 Suppose we do take the broadest interpretation of ‘every’. One question is whether we will be left with any useful relation of logical consequence at all. Logics which are arrived at by quantifying over extra cases have a tendency to be weaker—that is, to classify fewer arguments as valid—since the more cases we include, the better our chances of including one in which the premises of a particular argument are true and the conclusion false. Dialetheists would include cases in which both a sentence and its negation are true, and this means we can have cases where P and ¬P are true, but Q is false, making both P ∨ Q and ¬P true, even though Q is not, and thus providing a counterexample to the argument form disjunctive syllogism. If this is acceptable, one might think, why not allow cases where A ∧ B is true, but B is not? Or worse. Perhaps if we construe ‘every case’ broadly enough, we will find that there are no valid arguments left, and hence the result will not be logical monism, but a form of logical nihilism, or something close to it: 