Logic / Unit 5 Logic 218 worked example, 60 to 90 seconds
Indirect Proof Walkthrough
The idea
Indirect proof assumes the denial of what it wants, derives an explicit contradiction from that assumption, then discharges it — the contradiction showing the assumption could not have held.
In practice
Premises: A wedge B, and tilde B. Prove A. Line three: assume tilde A, indenting from here. Line four: B, from lines one and three by disjunctive syllogism, since the assumption denies the left disjunct. Line five: B dot tilde B, from lines four and two by conjunction. That line is an explicit contradiction, written out rather than merely noticed. Discharge. Line six: A, citing lines three through five as an indirect proof. Now the honest observation: disjunctive syllogism on lines one and two proves A in a single step, with no assumption at all. Indirect proof was not needed here, which is exactly why it is the right example to learn on — the machinery can be watched without a hard problem competing for attention.
Where people slip
The contradiction has to be written as a line, not merely spotted. A proof that stops at the moment two lines look incompatible has skipped the step that licenses the discharge, and skipping it becomes a habit that fails on longer proofs where the incompatibility is several moves apart.
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