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Beall and Restall (2000, 2006) argue for a pluralistic conception of logic, which may be called Background Pluralism. In the first part of this paper, I outline the core tenets of Beall and Restall’s position. In the second part I consider a particular line of criticism presented in Read (2004, 2006) and Priest (2006). Finally, in the last part of the paper, I develop a new argument which is directed against the fundamental thesis of Beall and Restall’s pluralistic theory. Since the argument attempts to show that the fundamental thesis incorporates a self-defeating feature, it will be called the Instability Argument.