Argumentum a contrario

In logic, an argumentum a contrario (Latin: "appeal from the contrary" or "argument based on the contrary") denotes any proposition that is argued to be correct because it is not disproven by a certain case. It is the opposite of the analogy. Arguments a contrario are often used in the legal system as a way to solve problems not currently covered by a certain system of laws. Although it might be used as a logical fallacy, arguments a contrario are not by definition fallacies.

Examples

• "§ 123 of the X-Law says that green cars need to have blue tires. As such, red cars don't have to have blue tires."

Here the argument is based on the fact that red cars are not green cars and as such § 123 of the X-Law cannot be applied to them. This requires the law to be interpreted to determine which solution would have been desired if the lawmaker had considered red cars. In this case it's probably safe to assume that they only wanted to regulate green cars and not regulate cars of other colors.

On the other hand, this example:

• "§ 456 of the Y-Law says that it's irrelevant whether a message is sent by letter or by telegraph. As such, messages cannot be sent by fax machines."

As with the example above, the argument is based on the fact that the law does not mention fax machines and they must therefore not be used. Here the interpretation that the lawmaker consciously did not mention fax machines is less valid than the assumption that fax machines did not exist at this time and that, were the law passed today, they would have been mentioned. Here the argument a contrario is used fallaciously since it places the letter of the law above its intent

See also

• Analogy
• A minore ad maius
• A maiore ad minus