Part II: Examples

Within the following section, we will be looking through a couple of examples depicting uses of Modus Ponens and Modus Tollens.

Activity: Take the two short paragraphs, which each represent an example of the law of Modus Ponens. In each case, identify the hypothetical compound proposition, and determine which portion is the antecedent, and which is the consequent. 

i. Modus Ponens in the real world

1. Suppose I know that if my dog sees a squirrel, then it will chase that squirrel. Now, suppose that I can see that my dog is looking at a squirrel. I will infer from this that my dog will chase the squirrel. This inference is an example of Modus Ponens. 

2. Suppose that the book, Crime and Punishment by Fyodor Dostoevsky is on your favorite bookshelf in your room. Your brother walks into your room and says that all of the books on your favorite bookshelf are some of his favorite books. You infer (by Modus Ponens) that Crime and Punishment is one of your brother’s favorite books.

II. Modus Ponens in the form of a syllogism

1. (1) If Johnny is a lawyer, then Johnny studies the law (if p, then q)

     (2) Johnny is a lawyer (p)

      (3) Therefore, Johnny studies the law (therefore, q)

2. (1) All men are mortal (All A’s are B’s)

     (2) Socrates is a man (C is an A)

     (3) Therefore, Socrates is mortal (C is a B)

Activity: Come up with 2-3 real world examples of reasoning using Modus Ponens; discuss these with a classmate to make sure they are actually representative. Try to put these examples into the form of a syllogism.

iii. Modus Tollens in the real world.

1. As from before, suppose that I know that if my dog sees a squirrel, then it will chase that squirrel. Now, suppose that I know that my dog has not chased any squirrels today. I will infer from this that my dog hasn’t seen any squirrels today. This inference is an example of Modus Tollens. 

2. Suppose you know that any person who has studied Aristotelian Logic would know who Aristotle was. You ask your friend if they know about Aristotle, and she says that she does not. You infer that she has not studied Aristotelian Logic.

iv. Modus Ponens in the form of a syllogism

1.  (1) If Newton was right about everything, then he would have no false theories (if p, then q)

      (2) He has false theories (not-q)

      (3) Therefore, Newton was not right about everything (therefore, not-p)

2. (1) All chickens are animals (All A’s are B’s)

     (2) No robots are animals (C is not a B)     

     (3) Therefore, robots are not chickens (therefore, C is not an A)

Activity: As before, come up with 2-3 real world examples of reasoning using Modus Tollens; discuss these with a classmate to make sure they are actually representative. Try to put these examples into the form of a syllogism.