If, in the course of an argument, an arguer contradicts himself or herself, then we need not accept their conclusion. This is because if an argument rests on contradictory claims, then at least one of those claims must be false, and false claims prove nothing.

Examples

“Murder is the worst crime that there is. Life is precious; no human being should take it away. That’s why it’s important that we go to any length necessary to deter would-be killers, including arming the police and retaining the death penalty.”

This argument both affirms that no human being should take the life of another, and that we should retain the death penalty. Until this inconsistency is ironed out of the argument, it won’t be compelling.

“We don’t tell the government what to do, so they shouldn’t tell us what to do!” These were the words of an angry smoker interviewed on the BBC News following the introduction of a ban on smoking in enclosed public places in England. Her claim that she doesn’t tell the government what to do is instantly refuted as she proceeds to do just that.