What is a categorical syllogism?

A categorical syllogism uses "is" statements to draw a sure conclusion. 1. Cats are mammals. (Major premise) 2. Tabby is a cat. (Minor premise) 3. Therefore, Tabby is a mammal. (Conclusion)

Is modus ponens and a disjunctive syllogism the same?

No. Modus ponens is a type of hypothetical syllogism, which is different from a disjunctive syllogism.

Is syllogism deductive or inductive?

Syllogism is a form of deductive reasoning.

Syllogism: Definition, Examples & Rules

Q: What is the definition of syllogism?

A syllogism is a three-part line of reasoning with a major premise , minor premise , and conclusion .

Q: Is syllogism a fallacy?

Syllogisms can be valid and sound or they can be fallacious. It depends on the syllogism.

Syllogism

Although you might not know what a "syllogism" is, it is actually foundational to drawing a logical conclusion through deduction. Syllogisms are the basis for sound logic. If you don't follow an accurate blueprint, your arguments can collapse into logical fallacies, and that's a problem. Learning the rules of syllogisms will improve your logical arguments.

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Syllogism Definition

This is the most basic definition of syllogism:

A syllogism is a three-part line of reasoning with a major premise, minor premise, and conclusion.

Here's what that looks like:

1. Cats are mammals. (Major premise)

2. Tabby is a cat. (Minor premise)

3. Therefore, Tabby is a mammal. (Conclusion)

This syllogism is specifically a categorical syllogism.

A categorical syllogism uses "is" statements to draw a sure conclusion.

Categorical syllogisms are the strongest form of deductive syllogisms, so we'll focus on them for now.

In a categorical syllogism:

The major premise is broad. (ALL CATS are mammals.)
The minor premise is specific. (TABBY is a cat.)
And the conclusion distributes the broad conclusion to the specific conclusion. (The qualities of ALL CATS are distributed to TABBY.)

Thus, TABBY is what ALL CATS are: a mammal.

This example is a flawless example of deductive reasoning.

Deductive reasoning is drawing specific conclusions from general observations.

That said, a categorical syllogism can become a fallacy if you don't apply the correct rules.

Syllogisms can be valid and sound, or they can be fallacious. It depends on the syllogism.

Syllogism Rules

Obey these three rules to create a sound categorical syllogism.

1. Your conclusion needs to go from broad to specific. This covers a lot of ground. The major premise needs to be broad, the minor premise needs to be narrow, and the conclusion needs to connect the two in this format:

1. A is B.

2. C is A.

3. Therefore, C is B.

This is the same format as the Tabby/cat/mammal example.

2. The major and minor premises must be true. They cannot be best guesses or possibilities. They must be verifiable facts.

3. Obey the two rules of negatives:

If either premise is negative, the conclusion must be negative.
A syllogism cannot contain two negative premises.

Here's an example of the first rule of negatives in action:

1. Cats are animals. (Positive)

2. A rock is not a cat. (Negative)

3. Therefore, a rock is not an animal. (Negative)

Syllogism, Rock example, StudySmarter Fig. 1 - Follow the rules to create an accurate syllogism about rocks or otherwise!

Other syllogisms have their own rules, but they are similar to these. The rules for categorical syllogisms are the most important syllogistic rules for deduction.

Other Types of Syllogism

Besides the categorical syllogism, there are hypothetical and disjunctive syllogisms. Like all syllogisms, these syllogisms contain a major premise, minor premise, and conclusion. Theirs, however, look different from those of the categorical syllogism.

Hypothetical Syllogism

Unlike a categorical syllogism, a hypothetical syllogism is never necessarily true because its premises are technically hypothetical.

A purely hypothetical syllogism contains an "if statement" in all premises: the major premise, the minor premise, and the conclusion.

Here's how that looks:

1. If Tabby is a cat, then she is a mammal. (Major premise)

2. If Tabby is a mammal, then she is warm-blooded. (Minor premise)

3. Therefore, if Tabby is a cat, then she is warm-blooded. (Conclusion)

This conclusion is only true if you accept the conditions of the two premises. Because of this, hypothetical syllogisms are also called conditional syllogisms.

"If statements" are not as strong as "is statements," which is why categorical syllogism is a stronger form of deductive reasoning than hypothetical syllogism.

Even if just one of your three statements contains an if, then your syllogism is still a hypothetical syllogism (not a "pure" one). Here's an example;

1. If Tabby is a cat, then she is a mammal. (Major premise)

2. Mammals are warm-blooded. (Minor premise)

3. Therefore, Tabby is warm-blooded. (Conclusion)

This kind of hypothetical syllogism is also called modus ponens (Latin for "method of affirming"). Things can go wrong here, but more on that later.

