To prove something true, assume it's false and show that leads to absurdity. How does "proof by contradiction" work?

"Lying is wrong" just asserts the opposite—it doesn't SHOW why the position fails. The person already disagrees! Direct assertion can lead to clash of opinions. Better: show their position leads to ABSURDITY they can't accept. Let them see the problem themselves.

REDUCTIO AD ABSURDUM: "Okay, suppose everyone should always lie. Then I could lie to YOU about your performance. You could lie to ME about mine. Nobody would know what to improve. We'd all fail while feeling fine." The position DESTROYS ITSELF. That's more powerful than "lying is wrong."

THE METHOD: (1) Assume the opposite of what you want to prove; (2) Follow the logical consequences; (3) Reach a CONTRADICTION or absurdity; (4) Conclude the assumption was false. The logic: if "not X" leads to impossibility, "not X" is false, so X is true.

Direct argument works when you have strong positive evidence. Reductio works when you can show the opposing position is self-defeating. Counter-examples work when one case disproves a universal claim. Each has its place—reductio is especially powerful for positions that SOUND good but don't survive scrutiny.

Exactly! REDUCTIO AD ABSURDUM shows a position destroys itself. "If everyone always lied: nobody could trust anyone, lies would lose meaning, truth couldn't be communicated, relationships would collapse." The position leads to absurdity, so the position is false. You don't need to assert "lying is wrong"—you let them SEE it.

THE METHOD: (1) Assume the opposite of what you want to prove; (2) Follow the logical consequences; (3) Reach a CONTRADICTION or absurdity; (4) Conclude the assumption was false; (5) Therefore your target is true. The logic: if "not X" is impossible, X must be true.

CLASSIC EXAMPLE—√2 is irrational: Assume it IS rational (a/b in lowest terms). Then a² = 2b², so a is even. Then b must also be even. CONTRADICTION: both even means not lowest terms. Our assumption was false, so √2 is irrational. This proof is 2,500 years old and still perfect.

CAUTION: The contradiction must be GENUINE, not just "sounds bad." Bad reductio: "If we do X, bad things MIGHT happen." (Possibility ≠ contradiction.) Good reductio: "If we do X, we'd contradict Y, which we already accept." Also: every step must follow logically—if any inference fails, the reductio fails.

A counter-example shows a case where the rule fails—useful for disproving "always" claims. But reductio is more powerful here: it shows the ENTIRE position is self-defeating, not just that one case went wrong. One lie causing harm could be dismissed as exception; showing the rule destroys itself can't be.

REDUCTIO: "If everyone always lied: nobody could trust anyone, lies would be expected so they'd lose meaning, truth couldn't be communicated, the concept of 'sparing feelings' requires being believed but nobody believes liars..." The rule is SELF-UNDERMINING. That's decisive.

Counter-examples are best for: "All X are Y" claims (one non-Y X disproves it). "All swans are white" → show a black swan. But "Everyone should always lie" isn't disproved by one harmful lie—they could say "that was a bad execution, not a bad rule." Reductio attacks the rule itself.

THE METHOD: (1) Assume the position is true; (2) Follow the logical consequences; (3) Reach a CONTRADICTION or absurdity; (4) Conclude the position was false. If "always lie" leads to impossibility, "always lie" is wrong. The position refutes itself.