The Art of Logic · Part 14 · Reasoning · B2–C1
If… Then: The Hypothetical Syllogism
Part 14 of The Art of Logic: “If the lamp is lit, there is oil in it.” Two ways of reasoning from this are valid; two look almost the same and are not. Conditionals in argument (if, only if, unless, provided that, if and only if), with Philo, Sophia, Marcos and Demetria.
In grammar you learned their forms. Tonight you learn which conclusions they allow, and which they do not.
And so did your own teacher Hillel, though he used it to read the law.
In a conditional proposition, “If P, then Q”, P is the antecedent and Q the consequent. Sister Miriam Joseph gives two valid moves. Affirming the antecedent: if P then Q; P; therefore Q. Denying the consequent: if P then Q; not Q; therefore not P. Later logicians called them modus ponens and modus tollens.
And two fallacies that look almost the same. Affirming the consequent: if P then Q; Q; therefore P. Denying the antecedent: if P then Q; not P; therefore not Q. If the lamp is lit, there is oil in it; there is oil in it; so it is lit? No: an unlit lamp can be full of oil.
The rules hold for an ordinary “if”. “Only if” reverses the direction: “P only if Q” means “if P, then Q”. “If and only if” works both ways.
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