After learning direct rules of inference, it is tempting to treat every conditional pattern as a valid deduction. Invalid conditional reasoning studies two common mistakes: affirming the consequent and denying the antecedent. These errors look similar to Modus Ponens and Modus Tollens, but their logical forms are different. In this lesson, invalid conditional reasoning will be identified by form, by examples, and by counterexamples.

Let $p$ and $q$ be statements. The argument form $$\begin{equation*} p\to q,\ q\ \therefore\ p \end{equation*}$$ is called the \textbf{converse error} or the \textbf{fallacy of affirming the consequent}. This is not a valid rule of inference.