 Notice that our presentation of Fitch’s reasoning makes no explicit mention of the assumption that \(Kp \wedge \neg Kp\) is impossible. So here we attempt to pinpoint exactly where Fitch’s reasoning goes wrong on the above account. It is claimed at line 9 (in the first section of this entry) that \(K(p \wedge \neg Kp)\) is impossible. Of course \(K(p \wedge \neg Kp)\) entails the contradiction \(Kp \wedge \neg Kp\). And so, if the reasoning is that \(K(p \wedge \neg Kp)\) is impossible because contradictions are impossible, then Beall would be directly attacking the argument presented herein. But notice the argument here is subtly different. It goes like this. \(K(p \wedge \neg Kp)\) entails the contradiction \(Kp \wedge \neg Kp\). So, by reductio, \(K(p \wedge \neg Kp)\) is false. By necessitation, it follows that \(K(p \wedge \neg Kp)\) is necessarily false. Depending on the paraconsistent logic, the paraconsistist may object to use of reductio, or may object to other inferences. The claim that \(K(p \wedge \neg Kp)\) is impossible (at line 9) is inferred from this claim that \(K(p \wedge \neg Kp)\) is necessarily false. This may trouble the paraconsistentist. By the lights of one living with contradiction, it may not follow that an inconsistent statement is impossible even if it is necessarily false. After all, on this account a necessarilly false statement may be both false and true at some world, in which case the statement is both necessarily false and possible. If this is right then the inference from \(\Box \neg p\) to \(\neg \Diamond p\) has counterexamples and may not be employed to infer \(\neg \Diamond K(p \wedge \neg Kp)\) from \(\Box \neg K(p \wedge \neg Kp)\).