Affirming the Consequent


Also called Confusing A Sufficient With A Necessary Cause.

Any argument of the following form is invalid: If p1 then p2; p2; therefore p1.


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 p2 is not enough to conclude that we have p1.


If I am in Calgary, then I am in Alberta. I am in Alberta, thus, I am in Calgary.
Of course, even though the premises are true, I might be in Edmonton, Alberta.

If the mill were polluting the river then we would see an increase in fish deaths. And fish deaths have increased. Thus, the mill is polluting the river.




Show that even though the premises are true, the conclusion could be false. In general, show that p2 might be a consequence of something other than p1. For example, the fish deaths might be caused by pesticide run-off, and not the mill.