Definition · Plain-language
Syllogism
A syllogism is a form of deductive argument in which a conclusion is drawn from two premises that share a common term.
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Structure and terms
A categorical syllogism contains exactly three terms, each appearing twice. The major premise contains the predicate of the conclusion (the major term); the minor premise contains the subject of the conclusion (the minor term); and the middle term appears in both premises but not the conclusion, linking them together. In "All men are mortal (major premise); Socrates is a man (minor premise); therefore Socrates is mortal (conclusion)", "mortal" is the major term, "Socrates" the minor term, and "man/men" the middle term that connects the two.
Validity and form
A syllogism’s validity depends on its form, not its content. A valid form guarantees that if the premises are true, the conclusion must be true. The traditional valid mood known as Barbara has the pattern: All M are P; All S are M; therefore All S are P. Logicians since Aristotle have catalogued which combinations of premise types yield valid conclusions. An invalid syllogism may look persuasive yet allow true premises with a false conclusion, which is precisely what validity rules out.
Validity is not truth
A syllogism can be valid yet have a false conclusion if one of its premises is false. "All birds can fly; a penguin is a bird; therefore a penguin can fly" is valid in form but unsound, because the first premise is false. Conversely, a syllogism with true premises and true conclusion can still be invalid if the conclusion does not follow from the form. A syllogism that is both valid and has all true premises is called sound, and only a sound syllogism guarantees a true conclusion.
Key facts
At a glance
- Definition: a deductive argument with two premises and a conclusion
- Origin: formalised by Aristotle in the Prior Analytics
- Terms: three — major, minor and middle (each used twice)
- Classic example: All humans are mortal; Socrates is human; ∴ mortal
- Barbara form: All M are P; All S are M; ∴ All S are P
- Validity: a matter of form, not the truth of the premises
Common misconceptions
What people often get wrong
Often heard: If a syllogism is valid, its conclusion must be true.
Actually: Validity only guarantees that the conclusion follows if the premises are true. A valid syllogism with a false premise can have a false conclusion. Only a sound syllogism — valid with all true premises — guarantees a true conclusion.
Often heard: A syllogism can have any number of premises.
Actually: A standard categorical syllogism has exactly two premises and one conclusion, built from three terms. Arguments with more premises are chains of reasoning or polysyllogisms (sorites), not single categorical syllogisms.
Often heard: A believable conclusion means the syllogism is logically valid.
Actually: Validity is about form, not believability. A syllogism can reach a true-sounding conclusion through invalid reasoning, and a valid syllogism can reach an absurd conclusion from false premises. You must test the structure, not just whether the conclusion seems right.
Going deeper
