Definition

Also called Confusing A Necessary With A Sufficient Cause.

Any argument of the following form is invalid: If p₁ then p₂; not-p₁; therefore, not-p₂.

Explanation

This is mathematically incorrect. p₁ is a sufficient cause of p₂ and that means that if we have not-p₂, we can conclude that we have not-p₁ (the negation of "if p₁ then p₂"). But having not-p₁ is not enough to conclude that we have not-p₂.

Examples

If you get hit by a car when you are six then you will die young. But you were not hit by a car when you were six. Thus you will not die young.
Of course, you could be hit by a train at age seven, in which case you still die young.

If I am in Calgary then I am in Alberta. I am not in Calgary, thus, I am not in Alberta.

Counter-examples

None.

Advices

Show that even though the premises are true, the conclusion may be false. In particular, show that the consequence p₂ may occur even though p₁ does not occur.