The Art of Logic · Part 12 · Reasoning · B2–C1
The Syllogism: Three Terms and the Rules
Part 12 of The Art of Logic: two premises, three terms, one conclusion. If the rules are kept, and the premises are true, the conclusion cannot be false. Premise and conclusion indicators (since, given that, therefore, hence, it follows that), with Philo, Sophia, Marcos and Demetria.
Tonight, the heart of Aristotle’s logic: the syllogism.
All men are mortal; Socrates is a man; therefore Socrates is mortal.
That one. Every schoolchild will learn it, though Aristotle himself never used Socrates as his example.
Easy to make; easy to get wrong. Tonight, the rules.
A categorical syllogism has two premises and a conclusion, and exactly three terms. The major term is the predicate of the conclusion (mortal); the minor term is its subject (Socrates); the middle term appears in both premises but not in the conclusion (man). It links the other two.
Sister Miriam Joseph gives the rules of validity. There must be exactly three terms, used in the same sense. The middle term must be distributed at least once. No term may be distributed in the conclusion unless it was distributed in a premise. From two negative premises, nothing follows. If one premise is negative, the conclusion must be negative. From two particular premises, nothing follows.
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