# Denying the Antecedent

This fallacy takes the form:

P1. If A then B

P2. Not A

C. Therefore not B

Explanation: this fallacy involves reasoning that since one thing implies a second thing, the absence of the first thing allows us to infer the absence of the second. This is fallacious, as it confuses necessary and sufficient conditions. Statements of the form ‘if A then B’ mean that A is sufficient for B, so that if A occurs or exists, then so will B. Such statements do not, however, mean that A is necessary for B, which (if true) would entail that the only way for B to be true is for A to also be true. Counterexamples to such reasoning are very easy to provide. For example, suppose that if my alarm clock goes off correctly then I will always be on time for work. This does not entail, however, that if my alarm clock fails to go off then I will necessary be late for work. Though it might seem natural, this cannot be assumed because it was never stated that my alarm must go off in order for me to be on time for work. I might still be able to get to work on time even if my alarm doesn’t go off, for example if I skip breakfast and get dressed in a hurry. My alarm going off is this a sufficient condition for me being on time for work, but it is not a necessary condition for being on time.

Example: “If you go to university then you are sure to get a good job. Since you aren’t going to university, you will never get a good job.”