What Is a Syllogism? | Definition & Examples
A syllogism is an argument that consists of two premises and a conclusion. Syllogisms express deductive reasoning, forming specific conclusions from general principles.
- No fish can survive without water.
- Sharks are fish.
- Therefore, sharks cannot survive without water.
The main purpose of a syllogism is to prove a conclusion with logical certainty.
Syllogisms are typically found in academic and professional domains, such as formal logic and mathematics. We often use syllogistic reasoning to make decisions in everyday life even if we don’t often express these thoughts verbally.
What is a syllogism?
Syllogisms are formal arguments with two premises and a conclusion. Although there are several types of syllogisms, they all express deductive reasoning.
A syllogism can involve expressing relationships between categories (categorical syllogisms), exploring hypotheticals (hypothetical syllogisms), or choosing between two alternatives (disjunctive syllogisms).
Syllogisms are meant to form air-tight cases for their conclusions by structuring two premises in such a way that, if both are true, the conclusion must necessarily follow.
Aristotle is credited with the invention of syllogisms, which have played an essential role in the development of formal logic and Western philosophy.
A syllogism is valid if its premises logically necessitate its conclusion. If a syllogism has a structural flaw that renders it invalid, it commits a formal logical fallacy (or non sequitur fallacy).
- If Ava is in Paris, then she is in France.
- Ava is in France.
- Therefore, Ava is in Paris.
This syllogism is invalid because the premises could both be true while the conclusion is false (e.g., Ava might be in Bordeaux). This structural error is called affirming the consequent because the second premise mistakenly affirms the “then” statement (the consequent) instead of the “if” statement (the antecedent).
Syllogism examples
In philosophy, syllogisms play an important role in domains such as formal logic, epistemology (i.e., the study of knowledge), and ethics (i.e., the study of moral principles).
- Premise: It’s wrong to hurt innocent beings for fun.
- Premise: Puppies are innocent beings.
- Conclusion: Therefore, it’s wrong to hurt puppies for fun.
In this syllogism, the premises first establish a general moral principle and then identify a specific instance related to that principle. The conclusion then follows logically from the premises.
Syllogistic reasoning plays a more-or-less explicit role in many academic and professional domains outside philosophy, including mathematics, science, and law among other fields.
- Premise: Either the defendant should be convicted or there is reasonable doubt.
- Premise: There is reasonable doubt.
- Conclusion: Therefore, the defendant should not be convicted.
In this syllogism, one of the two alternatives is true (i.e., there is reasonable doubt), so the other must logically be false (i.e., it is false that the defendant should be convicted).
What are the main types of syllogisms?
Syllogisms are typically divided into three categories:
Disjunctive syllogisms
A disjunctive syllogism presents two alternatives and draws a conclusion based on which of them is false.
- All natural numbers are either even or odd.
- The natural number y is not even.
- Therefore, y is odd.
Disjunctive syllogisms involve a process of elimination. In this example, one of the options is declared false in the second premise (i.e., y is not even). The other must be true (i.e., y is odd).
Hypothetical syllogisms
A hypothetical syllogism (or conditional syllogism) involves an if—then relationship.
- If demand exceeds supply, then prices increase.
- Demand for oil has exceeded supply.
- Therefore, oil prices will increase.
In this hypothetical syllogism, the “if” statement is declared true in the second premise. It follows logically that the “then” statement must also be true.
Categorical syllogisms
A categorical syllogism expresses a relationship between classes or categories of things. The first premise states a broad principle, and the second premise applies the principle to a specific example.
| Major premise | All dogs are good. |
| Minor premise | Rufus is a dog. |
| Conclusion | Therefore, Rufus is good. |
Categorical syllogisms explain relationships between categories (e.g., “dogs” and “good”). They start with a major premise that expresses a generalization. The minor premise follows, narrowing the argument’s focus. The middle term (in this example, “dog”) appears in both of the two premises and links them together.
Frequently asked questions about syllogisms
- How is “syllogism” pronounced?
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The word “syllogism” is pronounced SIL-uh-jiz-uhm (IPA: /ˈsɪləˌdʒɪzəm/).
- What is a synonym for “syllogism”?
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“Syllogism” has several near-synonyms:
- formal argument
- deductive argument
- deductive reasoning
- logical deduction
- logical inference
Our AI Rewriter can help you find synonyms for words like “syllogism.”
- 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.
- 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
The main distinction between them is the relationships expressed by their premises.
