The Art of Logic · Part 15 · Reasoning · B2–C1
Either… Or: The Disjunctive Syllogism and the Dilemma
Part 15 of The Art of Logic: “Either the scroll is in the Library or it is in the Museum. It isn’t in the Library…” Reasoning from alternatives, and the dilemma, which tries to trap you between two horns. Alternatives (either… or, neither… nor, whether… or, otherwise), with Philo, Sophia, Marcos and Demetria.
Tonight, the logic of or, and the most dangerous argument in the market: the dilemma.
Because it seems to leave you no way out. Either this or that, and both are bad. But a good logician can usually find the door.
A disjunctive syllogism reasons from alternatives: either P or Q; not P; therefore Q. This is always valid. But “either P or Q; P; therefore not Q” is valid only if the “or” is exclusive, meaning not both. Many “or”s are inclusive: “Bring a lamp or a candle” does not forbid bringing both.
A dilemma combines conditionals with a disjunction: if A, then C; if B, then D; either A or B; therefore either C or D. It presents two “horns”, and claims that you must be caught on one of them.
Sister Miriam Joseph gives three escapes. Grasp a horn: show that one conditional is false. Go between the horns: show that there is a third possibility, because the disjunction is incomplete, a false dilemma. Rebut it: build a counter-dilemma that reaches the opposite conclusion.
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