Introducing the Syllogism by Example Example Example

Does a friend's refusal make him a bad friend?

“All men are mortal,” you tell your class as they nod.  “Socrates is a man,” you continue as some students glance at the clock.  “Therefore, Socrates is mortal,” you finish with a flourish as a student in the back yells, “Who’s Socrates?”  You wilt.

Although Aristotle’s pronouncement, in perfect syllogistic validity and truth, may be the most famous of all categorical syllogisms, it won’t necessarily have much of an impact on our students.  That’s not to say it isn’t important or shouldn’t be discussed; perhaps it just isn’t the best way to begin a lesson on syllogisms. It’s much more likely we’ll capture our students’ attention and interest if we use examples of deductive logic they use on a daily basis, then link those situations to valid syllogism forms.

To start, begin with a short and sweet introduction to deductive reasoning, perhaps including how it is different from inductive reasoning. Be sure students understand the following key terms:

Syllogism - A form of deductive reasoning that includes two premises and a conclusion based on those premises.
Valid - When a syllogism follows the prescribed form, it is considered valid.
Sound - When a syllogism's premises are true and the form is valid, we can say the reasoning is sound.

After these basics are established, allow the students to experiment with some of the syllogism forms. The following three examples are hypothetical syllogisms, but categorical syllogisms may work just as well. 

Example Hypothetical Syllogisms

The Modus Ponens Syllogism

A fantastic example of an affirming syllogism, a modus ponens syllogism, comes from the Sherry Diestler text, Becoming a Critical Thinker: A User Friendly Manual (2009, pg. 81).

• If our team wins the playoff game, it will be in the championship game.
• Our team did win the playoff game.
• Therefore, our team will be in the championship game.

Using an example the students can understand, even if they are not sports fans, can help them visualize a real situation.  The ability to visualize a concrete situation can help students both retain the new vocabulary and the process for creating syllogisms.  By asking students to confirm the truth in each of your premises before moving to the next, you can also help instill in them the habit of questioning the truth of premises right from the start.

After asking the students to visualize your concrete example of modus ponens, you can label the premises and conclusion, explain the valid form, and ask them to create their own real-life examples.  Again, be sure to emphasize the importance of confirming the truth of the premises before coming to a conclusion.

• Major premise, If A, then B: If our team wins the playoff game, it will be in the championship game.
• Minor premise, A: Our team did win the playoff game.
• Conclusion, Therefore B: Therefore, our team will be in the championship game.

The Modus Tollens Syllogism

John Chaffee’s Thinking Critically  text approaches examples of modus tollens syllogisms a little bit differently.  Chaffee uses premises that are somewhat questionable, which can work in an introductory lesson to emphasize the importance, again, of questioning the truth of each premise (2012, pg. 434).

• If Michael were a really good friend, he would lend me his car for the weekend.
• Michael refuses to lend me his car for the weekend.
• Therefore, Michael is not a really good friend.

When you use this example, you will have students who will question the truth in the first premise.  They are right to do so: It is not an objective truth, but a subjective truth that relies too heavily on the vague language “really good friend.”  You can use this as a springboard to discuss with your students the importance of specific language and an objective definition of all terms.

Once the students understand the form of this syllogism, you can ask them to create their own using specific language and objective terms.

• Major premise, If A, then B: If Michael were a really good friend, he would lend me his car for the weekend.
• Minor premise, Not B: Michael refuses to lend me his car for the weekend.
• Conclusion, Therefore, Not A: Therefore, Michael is not a really good friend.

The Chain Argument

The Critical Thinking text by Moore and Parker (2012, pg. 314) offers a great example of a chain argument all students can understand.  It’s the age-old problem of who’s going where. 

• If Casey goes to the meeting, then Simone will go.
• If Simone goes, then Chris will go.
• If Casey goes to the meeting, then Chris will go.

Of course, this example will prompt some students to question the premises because everyone knows that even though someone says they’ll go, they do not always go.  You can use that as a great teachable moment to explain that the truth and certainty in this conclusion relies on the specific premises as stated, and the principle of charity, or granting benefit of the doubt.  If it is a class of applied linguistics or philosophy majors, be prepared for questions concerning intentions, truth, ethics, and even speech act theory.  Again, all of these are great springboards for further discussion.

• Major premise, If A, then B: If Casey goes to the meeting, then Simone will go.
• Minor premise, If B, then C: If Simone goes, then Chris will go.
• Conclusion, Therefore, if A, then C: If Casey goes to the meeting, then Chris will go.

Common Mistakes in Validity

Two types of common mistakes that affect the validity of a syllogism are called "denying the antecedent" and "affirming the consequent." In short, both are names of invalid forms that occur when the A's and B's get swapped. Students should carefully look over their example syllogisms to be sure they have not created invalid syllogisms.

The following is a sample syllogism about Ben and his ability as a gamer.  Students can practice identifying mistakes in form, and even more importantly, they can subsequently practice correcting those mistakes.

"Denying the Antecedent" and "Affirming the Consequent" types of invalid syllogisms

Either of these errors in form can be corrected by carefully examining the faulty syllogisms and replacing the erroneous forms with either the Modus Ponens or the Modus Tollens form. Of course, this still leaves the subjective adjective "great" to discuss, not to mention the variations on types of games and how long they should take to beat, so be prepared for additional lively discussion.

Correct the faulty syllogisms by creating valid Modus Ponens or Modus Tollens syllogisms.

Using examples to help students understand this seemingly abstract concept of deductive reasoning can certainly bring it to life in the classroom.  It's a great way to introduce the syllogism while setting the bar for its use in more realistic contexts later in the course - and more importantly, beyond the course.

Want to read more about critical thinking?  Try 

Sticky Theories: A Lesson in Critical Thinking

Writing an Argumentative Essay: Basic Terminology

Stages in the Development of Critical Thinking
Assessing Critical Thinking
The Syllogism as Structure in Essays and Speeches

References

• Moore, B. N. & Parker, R. (2012). Critical Thinking (10th ed.). New York, NY: McGraw Hill.
• Chaffee, J. (2012). Thinking Critically (10th ed.). Boston, MA: Wadsworth Cengage Learning.
• Diestler, S. (2009). Becoming a Critical Thinker: A User Friendly Manual (5th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.