# Syllogism: Definition & Examples

Instructor: Krista Langlois

Krista has taught language arts for 14 years. She has a master's degree in teaching and loves researching, reading, and introducing others to the wonders of literature and language.

The Greeks started the study of reasoning and logic long, long ago. In this lesson, we will look at deductive reasoning through a brief introduction to syllogism.

## Introduction to Syllogism

The detective stalked around the room staring at each of the suspects in the murder of Fred Jones. ''We know,'' he said ''that the killer was left handed.'' He stopped pacing and pointed to the woman twisting her necklace in her hand. ''And you, Ms. Red, are the only person here who is left handed. You killed Mr. Jones! Police, take her away!'' As the killer was taken away, the police chief said to the detective, '' How did you know she did it?'' He smiles and replies, ''It was easy; I used a syllogism!''

## What's a Syllogism?

A syllogism is a type of logical argument that is usually brief in form. It was first put forth as a type of reasoning by the Greeks, specifically Aristotle. It is a type of deductive reasoning that establishes a conclusion based on two joined premises. The syllogism is created using two premises and the logical conclusion that follows. The conclusion must be specific and cannot be more general than either premise. It follows that if the premises are true, the conclusion must be true.

Also, in order to be a syllogism, there must be three distinct terms within the premises and the conclusion; the major, the minor and the middle terms. The major term is the predicate term of the conclusion. The minor term is the subject term of the conclusion. The middle term is the term that appears twice in the premises.

### Say what?!

Let's look at a most basic explanation. In the introduction above, the detective uses the following syllogism:

• Premise one: A left handed person is the killer (Killer is the major term--predicate of the conclusion)
• Premise two: Ms. Red is the only left handed person (Left handed is the middle term--found in both premises)
• Conclusion: Ms. Red is the killer (Ms. Red is the minor term--subject of the conclusion)

The detective's syllogism could be presented as such: The killer is left handed. Ms. Red is the only left handed person involved in the case. Therefore, Ms. Red is the killer. It might not be 'elementary', as the master of deduction Sherlock Holmes has been known to say, but it certainly is logical.

## Wait! There's More!

Now that the least confusing part is out of the way, it's also important to know that there are three main types of pure syllogism (if you study logic and reasoning, though, you will find an infinite number of syllogisms can be created, including impure/mixed syllogisms). These main types are categorical, conditional, and disjunctive.

### Categorical Syllogism

The categorical syllogism is what you see used above by our detective; we assume all premises are true:

premise A is true

premise B is true

conclusion must be true

### Conditional Syllogism

The conditional syllogism uses an 'if' in the premises:

• If John always walks the dog on Saturday
• And if today is Saturday
• John will walk his dog today!!

### Disjunctive Syllogism

The disjunctive syllogism uses an either/or premise:

• Either Sally is playing basketball or she is playing with her puppy
• Sally is not playing basketball
• Sally is playing with her puppy

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