Part V: Exercises

Consider the following propositions and answer the following questions: What type of proposition is this? What proposition would be its contrary? What proposition would be its subaltern? What proposition would be its contradiction? What proposition would be its subcontrary? (hint: some propositions, depending on the type, might not have subalterns or contraries or subcontraries. Use the square of opposition to help you.)

*hint: if a value is missing fill in the field with “none”
1. “All dogs are friendly” is a proposition. Its contrary would be . Its subaltern would be . Its contradiction would be .
2. “Some houses are not expensive” is a proposition. Its subcontrary would be . Its contradiction would be .
3. “Some bumblebees are loud” is a . Its subcontrary is . Its contradiction is .
4. “No philosophers are musicians” is a proposition. Its contrary is . Its contradiction is that . Its subaltern is .

Describe in your own words why particular categorical propositions do not have subalterns.

This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.

(Challenge) Take the word “always.” If you had to draw a square of opposition for it, what corner would you put it in? What would be its contrary? What would be its subaltern? (hint: contrast “always” with “never” and “sometimes.”

This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.

(Challenge) Are the propositions “some unicorns have horns” and “some unicorns do not have horns” a good example of a subcontrary pair? Hint: Aristotle’s system only works for objects that exist.

This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.

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