Denying the Antecedent

Disciplines > Argument > Fallacies > Denying the Antecedent

Description | Discussion | Example | See also

Description

If A is true then B is true. A is not true, therefore B is not true.

To disprove something, show how it can be caused by something else. Then show that the cause does not happen (then assume that this proves the antecedent is also false).

Example

If you give a man a gun, he may kill someone. If he has no gun, then he will not kill anyone.

If you work hard, you will get a good job. If you do not work hard you will not get a good job.

I am in London, England. I am not in London, therefore I am not in England.

Discussion

In an 'If A then B' statement, A is the antecedent and B is the consequent.

When you know that 'If A is true then B is true', this statement is only valid for truth of A and B. If A is false, then it does not necessarily follow that B is also false. A place where this is true is in Boolean logic, where A and B are binary variables and can only be true or false. In life, there are often situations where A and B can have many other states.

Classification

Non sequitur, syllogistic