5) Construct two squares of opposition, one traditional, the other m

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5) Construct two squares of opposition, one traditional, the

other modern, using the terms professors and great

teachers.

Solution

Squares of Opposition :

A square of opposition shows the logical relations among

categorical statements. There are two squares of

opposition:

1.The Modern Square of Opposition :

The only logical relation in the Modern Square of

Opposition is the contradictory relation.

The Contradictory Relation

To say that two statements are contradictory to each other

means that they necessarily have opposite truth value.

That is, if one of them is true, the other must be false, and

if one of them is false, the other must be true.

There are mainly 4 types of statements.Let us say S and P

are 2 sets. By using these 2 sets the types of statements

can be written as:

A : All S are P

E : No S are P

I : Some S are P

O : Some S are not P

For example, the A statement “All bats are mammals” and

the O statement “Some bats are not mammals” contradict

each other.

The contradictory relation also exists between the E

statement “No swans are black birds” and the I statements

“Some swans are black birds.”

We can use Venn Diagrams to illustrate why the

contradictory relation holds between the A and O

statements. When the A statement is true, the area is

empty. But if the area is empty, then no member of S can

be in the area . This contradicts the O statement, which

says that there is at least one member of S in the area ,

i.e., the area is not empty.

2.The traditional square of Opposition

If we assume that the set denoted by the subject term

cannot be an empty set, then there are four logical

relations among the A, E, I, O statements. They are shown

in the Traditional Square of Opposition. The four relations

are:

Contradictory

Contrary

Subcontrary

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5) Construct two squares of opposition, one traditional, the other modern, using the terms professors and great teachers. Solution Squares of Opposition : A square of opposition shows the logical relations among categorical statements. There are two squares of opposition: 1.The Modern Square of Opposition : The only logical relation in the Modern Square of Opposition is the contradictory relation. The Contradictory Relation To say that two statements are contradictory to each other means that they necessarily have opposite truth value. That is, if one of them is true, the other must be false, and if one of them is false, the other must be true. There are mainly 4 types of statements.Let us say S and P are 2 sets. By using these 2 sets the types of statements can be written as: A : All S are P E : No S are P I : Some S are P O : Some S are not P For example, the A statement “All bats are mammals” and the O statement “Some bats are not mammals” contradict each other. The contradictory relation also ex ists between the E statement “No swans are black birds” and the I statements “Some swans are black birds.” We can use Venn Diagrams to illustrate why the contradictory relation holds between the A and O statements. When the A statement is true, the area i s empty. But if the area is empty, then no member of S can be in the area . This contradicts the O statement, which says that there is at least one member of S in the area , i.e., the area is not empty. 2.The ...
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