Law of Syllogism | Explanation & Examples
The law of syllogism is a fundamental rule used in deductive reasoning. This law connects two conditional statements to form a new conclusion.
The law of syllogism is typically expressed as:
- If A → B [If A is true, then B is also true.]
- And B → C [If B is true, then C is also true.]
- Then A → C [If A is true, then C is true.]
- If it is raining, then the ground gets wet.
- If the ground gets wet, then the plants will grow.
- Therefore, if it is raining, then the plants will grow.
What is the law of syllogism?
The law of syllogism is a specific logical rule used for chaining conditional statements. It’s used in mathematics (particularly in geometry proofs), logic, philosophy, and computer science.
“Syllogism” comes from the Ancient Greek συλλογισμός (romanized as syllogismos), which translates as “conclusion” or “inference.”
In the law of syllogism, the first part of the statement is called the “hypothesis” or “antecedent,” and the second part is called the “conclusion” or “consequent.” For example, in “A → B,” A is the “hypothesis” and B is the “conclusion.”
If the conclusion of the first statement matches the hypothesis of the second, you can combine them into a new conditional statement.
For example:
- If P, then Q (lays out the conditional statement).
- P (the hypothesis is true).
- Then you can conclude Q (if P is true, then Q is true).
Notice the use of the letters P, Q, and R. These letters are conventional labels in formal logic, mathematics, and philosophy and can also be used to annotate the law of syllogism.
For example:
- If it’s Tuesday, I have math class. (The conclusion of this conditional statement is “I have math class.”)
- If I have math class, I need my pencils. (The hypothesis of this conditional statement—“I have math class”—matches the conclusion of the first.)
- If it’s Tuesday, I need my pencils. (As the first two statements matched, they can be combined using the law of syllogism to create a new conditional statement.)
Syllogism can also be used as a standalone expression to describe a general logical argument with two premises and a conclusion. Unlike the law of syllogism, it refers to a broad category of logical argument that can take different forms
| Type | Explanation | Example |
| Hypothetical syllogism | Involves an if-then relationship | If I wake up late, I’ll miss the bus.
If I miss the bus, I’ll be late. Therefore, if I wake up late, I’ll be late. |
| Disjunctive syllogism | Presents two options and comes to a conclusion based on which one is false | I’ll have coffee or tea.
I’m out of tea. Therefore, I’ll have coffee. |
| Categorical syllogism | Explores the relationship between categories or classes | All cats are cute.
Louis is a cat. Therefore, Louis is cute. |
For example:
- If it rains, the street gets wet.
- The street is wet.
- Therefore, it must have rained.
Law of syllogism examples
The law of syllogism is often used in mathematics.
- If a number is divisible by 6, then it is divisible by 3.
- If a number is divisible by 3, then it is not a prime number.
- Therefore, if a number is divisible by 6, then it is not a prime number.
It’s also commonly used in the field of computer science.
- If a user logs in successfully, then they will be redirected to the dashboard.
- If they are redirected to the dashboard, then they can access their profile.
- Therefore, if a user logs in successfully, they can access their profile.
The law of syllogism is also used in the fields of logic and philosophy.
- If a being is human, then it is mortal.
- If a being is mortal, then it will die eventually.
- Therefore, if a being is human, it will die eventually.
You can also apply the law of syllogism to other domains as well, like education.
- If a student turns in all their assignments on time, then they will pass the course.
- If a student passes the course, then they will graduate.
- Therefore, if a student turns in all their assignments on time, they will graduate.
Or, it could be applied in cooking.
- If you use a bain-marie, the cheesecake will be creamier.
- If the cheesecake is creamier, it will be more delicious.
- If you use a bain-marie, the cheesecake will be more delicious.
Frequently asked questions about law of syllogism
- What is a synonym for “syllogism”?
-
“Syllogism” has several near-synonyms:
- formal argument
- deductive argument
- deductive reasoning
- logical deduction
- logical inference
For example, in math, the law of syllogism could be thought of as the “law of deductive reasoning.”
Our AI Rewriter can help you find synonyms for words like “syllogism.”
- How many types of syllogisms are there?
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There are three main types of syllogisms in classical logic:
- Hypothetical syllogisms (also known as conditional syllogisms)
- Disjunctive syllogisms
- Categorical syllogisms
Each incorporates the law of syllogism. The main distinction between them is the relationships expressed by their premises. The main distinction between them is the relationships expressed by their premises.
Try QuillBot’s AI Chat if you want to ask more questions about syllogisms.
- What is the literary definition of “syllogism”?
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A literary syllogism mirrors formal logic by presenting two premises, often implicit, followed by a conclusion, enhancing a narrative’s depth and complexity.
For example, in To Kill a Mockingbird, Atticus Finch’s argument that all humans are created equal, coupled with evidence of Tom Robinson’s innocence, leads to the conclusion that Tom should be acquitted.
In other areas, like mathematics, the law of syllogism is used in proofs or reasoning.
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