Glossary
Syllogism
What is a syllogism?
A syllogism is a form of deductive argument. A traditional categorical syllogism has two premises and a conclusion. If its form is valid and its premises are true, its conclusion must be true.
A categorical syllogism
- All mammals are animals.
- All dogs are mammals.
- Therefore, all dogs are animals.
This universal affirmative form is traditionally called Barbara. “Mammals” is the middle term: it connects the premises and does not appear in the conclusion. The major premise contains the conclusion's predicate, animals; the minor premise contains its subject, dogs. Both premises can be general statements.
A disjunctive syllogism
- The book is in room A or room B.
- It is not in room A.
- Therefore, it is in room B.
Conditional and Hypothetical Syllogisms
Modus ponens has the form: if P, then Q; P; therefore Q. For example: if it rains, the ground will be wet; it rains; therefore, the ground is wet.
A hypothetical syllogism chains conditionals: if P, then Q; if Q, then R; therefore, if P, then R. These are different argument forms.
Why it matters
A conclusion can sound believable without following from the premises. Belief bias is the influence of that plausibility on judgments of validity.
Validity concerns the structure. Soundness also requires true premises. A valid form cannot rescue a false starting assumption.