Syllogism
A syllogism is a deductive argument that derives a conclusion from two premises by a fixed logical form. Aristotle developed the first such systems.
Why fix the form?
Standardizing forms lets you check validity by shape alone, independent of the specific terms plugged in.
A categorical syllogism reasons about categories using four standard sentence forms:
| Code | Form | Name |
|---|---|---|
| A | All S are P | universal affirmative |
| E | No S are P | universal negative |
| I | Some S are P | particular affirmative |
| O | Some S are not P | particular negative |
A classic example:
P1) All men are mortal. (A)
P2) Socrates is a man. (A, singular)
∴
C) Socrates is mortal.
Counter-example method
To show a categorical syllogism is invalid, construct another argument with the same form that has obviously true premises and an obviously false conclusion.
Modern sentential logic gives five core valid syllogistic forms: Modus Ponens, Modus Tollens, Disjunctive Syllogism, Hypothetical Syllogism, Constructive Dilemma. The classic invalid pattern is Affirming the Consequent.