An argument is inconsistent if makes two or more contradictory claims. If an argument is inconsistent, then we don’t have to accept its conclusion.

This is because if claims are contradictory, then at least one of them must be false. An argument that rests on contradictory claims  must therefore rest on at least one false claim, and arguments that rest on false claims prove nothing.

In an argument that makes contradictory claims, whichever of those claims turns out to be false the arguer won’t have proved their conclusion. This means that it is reasonable to dismiss an inconsistent argument even without finding out which of its contradictory claims is false.

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 to the teeth 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.