Disjunctive Syllogism

The final kind of syllogism is the disjunctive syllogism.

A disjunctive syllogism draws a conclusion using a dichotomy.

In its first form, a disjunctive syllogism uses an "or statement" in the major premise and a negative statement in the minor premise.

1. Tabby is either a cat or a dog. (Major premise – the dichotomy)

2. Tabby is not a dog. (Minor premise)

3. Therefore, Tabby is a cat. (Conclusion)

In its second form, a disjunctive syllogism uses a "not both statement" in the major premise and a positive statement in the minor premise.

1. Tabby is not both a cat and a dog. (Major premise – the dichotomy)

2. Tabby is a cat. (Minor premise)

3. Therefore, Tabby is not a dog. (Conclusion)

Syllogism, Cat example, StudySmarter Fig. 2 - A disjunctive syllogism can define something by saying what it's not.

Examples of Syllogism

Here are a few syllogisms. Try to identify whether these are categorical, hypothetical, or disjunctive syllogisms.

Practice Example 1

What kind of syllogism is the following?

Your phone fell out a window.

If your phone falls out a window, it breaks.

Your phone is broken.

This is a hypothetical syllogism because it contains an "if statement."

Practice Example 2

What kind of syllogism is the following?

Tacos are not sandwiches.

You're eating a taco.

You're not eating a sandwich.

This is a categorical syllogism containing a negative major premise. It is categorical because it contains all "is statements."

Practice Example 3

What kind of syllogism is the following?

Follow the leader or get left behind.

You don't follow the leader.

You will get left behind.

This is a disjunctive syllogism because the major premise presents an "or statement."

Remember, a "not both statement" is also disjunctive!

Fallacies of Syllogism

Now that you understand the three types of syllogisms, you should know how they can go south in a hurry. Here is how each kind of syllogism can be a logical fallacy.

Logical Fallacies in Categorical Syllogisms

Categorical syllogisms can only go wrong in one way: not being true.

1. All cats are mammals.

2. The manta ray is a cat.

3. Therefore, the manta ray is a mammal.

This is a categorical syllogism like the ones you have seen, except it is patently wrong because a manta ray is not a cat. The logic of this example is technically correct, but the conclusion isn't accurate because one of the premises is untrue.

This phenomenon is called an informal logical fallacy, which means the fallacy lies not in the structure of the logic (which would be a formal logical fallacy), but rather in something else about the argument.

Logical Fallacies in Hypothetical Syllogisms

The purely hypothetical syllogism cannot contain an error because the conclusion is hedged in by "if statements." Look at this example.

1. If Tim works at Area 51, then he hunts aliens.

2. If someone hunts aliens, then they have seen an alien.

3. Therefore, if Tim works at Area 51, he has seen an alien.

This is a wild hypothetical syllogism, but because it is totally hypothetical, no part of it can be untrue. The hedge "if" protects it from many logical fallacies. At the same time, the hedge "if" prevents the purely hypothetical syllogism from ever being verifiably true as well, which makes the hypothetical syllogism a poor choice in an argumentative essay.

Syllogism, Hedge example, StudySmarter Fig. 3 - Although not strong, hedged statements protect you from fallacies.

Mixing "if" and "is statements" is where things can go wrong. These mixed or impure hypothetical syllogisms are not fully hedged in by "if statements," which means they can be untrue.

1. If Tim works at Area 51, then he hunts aliens.

2. People who hunt aliens have seen aliens.

3. Therefore, Tim has seen an alien.

This syllogism contains a falsehood in the minor premise, meaning its conclusion is untrue. While the major premise is protected by a hedge, the minor premise contains the easily refutable claim that "people who hunt aliens have seen aliens."

Logical Fallacies in Disjunctive Syllogisms

You have probably picked up on a pattern. Syllogisms go wrong when their premises are totally or partially untrue. The disjunctive syllogism is no different:

1. You are either a Republican or a Democrat.

2. Gabriella isn't a Republican.

3. Therefore, Gabriella is a Democrat.

The major premise here isn't true. To name one obvious loophole, Gabriella might not be American in the first place! This fallacy is known as the false dichotomy.

When analyzing or writing syllogisms, check if they contain informal fallacies.

Syllogism - Key Takeaways

A syllogism is a three-part line of reasoning with a major premise, minor premise, and conclusion.
A categorical syllogism uses "is" statements" to draw a sure conclusion.
A purely hypothetical syllogism contains an "if statement" in all the major premise, minor premise, and conclusion. A mixed hypothetical syllogism contains a mixture of "if" and "is statements."
A disjunctive syllogism draws a conclusion using a dichotomy.
If your premises are untrue, your syllogistic conclusions will be logical fallacies.

Syllogism

StudySmarter Editorial Team

Syllogism Definition

Syllogism Rules