Forms of Logical Argument

The study of logic as a discipline has existed for thousands of years. Greek mathematicians and philosophers as far back as 600 BCE attempted to define how to argue logically. Two types of argument forms come from ancient times and have Latin names—modus ponens and modus tollens.

For Exercises 1–6, identify whether the argument is of the form modus ponens, modus tollens, or neither.

1.  If it rains in Spain, then it rains on the plain.

It is raining in Spain. Therefore, it is raining on the plain.

2.  If the scissor-tail swallows have returned, then it is not freezing outside.

It is freezing outside. Therefore, the scissor-tail swallows have not returned.

3.  You cannot get a speeding ticket if you do not speed.

You do not speed. Therefore, you cannot get a speeding ticket.

4.  If the animal is a dog, then the animal barks.

The animal barks, therefore it is a dog.

5.  If the train is on time, I will get to work on time.

If I get to work on time, I get to take a full hour for lunch.

I didn’t get to take a full hour for lunch. Therefore, the train wasn’t on time.

6.  If I think, then I am.

I think, therefore I am.

7.  Open-Ended Write an argument that uses modus ponens.

8.  Open-Ended Write an argument that uses modus tollens.