Affirming the Consequent

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Affirming the Consequent is a formal fallacy, meaning that unlike some other fallacies you have seen, the problem with this reasoning has to do with the form or pattern of the argument itself.

That is, any argument having the following form is invalid:

If p then q
q
Therefore, p.

Examples:

If Napoleon was killed in a plane crash, then Napoleon is dead. (if p -> q)
Napoleon is dead. (p)
Therefore, Napoleon was killed in a plane crash. (q)

Notice that the premises are both true but the conclusion is false.
If I am in Minneapolis, then I am in Minnesota.
I am in Minnesota.
Therefore, I am in Minneapolis.

(Of course, even though the premises are true, I might be in St Paul, Minnesota.)
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.

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

References
Barker: 69, Cedarblom and Paulsen: 24, Copi and Cohen: 241

Note: There are vaild forms of reasoning that use conditional statements, such as Modus Ponens and Modus Tollens.

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