How to Recognize the Hypothetical Syllogism Argument Form

Hypothetical syllogism is one of the proof rules in classical logic. It is a famous valid argument form. This kind of argument states that if one implies another, and that other implies a third, then the first implies the third.

Difficulty: Moderately Challenging

Instructions

1. Remember that hypothetical syllogism has three parts.
   1. If A, then B.
   2. If B, then C.
   So, 3. If A, then C.

2. If my cat Zora continues to eat 2 treats a day in addition to her food, then she will gain too much weight.
   If she gains too much weight, it is unhealthy for her.
   So, if she eats 2 treats a day in addition to her food, it is unhealthy for her.

3. The argument form is called hypothetical syllogism because it involves only hypothetical statements. Syllogism is derived from Greek roots meaning "to reason together" or to put statements together into a pattern of reasoning. Every argument that exemplifies this form is a valid one.

4. You should also pay special attention to the conclusion of a hypothetical syllogism. It is a conditional statement.

Resources

• The Power of Logic 4e
• Philosophy at UNCG
• Wikipedia Hypothetical Syllogism