Syllogism: Reasoning and Fallacy

6 min readJan 8, 2021

Syllogism is a form of deductive reasoning where you arrive at a specific conclusion by examining two other premises or ideas.

Hello, my name is Fidel Andrada. Syllogism derives from the Greek word syllogismos, meaning conclusion or inference.

Some syllogisms contain three components:

Major Premise
Minor Premise
Conclusion

For example, all roses are flowers (major premise).

This is a rose (minor premise).

Therefore, I am holding a flower (conclusion).

Types of Syllogism

The type of syllogism that typically contains these three components is a categorical syllogism. However, there are two other major kinds of syllogism. We’ll discuss each one here, plus enthymemes and syllogistic fallacy.

Categorical Syllogism

As we know, our first example about roses was a categorical syllogism. Categorical syllogisms follow an “If A is part of C, then B is part of C” logic.

Let’s look at some more examples of syllogism.

All cars have wheels. I drive a car. Therefore, my car has wheels.

Major Premise: All cars have wheels.
Minor Premise: I drive a car.
Conclusion: My car has wheels.

All insects frighten me. That is an insect. Therefore, I am frightened.

Major Premise: All insects frighten me.
Minor Premise: That is an insect.
Conclusion: I am frightened.

Conditional Syllogism

Conditional syllogisms follow an “If A is true, then B is true” pattern of logic. They’re often referred to as hypothetical syllogisms because the arguments aren’t always valid. Sometimes they’re merely an accepted truth.

If Katie is smart, then she will get into a good college.

Major premise: Katie is smart.
Minor premise: Because she is smart Katie will get good grades.
Conclusion: Katie will get into a good college.

If Richard likes Germany, then he must drive an Audi.

Major premise: Richard likes Germany.
Minor premise: Richard likes all German things.
Conclusion: Richard drives a German car.

Disjunctive Syllogism

Disjunctive syllogisms follow a “Either A or B is true, if it’s A, B is false” premise. They don’t state if a major or minor premise is correct. But it’s understood that one of them is correct.

This cake is either red velvet or chocolate.

It’s not chocolate.
This cake is red velvet.

On the TV show Walking Dead, Claire’s husband is either dead or alive.

He’s not dead.
Claire’s husband is alive.

Enthymemes

An enthymeme is not one of the major types of syllogism but is what’s known as rhetorical syllogism. These are often used in persuasive speeches and arguments.

Generally, the speaker will omit a major or minor premise, assuming it’s already accepted by the audience.

He couldn’t have stolen the jewelry. I know him.
Major Premise: He couldn’t have stolen the jewelry.
Minor Premise: I know his character.

Her new purse can’t be ugly. It’s a Louis Vuitton.
Major Premise: Her new accessory can’t be ugly.
Minor Premise: It’s made by famous designer Louis Vuitton.

In an enthymeme, one premise remains implied. In the examples above, being familiar with someone or something implies an understanding of them.

Syllogistic Fallacy

Some syllogisms contain false presumptions. When you start assuming one of the major or minor premises to be true, even though they’re not based in fact — as with disjunctive syllogisms and enthymemes — you run the risk of making a false presumption.

All crows are black. The bird in my cage is black. Therefore, this bird is a crow.

Major Premise: All crows are black.
Minor Premise: The bird in my cage is black.
Conclusion: This bird is a crow.

The scenery in Ireland is beautiful. I’m in Ireland. Therefore, the scenery must be beautiful.

Major Premise: The scenery in Ireland is beautiful.
Minor Premise: I’m in Ireland.
Conclusion: The scenery is beautiful.

Of course, not every black bird is a crow and not all of Ireland is beautiful. When preparing a speech or writing a paper, we must always make sure we’re not making any sweeping generalizations that will cause people to make false presumptions.

Rules of Syllogism

There are six known rules of syllogism. However, they mainly apply to categorical syllogism, since that is the only category that requires three components: major premise, minor premise, conclusion. Here are six rules that will ensure you’re making a strong and accurate argument.

Rule One: There must be three terms: the major premise, the minor premise, and the conclusion — no more, no less.
Rule Two: The minor premise must be distributed in at least one other premise.
Rule Three: Any terms distributed in the conclusion must be distributed in the relevant premise.
Rule Four: Do not use two negative premises.
Rule Five: If one of the two premises are negative, the conclusion must be negative.
Rule Six: From two universal premises, no conclusion may be drawn.

Further Examples of Syllogism

Literature

Syllogisms make for colorful literary devices. They explain situations indirectly, affording readers the opportunity to practice reasoning and deduction skills. Shakespeare was a master of many things, including syllogism. Here is an example of a syllogism fallacy in The Merchant of Venice:

Portia was a woman desired by many men. It was arranged she would marry the man who could correctly guess which of three caskets contained her portrait. One casket was inscribed with, “Who chooseth me shall gain what many men desire.” One man concluded that, since many men desired Portia, her portrait must be in that casket.

He was wrong. His assumption falls under the category of syllogistic fallacy. One cannot deduce that, since this casket contains what men desire, it’s automatically the portrait. Men also desire fortune and power, for example. There wasn’t enough evidence to leap from premise to conclusion here.

Philosophy

Socrates is the subject of one of the most famous, and easily understood, examples of syllogism in philosophy. Note that it clearly follows the rule of three components.

All men are mortal. Socrates is a man. Therefore, I am mortal.

This draws a clear picture of how one statement, when known to be universally true, should point perfectly to another clear claim, thus drawing an accurate conclusion.

Modern Culture

Keep syllogisms in mind when viewing advertisements. Many leaps are made in advertising, skipping either a major or minor premise:

Women love men who drive a Lexus.

Get ready for an enthymeme or syllogism fallacy. A blanket statement such as this skips one of the two required premises. Every time a woman likes a man, it can’t be assumed he drives a Lexus.

Persuasive Speeches and Writing

Understanding syllogisms will help you create masterful persuasive speeches and essays. They create a formula for you to abide by, in order to ensure your main point is flawless.

Syllogisms also allow you to test your theories according to syllogistic fallacies. When examining your main argument or point for discussion, be sure you haven’t made any presumptions that your audience might disagree with.