Logical nihilism is the view that there is no logic, or more precisely that no single, universal consequence relation governs natural language reasoning. Here, I present three different arguments for logical nihilism from philosophically palatable premises. The first argument comes from a combination of pluralism with the desideratum that logical consequence should be universal, properly understood. The second argument is a slippery slope argument against monists who support weak logical systems on account of their power to characterize a vast range of true theories. The third argument is a general strategy of generating counterexamples to any inference rule, including purportedly fundamental ones such as disjunction introduction. I close by discussing why a truth-conditional approach to the meaning of the logical connectives not only does not force us to reject such counterexamples but also reveals that right truth-conditions are far more general than the classical ones, at the price of nihilism.