Describe the Square of Opposition

a. What is categorical logic?
b. What is the purpose of the Square of Opposition?
c. Identify key features of the Square of Opposition.
d. Explain how the Square of Opposition is used to translate statements into standard-form claims and corresponding standard-form claims including description of the relationships that are depicted within the square.

Categorical Logic defines & relates various kinds of logical statements. Traditional square of opposition is a particular relationship between 4 kinds of propositions : A, E, I, O.

Explanation:

Categorical Logic is scientific method of defining & connecting : various statements about - various category or classes of objects.

Traditional square of opposition shows relationship between various kinds of propositions, asserting or denying something about - all or few members of a group :

A : Universal Affirmative ; eg -  'All S are P' E : Universal Negative ; eg - 'No S are P'I : Particular Affirmative ; eg - 'Some S is P' O :  Particular Negative ; eg - 'Some S is not P'

Relationships between them :

Contradictories : [A, O]  & [E , I] : Opposite Truth Value - If one True , other is False & vice versa Contraries : [A , E] : Can't be true together, but can be false together Subcontraries : [I, O] : Can be true together , but cant be false together Sub alternates [A, I] & [E,O] : First 'A' or 'E' true implies second 'I' or 'O' true respectively. Second 'I' or 'O' false implies first 'A' or 'I' false respectively

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