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Traditional Square of Opposition: Categorical Logic
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This lecture notes discusses the traditional square of opposition in Categorical Logic.
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Traditional Square of Opposition: Categorical LogicThese notes discuss in detail the nature and dynamics of the traditional square of
opposition in categorical logic.
Two categorical propositions stated in standard form having the same subject and
predicate terms may differ in either quantity and quality or both. The term “opposition”
is used by logicians to illustrate these differences. However, “opposition” should not be
understood as “disagreement” in ordinary language. For example, given two
propositions having the same quality but different in quantity, such as “All students are
intelligent” and “Some students are intelligent”, the ideas they express do not disagree;
they are only opposed.
The relationship of opposing propositions can be schematically presented by placing
them on different angles of a square. Please see the illustration below.
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