Square of opposition

PROPOSITIONS

In logical reasoning propositions are the statements that explains the relation between two or more terms in syllogism. Proposition is either true or false but not both at a same time. 

Parts of proposition

1) QUANTIFIERS: It indicates the quantity or category of the statement.

Example: All, No are universal  quantifiers and Some , Some not are particular quantifiers.

2) Subject: This represents about something is being said.

3)Copula: It is a linking term that connects the subject and predicate.

4) Predicate: Predicate is something that affirms or denies about the subject.

TYPES OF PROPOSITIONS

1) HYPOTHETICAL PROPOSITION: The hypothetical preposition is also known as a conditional preposition that express a relationship between two or more conditions.

Example: If it's rains, people will not go outside.

2)DISJUNCTIVEPREPOSITION:Disjunctive propositions are the specific type of logical statement that assert one of two or more alternatives to be true. 

Example: "Either it's cold or it's hot".

3)CATEGORICAL PROPOSITION: Categorical proposition is the statement that describes the relationship between two terms(Subject and predicate). These propositions are typically in the form "All S is P", "No S is P", "Some S is P", Some S is not P, here S and P represents classes of categories.

Example: All men are mortal

TYPES OF CATEGORICAL PROPOSITIONS.

1)UNIVERSAL AFFIRMATIVE (A type):These propositions states that every member of one class(Subject) is also member of second class(Predicate). A type statements are universal positive sentences. These are in form of all A are B.

Example: All dogs are animals

                  All men are mortal

                  All  cows are birds

Venn diagram

2) UNIVERSAL NEGATIVE  (E):Universal negative Statements states that no members of one class is member of second class. These are E type statements which are in form of No A is B.

Example: No dogs are cats

                  No bags are books

                  No books are pens

Venn diagram

3) PARTICULAR AFFIRMATIVE  (I):These propositions describes atleast some members of subject class are members of the Predicate class. These are in form of Some A are B

Example: Some cats are friendly

                  Some bags are books

                  Some dogs are cats

Venn diagram

4)PARTICULAR NEGATIVE (O):Particular negative propositions states that some members of subject class are not members of Predicate class. i.e some A are not B

Example: Some birds are not sparrows

                  Some bags are not books

                  Some windows are not chairs

Venn diagram

SQUARE OF OPPOSITION:Square of opposition is the diagrammatic representation that illustrates the logical relationship between the above categorical propositions(A E I O).

Following are four types of oppositions

1) CONTRADICTORY (A and O; E and I propositions):Contradictory statements are propositions that cannot be true and cannot be false at a same time, if the first statement is true then the second statement must be false. Here A is contradictory of O and E is contradictory of I.

Rules: If one is true other will be false

            If one is false other will be true

            Both can't be true or false at a same time

Example: "The rose is pink"

                   "The Rose is not pink"

2) CONTRARIES (A and E propositions):A and E proposition are contraries to each other because the can't be both true but can be both false. A is contrary to E opposition.

Rules: Both statements can't be true at a same                   time but both can be false

             If one is true other will be false

             If one is false other will be true

             It is always between universal

Example: If All human can swim is true then no human can swim is false.

3) SUBCONTRARY (I and O  Propositions)

Subcontrary in square of opposition are pairs of propositions that can be true at a same time but can't be false, I is the subcontrary of O.

Rules: It is opposite to contrary

             If one is true other is doubtful

             If one is false other is true

             It is always between particulars

Example: If some flowers are red is false then some flowers are not red must be true.

4) SUBALTERN (A and I; E and O Propositions):A propositions imply I propositions and E propositions imply O Propositions.

Rules: 

If universal is true then the particular is  true 

If universal is false then particular is false 

 If particular is true then universal is doubtful

If  particular is false then the universal is doubtful

Example:If "All humans are mortal," then a subaltern proposition would be "Some humans are mortal".

The Square of Opposition helps to analyze the logical relationships between these propositions and is a foundational concept in classical logic.