The main viewpoints of logical exceptionalism are that logic is exceptional with respect to all other sciences, including natural science, social science and humanities, because logical propositions say nothing about the world, and are true or false based on the meanings of logical constants; that logical truth is analytical, necessary and a prior, so it is not revisable; and that logical laws are normative for how to think correctly. The representative figures of logical exceptionalism are Leibniz, Hume, Kant, Frege, Wittgenstein and Ayer. Logical exceptionalism has encountered at least four problems: how to justify logical laws? How to explain the appearance of deviant and competitive logics and choose from them? How to explain the universal applicability of logic laws? How to explain the normativity of logical laws for correct thinking? The conclusion of this paper is that logical exceptionalism is like sort of evasion, based on many presuppositions without serious clarification and critical examination, and has many insurmountable theoretical difficulties.