square-of-opposition.org/ International Congress on the Square of Opposition]

[[Category:Logic]]

[[Category:Logic]]