How to Recognize the Disjunctive Syllogism Argument Form ( Modus Tollendo Ponens)

A disjunctive syllogism is also known as modus tollendo ponens. It is a classically valid argument form. A disjunction is true when one or both of its components, also called disjuncts, are true, and false when both of its disjuncts are false.

Difficulty: Moderately Challenging

Instructions

1. Some argument forms use disjunctions. Disjunctions are statements of the form "Either A or B". The parts of a disjunction are called disjuncts. Disjunctive syllogism comes in two versions.

2. Example 1:
   Either Atlanta is a state or Atlanta is a city.
   Atlanta is not a state.
   So, Atlanta is a city.
   
   1. Either A or B
   2. Not A.
   So, 3. B

3. Example 2:
   Either Rover is a dog or Rover is a cat.
   Rover is not a cat.
   So, Rover is a dog.
   
   1. Either A or B.
   2. Not B.
   So, 3. A

4. Arguments use the form "A or B, but not both". This means you cannot use inclusive ors that mean A or B or both. Also notice that these forms are not disjunctive syllogism:
   
   Not disjunctive syllogism -
   Example 1:
   Either A or B; not both A and B;
   A; so, not B.
   
   Example 2:
   Either A or B;
   A;
   Therefore, not B.

Resources

• Wikipedia Disjunctive Syllogism
• The Power of Logic 4e