Non sequitur

Non sequitur is Latin for "it does not follow." To say that an argument is a non sequitur is simply to say that the conclusion does not follow from the premises. This term would apply to any argument that has a conclusion that doesn't follow from its premises. It is often used, however, to refer to particular types of arguments that clearly do not follow from their premises and never could.

For example, any argument that takes the following form is a non sequitur:

1. If A then B. (eg, If I am a monkey, I am a mammal)
2. B. (eg, I am a mammal)
3. Therefore, A. (Therefore, I am a monkey)

It is clear that this argument does not follow. Even if the premises and conclusion were all true, the conclusion is not a necessary consequence of the premises. This sort of non sequitur is also called affirming the consequent.

Another common non sequitur is this:

1. If A then B. (eg, If I am in Tokyo, I am in Japan)
2. Not A. (eg, I am not in Tokyo)
3. Therefore, not B. (eg, Therefore, I am not in Japan.)

The speaker could be in all kinds of other places in Japan. This sort of non sequitur is called denying the antecedent.