Question

1. Describe the Square of Opposition
   • What is categorical logic?
   • What is the purpose of the Square of Opposition?
   • Identify key features of the Square of Opposition.
   • 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.
2. Identify the components of the A, E, I and O standard-form claims (or propositions).
3. Using the diagram in your text as a guide, create one original example using an ordinary statement and translating it into standard-form claims (A, E, I and O statements) using the Square of Opposition. Identify the translation and claims in your example using the corresponding letter.
   • For each corresponding standard-form claim, explain how you identified the translation and corresponding claims and their relationship to one another based on the relationships depicted on the square. In other words, explain why each choice of claim in your example is correct for that particular relationship.

Answer 1

Describe the Square of Opposition.

In philosophical logic, the square of opposition is a diagram representing the relations between the four basic categorical propositions. The origin of the square can be traced back to Aristotle making the distinction between two oppositions: contradiction and contrariety.

What is categorical logic?

Categorical logic is the logic that deals with the logical relationship between categorical statements. A categorical statement is simply a statement about a category or type of thing.

For example:

Consider the following argument:

1. All humans are mortal (Premise 1)
2. All mortal things die (Premise 2)
3. Therefore, all humans die (Conclusion)

The first premise of the above argument is a statement about the categories of humans and things that are mortal. The second premise is a statement about the categories of things that are mortal and things that die.

What is the purpose of the Square of Opposition?

A square of opposition helps us infer the truth value of a proposition based upon the truth values of other propositions with the same terms.

Identify key features of the Square of Opposition.

Following are the key features:

A propositions, or universal affirmatives take the form: All S are P.

E propositions, or universal negations take the form: No S are P.

I propositions, or particular affirmatives take the form: Some S are P.

O propositions, or particular negations take the form: Some S are not P.