We can not be dogmatic about any subject (which is obviously a dogma). My question is: is it possible, through logic to prove that in essence and in reality there is no logic?

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Logic belongs to a class of things that I call absolute. What is absolute cannot be merely discarded, moreover, it laughs at your attempts to do so. Thus, it exists in every single context you can think of. Absolute belongs to a family of concepts that I will dub contextual categories. Other concepts